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VOLUME 27 NUMBER 4 NOVEMBER 2010 CONTENTS 409 Adrian Brasoveanu Decomposing Modal Quantification 437 Short Contribut...

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VOLUME 27 NUMBER 4 NOVEMBER 2010

CONTENTS 409

Adrian Brasoveanu Decomposing Modal Quantification

437

Short Contribution Eric Swanson On Scope Relations between Quantifiers and Epistemic Modals FORTHCOMING ARTICLES Márta Abrusán and Benjamin Spector: A Semantics for Degree Questions Based on Intervals: Negative Islands and Their Obviation Nathan Klinedinst: Quantified Conditionals and Conditional Excluded Middle John Beavers: An Aspectual Analysis of Ditransitive Verbs of Caused Possession in English Yael Sharvit: Covaluation and Unexpected BT Effects

529


Tamina Stephenson Control in Centred Worlds

JOURNAL OF SEMANTICS

JOURNAL OF SEMANTICS


Journal of

SEMANTICS www.jos.oxfordjournals.org

oxford

issn 0167-5133 (Print) issn 1477-4593 (Online)

JOURNAL OF SEMANTICS A N I NTERNATIONAL J OURNAL FOR THE I NTERDISCIPLINARY S TUDY THE S EMANTICS OF N ATURAL L ANGUAGE MANAGING EDITOR: ASSOCIATE EDITORS:

OF

Philippe Schlenker (Institut Jean-Nicod, Paris; New York University) Danny Fox (Massachusetts Institute of Technology) Rick Nouwen (Utrecht University) Maribel Romero (University of Konstanz) Robert van Rooij (University of Amsterdam) Mats Rooth (Cornell University) Bernhard Schwarz (McGill University) Roger Schwarzschild (Rutgers University) Yael Sharvit (University of Connecticut) Jesse Snedeker (Harvard University) Anna Szabolcsi (New York University) Zoltán Gendler Szabó (Yale University)

ADVISORY BOARD: Gennaro Chierchia (Harvard University) Beth Levin (Stanford University) Bart Geurts (University of Nijmegen) Barbara Partee (University of Massachusetts, Lila Gleitman (University of Pennsylvania) Amherst) Irene Heim (Massachusetts Institute of Technology) François Recanati (Institut Jean-Nicod, Paris) Laurence R. Horn (Yale University) Maribel Romero (University of Konstanz) Hans Kamp (Stuttgart University and University of Bernhard Schwarz (McGill University) Texas, Austin) Arnim von Stechow (University of Tübingen) Manfred Krifka (Humboldt University Berlin; ZAS, Berlin)Thomas Ede Zimmermann (University of Frankfurt)

EDITORIAL BOARD: Maria Aloni (University of Amsterdam) Pranav Anand (University of California, Santa Cruz) Ana Arregui (University of Ottawa) Nicholas Asher (IRIT, Toulouse; University of Texas, Austin) Chris Barker (New York University) Sigrid Beck (University of Tübingen) Rajesh Bhatt (University of Massachusetts, Amherst) Maria Bittner (Rutgers University) Peter Bosch (University of Osnabrück) Richard Breheny (University College London) Daniel Büring (University of California, Los Angeles) Emmanuel Chemla (Institut Jean-Nicod, Paris; LSCP, Paris) Jill G. de Villiers (Smith College) Paul Dekker (University of Amsterdam) Josh Dever (University of Texas, Austin) Regine Eckardt (University of Göttingen) Martina Faller (University of Manchester) Delia Fara (Princeton University) Lyn Frazier (University of Massachusetts, Amherst) Jeroen Groenendijk (University of Amsterdam) Elena Guerzoni (University of Southern California) Martin Hackl (Pomona College) Pauline Jacobson (Brown University) Andrew Kehler (University of California, San Diego) Chris Kennedy (University of Chicago) Jeffrey C. King (Rutgers University) Angelika Kratzer (University of Massachusetts,

Amherst) Peter Lasersohn (University of Illinois) Jeffrey Lidz (University of Maryland) John MacFarlane (University of California, Berkeley) Lisa Matthewson (University of British Columbia) Julien Musolino (Rutgers University) Ira Noveck (L2C2, CNRS, Lyon) Francis Jeffry Pelletier (University of Alberta) Colin Phillips (University of Maryland) Paul M. Pietroski (University of Maryland) Christopher Potts (Stanford University) Liina Pylkkänen (New York University) Gillian C. Ramchand (University of Tromsoe) Uli Sauerland (ZAS, Berlin) Barry Schein (University of Southern California) Benjamin Spector (Institut Jean-Nicod, Paris) Robert Stalnaker (Massachusetts Institute of Technology) Jason Stanley (Rutgers University) Mark Steedman (University of Edinburgh) Michael K. Tanenhaus (University of Rochester) Jos van Berkum (Max Planck Institute for Psycholinguistics, Nijmegen) Rob van der Sandt (University of Nijmegen) Yoad Winter (Utrecht University) Henk Zeevat (University of Amsterdam)

EDITORIAL CONTACT: [email protected] © Oxford University Press 2010 For subscription information please see back of journal.

Editorial Policy Scope Journal of Semantics aims to be the premier generalist journal in semantics. It covers all areas in the study of meaning, and particularly welcomes submissions using the best available methodologies in semantics, pragmatics, the syntax/semantics interface, cross-linguistic semantics, experimental studies of meaning (processing, acquisition, neurolinguistics), and semantically informed philosophy of language. Types of articles Journal of Semantics welcomes all types of research articles–with the usual proviso that length must be justified by scientific value. Besides standard articles, the Journal will welcome ‘squibs’, i.e. very short empirical or theoretical contributions that make a pointed argument. In exceptional circumstances, and upon the advice of the head of the Advisory Board, the Journal will publish ‘featured articles’, i.e. pieces that we take to make extraordinary contributions to the field. Editorial decisions within 10 weeks The Journal aims to make editorial decisions within 10 weeks of submission. Refereeing Articles can only be accepted upon the advice of anonymous referees, who are asked to uphold strict scientific standards. Authors may include their names on their manuscripts, but they need not do so. (To avoid conflicts of interest, any manuscript submitted by one of the Editors will be handled by the head of the Advisory Board, who will be responsible for selecting referees and making an editorial decision.) Submissions All submissions are handled electronically. Manuscripts should be emailed in PDF format to the Managing Editor [[email protected]], who will forward them to one of the Editors. The latter will be responsible for selecting referees and making an editorial decision. Receipt of a submission is systematically confirmed. Papers are accepted for review only on the condition that they have neither as a whole nor in part been published elsewhere, are elsewhere under review or have been accepted for publication. In case of any doubt authors must notify the Managing Editor of the relevant circumstances at the time of submission. It is understood that authors accept the copyright conditions stated in the journal if the paper is accepted for publication.

All rights reserved; no part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise without prior written permission of the Publishers, or a licence permitting restricted copying issued in the UK by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London W1P 9HE, or in the USA by the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923. Typeset by TNQ Books and Journals Pvt. Ltd., Chennai, India. Printed by Bell and Bain Ltd, Glasgow, UK

JOURNAL OF SEMANTICS A N I NTERNATIONAL J OURNAL FOR THE I NTERDISCIPLINARY S TUDY THE S EMANTICS OF N ATURAL L ANGUAGE MANAGING EDITOR: ASSOCIATE EDITORS:

OF

Philippe Schlenker (Institut Jean-Nicod, Paris; New York University) Danny Fox (Massachusetts Institute of Technology) Rick Nouwen (Utrecht University) Maribel Romero (University of Konstanz) Robert van Rooij (University of Amsterdam) Mats Rooth (Cornell University) Bernhard Schwarz (McGill University) Roger Schwarzschild (Rutgers University) Yael Sharvit (University of Connecticut) Jesse Snedeker (Harvard University) Anna Szabolcsi (New York University) Zoltán Gendler Szabó (Yale University)

ADVISORY BOARD: Gennaro Chierchia (Harvard University) Beth Levin (Stanford University) Bart Geurts (University of Nijmegen) Barbara Partee (University of Massachusetts, Lila Gleitman (University of Pennsylvania) Amherst) Irene Heim (Massachusetts Institute of Technology) François Recanati (Institut Jean-Nicod, Paris) Laurence R. Horn (Yale University) Maribel Romero (University of Konstanz) Hans Kamp (Stuttgart University and University of Bernhard Schwarz (McGill University) Texas, Austin) Arnim von Stechow (University of Tübingen) Manfred Krifka (Humboldt University Berlin; ZAS, Berlin)Thomas Ede Zimmermann (University of Frankfurt)

EDITORIAL BOARD: Maria Aloni (University of Amsterdam) Pranav Anand (University of California, Santa Cruz) Ana Arregui (University of Ottawa) Nicholas Asher (IRIT, Toulouse; University of Texas, Austin) Chris Barker (New York University) Sigrid Beck (University of Tübingen) Rajesh Bhatt (University of Massachusetts, Amherst) Maria Bittner (Rutgers University) Peter Bosch (University of Osnabrück) Richard Breheny (University College London) Daniel Büring (University of California, Los Angeles) Emmanuel Chemla (Institut Jean-Nicod, Paris; LSCP, Paris) Jill G. de Villiers (Smith College) Paul Dekker (University of Amsterdam) Josh Dever (University of Texas, Austin) Regine Eckardt (University of Göttingen) Martina Faller (University of Manchester) Delia Fara (Princeton University) Lyn Frazier (University of Massachusetts, Amherst) Jeroen Groenendijk (University of Amsterdam) Elena Guerzoni (University of Southern California) Martin Hackl (Pomona College) Pauline Jacobson (Brown University) Andrew Kehler (University of California, San Diego) Chris Kennedy (University of Chicago) Jeffrey C. King (Rutgers University) Angelika Kratzer (University of Massachusetts,

Amherst) Peter Lasersohn (University of Illinois) Jeffrey Lidz (University of Maryland) John MacFarlane (University of California, Berkeley) Lisa Matthewson (University of British Columbia) Julien Musolino (Rutgers University) Ira Noveck (L2C2, CNRS, Lyon) Francis Jeffry Pelletier (University of Alberta) Colin Phillips (University of Maryland) Paul M. Pietroski (University of Maryland) Christopher Potts (Stanford University) Liina Pylkkänen (New York University) Gillian C. Ramchand (University of Tromsoe) Uli Sauerland (ZAS, Berlin) Barry Schein (University of Southern California) Benjamin Spector (Institut Jean-Nicod, Paris) Robert Stalnaker (Massachusetts Institute of Technology) Jason Stanley (Rutgers University) Mark Steedman (University of Edinburgh) Michael K. Tanenhaus (University of Rochester) Jos van Berkum (Max Planck Institute for Psycholinguistics, Nijmegen) Rob van der Sandt (University of Nijmegen) Yoad Winter (Utrecht University) Henk Zeevat (University of Amsterdam)

EDITORIAL CONTACT: [email protected] © Oxford University Press 2010 For subscription information please see back of journal.

Editorial Policy Scope Journal of Semantics aims to be the premier generalist journal in semantics. It covers all areas in the study of meaning, and particularly welcomes submissions using the best available methodologies in semantics, pragmatics, the syntax/semantics interface, cross-linguistic semantics, experimental studies of meaning (processing, acquisition, neurolinguistics), and semantically informed philosophy of language. Types of articles Journal of Semantics welcomes all types of research articles–with the usual proviso that length must be justified by scientific value. Besides standard articles, the Journal will welcome ‘squibs’, i.e. very short empirical or theoretical contributions that make a pointed argument. In exceptional circumstances, and upon the advice of the head of the Advisory Board, the Journal will publish ‘featured articles’, i.e. pieces that we take to make extraordinary contributions to the field. Editorial decisions within 10 weeks The Journal aims to make editorial decisions within 10 weeks of submission. Refereeing Articles can only be accepted upon the advice of anonymous referees, who are asked to uphold strict scientific standards. Authors may include their names on their manuscripts, but they need not do so. (To avoid conflicts of interest, any manuscript submitted by one of the Editors will be handled by the head of the Advisory Board, who will be responsible for selecting referees and making an editorial decision.) Submissions All submissions are handled electronically. Manuscripts should be emailed in PDF format to the Managing Editor [[email protected]], who will forward them to one of the Editors. The latter will be responsible for selecting referees and making an editorial decision. Receipt of a submission is systematically confirmed. Papers are accepted for review only on the condition that they have neither as a whole nor in part been published elsewhere, are elsewhere under review or have been accepted for publication. In case of any doubt authors must notify the Managing Editor of the relevant circumstances at the time of submission. It is understood that authors accept the copyright conditions stated in the journal if the paper is accepted for publication.

All rights reserved; no part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise without prior written permission of the Publishers, or a licence permitting restricted copying issued in the UK by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London W1P 9HE, or in the USA by the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923. Typeset by TNQ Books and Journals Pvt. Ltd., Chennai, India. Printed by Bell and Bain Ltd, Glasgow, UK

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JOURNAL OF SEMANTICS Volume 27 Number 4

CONTENTS TAMINA STEPHENSON Control in Centred Worlds

409

ADRIAN BRASOVEANU Decomposing Modal Quantification

437

Short Contribution ERIC SWANSON On Scope Relations between Quantifiers and Epistemic Modals

Please visit the journal’s web site at www.jos.oxfordjournals.org

529

Journal of Semantics 27: 409–436 doi:10.1093/jos/ffq011 Advance Access publication June 16, 2010

Control in Centred Worlds TAMINA STEPHENSON Yale University

Abstract

1 INTRODUCTION I begin with a parallel involving ellipsis. First, consider the sentence in (1), focusing on how the predicate fun is interpreted. (1)

Sam thinks that roller coasters are fun, and Sue does too.

The first conjunct of (1), Sam thinks that roller coasters are fun, conveys something like the following: (i) Sam enjoys the experience of being on a roller coaster—that is roller coasters are fun for Sam, and (ii) Sam himself is aware of this fact. The second conjunct, Sue does too says, of course, that the same thing is true for Sue. Crucially, though, this only has a ‘sloppy identity’ (or ‘bound’) interpretation: Sue does too says that (i) roller coasters are fun for Sue and (ii) Sue is aware of this fact. Example (1) would not be true for example in a situation where both Sam and Sue were aware that roller coasters were fun for Sam, but where Sue was also aware that roller coasters were not fun for her. This mirrors a similar well-known fact about ellipsis in control constructions as in (2).1 (2)

Sam wants to be famous, and Sue does too.

1 It is unclear where the credit should go for this observation, but it seems to go back, in various forms, at least to Morgan (1970).

The Author 2010. Published by Oxford University Press. All rights reserved. For Permissions, please email: [email protected].

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This paper extends the framework of Lasersohn (2005) to give an updated semantic approach to control. On the view proposed here, all clausal constituents express (have as their semantic intensions) sets of centred worlds. In control constructions, the subject of the lower clause (‘PRO’) is identified with the ‘centre’ of a centred world. This view allows for a uniform semantic analysis of clauses, including those with and without null subjects, and for propositional attitude predicates.

410 Control in Centred Worlds

2 DE SE ATTITUDES AND CENTRED WORLDS I will begin by reviewing previous observations about the obligatory de se interpretation of control constructions, which was a key motivation for Chierchia’s (1989) property-based analysis.

2.1 The de se interpretation of control constructions It is well known that controlled PRO must be interpreted de se in the sense of Lewis (1979)—that is the attitudes expressed crucially involve the attitude holder’s access to their own ‘self ’. (See e.g. Morgan 1970; Chierchia 1989.) Consider (3), for example: (3) Pavarotti wants to be famous. (based on examples by Chierchia 1989) The observation is that if Pavarotti thinks to himself, ‘I want to be famous’, then this can be reported as (3). If, on the other hand, Pavarotti hears a recording of a talented singer on the radio, not realizing that it is a recording of his own voice, and thinks to himself, ‘I


Here, Sue does too means that Sue wants (herself) to be famous, not that Sue wants Sam to be famous. Again, the ellipsis in (2) allows only a ‘sloppy’ reading and not a ‘strict’ reading. In this paper, I will suggest that this is only one instance of a more general set of parallels, which arise from a close semantic connection between the experiencer of taste predicates such as fun and the implicit subject of embedded clauses in control constructions. In particular, I will propose here that both these items refer to the individual ‘centre’ of a centred world (treated as a world–individual pair), within a system where sentences in general express sets of centred worlds. The rest of the paper is organized as follows: In section 2, I set the stage by reviewing the phenomenon of de se attitudes and Chierchia’s (1989) property-based view of control. In section 3, I go through the centred worlds approach to the semantics of taste predicates developed in various forms by Lasersohn, myself and others. In section 4, I give the central proposal of this paper, which is to extend the centred worlds approach to control constructions. I show how this captures key properties of control, including locality phenomena and de se interpretation. Section 5 then compares my proposal with a pure property-based view like Chierchia’s and with a shifting-indexical view of the kind suggested by Anand & Nevins (2004). Sections 6 and 7 contain remaining problems and conclusions.

Tamina Stephenson 411

want the man on the radio to become famous’, this cannot be reported by (3). Similar facts hold for the Italian verb credere, ‘believe’ when it appears with an infinitival complement, as in (4). For example, if Pavarotti thinks to himself, ‘I am a genius’, his belief can be reported as (4); but if he unwittingly hears himself on the radio and thinks, ‘That man on the radio is a genius’, his belief cannot be reported this way. (4)

[Anand 2006, no. (1a); based on Chierchia 1989] De se attitudes were discussed earlier in a philosophical context by for example Castan˜eda (1966, 1968), Perry (1977, 1979) and Lewis (1979). A general approach to propositional attitudes that has come out of this work uses centred worlds. On the simplest formulation, these are just world–individual pairs <w, x>, which can be thought of as a world w experienced from the point of view of an individual x. We can then speak of a person x’s doxastic (belief) alternatives, for example as those centred worlds of which x might be the centre (as far as x’s beliefs are concerned). This definition is repeated more precisely in (5). Parallel definitions can be given for other attitudes, such as ‘want’ alternatives in (6). (5)

Doxastic Alternatives: Doxw,x ¼ {<w#, y> : it is compatible with what x believes in w that x (x’s self) is y in w#} (6) ‘Want’ Alternatives: Wantw,x ¼ {<w#, y> : it is compatible with what x wants in w for x (x’s self) to be y in w#}

Essentially, a person’s ‘want’ alternatives are those world–individual pairs <w#, y> such that their wants would be satisfied if they themselves were y in w#.

2.2 The property view of control Chierchia (1989) gives a proposal for control that is designed to capture the obligatory de se interpretation of sentences like (3) and (4). His proposal has two main components: first, giving control predicates meanings involving (sets of) centred worlds, and second, giving embedded clauses in control constructions the semantic type of


Pavarotti crede di essere un genio. Pavarotti believes COMP be a genius ‘Pavarotti believes that he’s a genius.’ [Lit.: ‘‘Pavarotti believes to be a genius’’]


a property. First, then, attitude predicates that participate in control constructions are given meanings (in addition to their normal noncontrol ones) that involve notions like doxastic or ‘want’ alternatives as in (5) and (6). For example, English want and Italian credere, ‘believe’ are given lexical meanings along the lines of (7) and (8). (7) ½½credere (‘believe’)w ¼ [kP<s, et> . [kze . "<w#, y> 2 Doxw,z: P(w#)(y) ¼ 1] ] (8) ½½wantw ¼ [kP<s, et> . [kze. "<w#, y> 2 Wantw,z: P(w#)(y) ¼ 1] ]

(9) a. Op1 [PRO1 [a] ] b. ½½ Op1 [PRO1 [a] ] w ¼ ½½aw This means, for example, that the infinitive to be a genius has the structure in (10a) and the property-type meaning in (10b). (10) a. Op1 [PRO1 [to be a genius] ] b. ½½to be a geniusw ¼ [ky . y is a genius in w] For example, then, (3), Pavarotti wants to be famous, is predicted to have the truth conditions in (11). (11) ½½(3)w ¼ ½½ Pavarotti wants [Op1 [PRO1 [to be famous] ] ] w ¼ ½½wantw ([kw# . [ ½½ Op1 [PRO1 to be famous] w#) (Pavarotti) ¼ ½½wantw ([kw# . [kx . x is famous in w#] ]) (Pavarotti) ¼ 1 iff "<w#, y> 2 Wantw,Pavarotti: y is famous in w# This says that Pavarotti wants to be famous is true iff in all world– individual pairs <w#, y> such that it is compatible with what Pavarotti 2 This will be the case provided that a does not contain a free variable with index 1. (Thanks to managing editor Philippe Schlenker for reminding me of this.)


According to (7), z crede P (‘z believes P’) is true iff all of z’s doxastic alternatives <w#, y> are such that y has property P in w#. According to (8), z wants P is true iff in all of z’s ‘want’ alternatives <w#, y>, y has the property P in w#. The second part of the account is to get infinitive clauses to have a property-type meaning. To achieve this, Chierchia assumes that PRO has the type of an individual (e) but is obligatorily bound by an abstraction operator. I will not go into the compositional details of the abstraction operator here, except to say that in the cases that will be relevant here, it has the effect that an expression with syntactic structure of the form in (9a) will have the denotation in (9b).2


wants for him to be y in w#, y is famous in w#. This is the correct meaning, and captures the de se interpretation of the attitude. It should be noted here that I am recasting Chierchia’s analysis in a system where the basic type of sentences is t, and they combine with attitude predicates by a rule of Intensional Functional Application. In extensional contexts, the simpler composition rule of Functional Application is used (see e.g. von Fintel & Heim 2009.) Since I will be positing modifications of these rules later on, I have included definitions in (12) and (13).

In this kind of system, attitude control predicates such as want and credere, ‘think’ have to be ambiguous between a property-taking meaning as in (7) and (8), used in control constructions, and a standard proposition-taking meaning to be used in non-control constructions. The second, proposition-taking meaning, would be along the lines of (14) and (15). (14) ½½thinkw ¼ ½½credere (‘believe’)w ¼ [kp<s, t> . [kze . "<w#, y> 2 Doxw,z: p(w#) ¼ 1]] (15) ½½wantw ¼ [kp<s, t> . [kze. "<w#, y> 2 Wantw,z: p(w#) ¼ 1] ] Note that these meanings still make reference to doxastic alternatives and ‘want’ alternatives that use centred worlds, but the world centre here is an idle wheel. For example, using the meaning in (14), the sentence Sam thinks that it’s raining in New Haven is true iff for all of the centred worlds <w#, y> compatible with Sam’s beliefs, it’s raining in New Haven in w#. Similarly, the sentence Sam wants it to rain in New Haven is true iff in all the centred worlds <w#, y> compatible with Sam’s desires, it’s raining in New Haven in w#.

2.3 Comment on semantic types On the view just described, control verbs require an argument of type <s, et>. The complement clauses (where PRO is bound by an individual binder) have semantic type <e, t>, and an extra world argument is in effect added by the compositional rule. Note, though,


(12) Functional Application (FA): If a is a complex expression formed by combining two expressions b and c, and ½½cw is in the domain of ½½bw, then ½½aw ¼ ½½bw (½½cw). (13) Intensional Functional Application (IFA): If a is a complex expression formed by combining two expressions b and c, and [kw#s . ½½cw#] is in the domain of ½½bw, then ½½aw ¼ ½½bw ([kw#s . ½½cw#]).


that <s, et> is also the type for a set of centred worlds (modulo currying). As far as the types are concerned, then, we could achieve the same effect if the embedded clause were type t (the basic type of a sentence), and the compositional rule added an extra centred world argument. This kind of system has in fact been proposed in a different domain, in particular for sentences containing taste predicates such as tasty and fun (e.g. Lasersohn 2005; Stephenson 2007). I will propose in section 4 below that this system be extended to control constructions, but first I need to give some background on taste predicates.

Let me begin with some background on the semantics of taste predicates.

3.1 Two uses of taste predicates The first thing to know about taste predicates is that (I claim) they have two distinct uses. First, they have a use where they seem to actually take an experiencer argument. This possibility comes out especially clearly in contexts where there is an obviously relevant experiencer who cannot plausibly be a participant in the conversation, and where it is unlikely for the participants in the conversation to have experienced the relevant thing—for example a situation where people are talking about whether some kind of cat food tastes good to their cat. This experiencer argument can be implicit as in (16a) (based on examples by Lasersohn 2005). It can also be explicit, as in (16b). Of course, if the experiencer argument is implicit, it must refer to an individual that is sufficiently salient in the context. (16) [Context: Sam is watching his cat, Princess, eat cat food. Princess is gobbling it enthusiastically. Sam says:] (a) Oh good, the new cat food is tasty. (b) Oh good, the new cat food tastes good to Princess. In this context, the perspective of the cat is particularly salient, and tasty in (16a) seems to be understood as ‘tastes good to Princess’. For the most part, I will be ignoring this use of taste predicates here, but it is important to keep in mind that I am assuming it is a separate use. Crucially, taste predicates have a second use in which they seem to be doing something more complicated, and this is the use which I will primarily deal with here. Consider the dialogue in (17).


3 TASTE PREDICATES AND CENTRED WORLDS


(17) Mary: How’s the cake? Sam: It’s tasty. Sue: No it isn’t!

(18) Mary: How’s the cake? Sam: It tastes good to me. Sue: No it doesn’t! In both (17) and (18), Sue seems to be contradicting or disagreeing with Sam—but not in the same way. In (17), it is very likely that Sue assumes Sam is speaking sincerely and believes that he likes the cake—she is just disagreeing because she does not like the cake. I will refer to this pattern of disagreement in dialogue as ‘subjective disagreement’. Compare this to (18), on the other hand, where Sue is not expressing anything about whether she herself likes the cake but is rather claiming that Sam does not really like the cake and/or that he is speaking insincerely. (We might call this ‘objective disagreement’.) In other words, Sue’s short answer response in (17) contains the ellipsis 3

More sophisticated ‘contextualist’ approaches have of course been proposed, for example by Stojanovic (2007) and von Fintel & Gillies (2008). Arguing against those views is beyond the scope of this paper.


On the most natural interpretation of (17), Sam is (in some sense) expressing or reacting to the fact that the cake tastes good to him and Sue is (in some similar sense) expressing or reacting to the fact that the cake does not taste good to her. The crucial point about this use of tasty (and parallel cases with other taste predicates) is that it cannot be treated simply as containing a contextually salient argument.3 This has been argued in some detail elsewhere, and I will only give a brief summary of the key points here. Essentially, the two most tempting approaches along these lines would be to say that (i) taste predicates such as tasty in (17) contain implicit speaker indexicals or (ii) they contain implicit generic pronouns. Let me briefly explain why neither of these approaches will work. For more detailed arguments, see for example Lasersohn (2005) and Stephenson (2007). First let us consider the ‘speaker indexical’ option. Note that in (17), Sam and Sue both seem to be expressing something about their own experience. Thus, one might be tempted to think that the experiencer is simply the speaker in each case—in other words, that tasty used in this way simply means ‘tastes good to me’ (i.e. to the speaker). But consider what happens if the experiencer is explicitly marked with a first-person indexical, as in (18).


shown in (19), whereas her response in (18) contains the ellipsis shown in (20). (19) Sue: No it isn’t [tasty]! (20) Sue: No it doesn’t [taste good to you]! Put simply, if tasty came with an understood first-person indexical, then we would expect (17) to be an incoherent discourse in the same way that (21) is. (21) Sam: I’m a doctor. Sue: # No, I’m not!

(22) This cake is tasty, although most people would hate it. (23) This cake is tasty, but I’m the only one who thinks so. (24) This cake is tasty, but everyone else I’ve asked seems to disagree. At this point, I will take it as given that a simple ‘implicit argument’ account will not work for taste predicates. Readers who would like additional convincing should refer to the works already cited. I should make it clear here that when I say taste predicates have two separate ‘uses’, I do not mean to claim that an actual ambiguity is involved. A systematic ambiguity would be one way to technically model the two uses, but in fact what I will be assuming is slightly different. As we will see below, I adopt a view where taste predicates come with an ‘experiencer’ argument slot that has the option of being filled in by two different kinds of things. I make reference to two separate ‘uses’ only to make it clear that the two options should not be confused with each other.


The dialogue in (17) may have the flavour of being a futile or childish disagreement to engage in, but it does not reach anywhere near the level of serious incoherence seen in (21). This is all another way of saying that when a taste predicate actually has a first-person experiencer, this represents the use of taste predicates illustrated in (16), rather than the more interesting use illustrated in (17). Now let us consider the ‘generic’ approach. One might suggest that in (17), tasty means something like ‘tastes good to people in general’ or ‘tastes good to most people’ (or something similar). The problem with this is that it would predict that sentences like (22) and (24) should sound contradictory (see Lasersohn 2005: 654–55). However, they sound perfectly coherent and seem to express the speaker’s awareness of their own unusual taste.


3.2 Centred worlds approach to taste predicates

(25) ½½tastyw,j ¼ [ky . [kx . x tastes good to y in w] ] ½½funw,j ¼ [ky . [kx . x is fun for y in w] ] ½½entertainingw,j ¼ [ky . [kx . x is entertaining to y in w] ] The first argument of these predicates is the experiencer of taste, enjoyment and so on. Lasersohn links this argument directly to the world centre (in his terms, the judge parameter), but I have argued (Stephenson 2007) that they should be connected only indirectly, which is what I will be doing here. In other words, tasty for example expresses the relation that holds between those pairs of individuals <x, y> such that x tastes good to y. In some cases, the first argument of a predicate of personal taste is overt, as in a sentence like The roller coaster is fun for Sam. In other cases, I assume, this argument is supplied covertly in one of two ways. The first possibility is for the context to provide a salient individual. This amounts to positing silent referential pronouns, which I will write as prox. So for example if the cat (let us call her Princess again) is particularly salient in the context, then tasty might take the silent item


Now let me summarize the analysis of taste predicates that I adopt here. This is essentially the view I developed in Stephenson (2007), which built on and modified the view of Lasersohn (2005). On this view, propositions are treated as sets of world–individual pairs rather than sets of worlds (or world–time–individual triples rather than world–time pairs; here I will be systematically ignoring times). In other words, a sentence is true not at a world but at a world–individual pair. Thus, sentence intensions in effect have type <s, et>. More generally, if the extension of an expression is of type r, its intension in this system will now be of type <s, er>. Lasersohn calls his new individual parameter the ‘judge’, reflecting the role of subjective judgment in determining what counts as tasty, fun and so on. Since I will be extending the view to cases without this obvious role for judgment, I prefer to construe the semantics in terms of centred worlds and will call this individual the ‘centre’ rather than the judge. In the discussion below, ordered pairs will stand for centred worlds; for example <w, j> stands for the world w centred on individual j. I will use [[a]]w,j for the denotation of an expression a at a centred world <w, j>. (Here, j is used after Lasersohn’s ‘judge’ terminology.) As I proposed in Stephenson (2007), I assume that on their basic meanings, taste predicates are two-place predicates, as shown in (25).


proPrincess as its first argument. The resulting meaning of the predicate would be as in (26). (26) ½½tasty proPrincessw,j ¼ [kx . x tastes good to Princess in w] This simply denotes the set of things that taste good to Princess. The second way that the first argument of a predicate of personal taste can be supplied covertly is in the form of a special silent nominal PROJ, which refers directly to the centre of the world of evaluation. That is, it has the lexical entry in (27). (27) ½½PROJw,j ¼ j

(28) ½½tasty PROJw,j ¼ [kx . x tastes good to j in w] Thus, the sentence The cake is tasty (where the implicit argument of tasty is taken to be PROJ) is true at a pair <w, j> iff the cake tastes good to j in w, as shown in (29). Note that the denotations in (27)–(29) rely crucially on the value of the world centre; I will call an expression ‘centre-dependent’ when this is the case. (29) ½½The cake is [tasty PROJ] w,j ¼ 1 iff the cake tastes good to j in w Here, I will be focusing on sentences like (29) in the case where they are embedded under attitude reports; we will see that this has an effect on the world centre that is somewhat akin to binding. For discussion of taste predicates and other centre-dependent expressions in unembedded sentences see for example Lasersohn (2005), Egan (2007) and Stephenson (2007). (Lasersohn discusses taste predicates, Egan discusses epistemic modals and my 2007 paper argues that the two should be given a similar treatment.)

3.3 Attitude predicates in a centred worlds semantics Once propositions are treated as sets of centred worlds rather than sets of worlds, it becomes particularly straightforward to capture de se attitudes. Recall for example the definition of doxastic alternatives from (5), repeated in (30). (30) Doxastic Alternatives: Doxw,x ¼ {<w#, y> : it is compatible with what x believes in w that x (x’s self) is y in w#}


For example, if tasty takes PROJ as its first argument, then the result (evaluated at a world w with centre j) is the set of things that taste good to j in w. This is shown in (28).


On the current approach, a person’s set of doxastic alternatives is simply a proposition—that is a set of centred worlds. Therefore, we can go back to treating attitude predicates as relations between individuals and propositions. For example, we can give think and want the meanings in (31) and (32). Here, pS indicates the set characterized by p, that is {<w#, x> : p(w#)(x) ¼ 1}. (31) ½½thinkw,j ¼ ½½believew,j ¼ [kp<s, et> . [kze . Doxw,z 4 pS] ] (32) ½½wantw,j ¼ [kp<s, et> . [kze . Wantw,z 4 pS ]

(33) ½½thinkw,j ¼ ½½believew,j ¼ [kp<s, et> . [kze . "<w#, y> 2 Doxw,z : p(w#)(y) ¼ 1] ] (34) ½½wantw,j ¼ [kp<s, et> . [kze . "<w#, y> 2 Wantw,z : p(w#)(y) ¼ 1] ] As written in (33) and (34), these meanings are essentially exactly the same as the ones given earlier in section 2.2, (7) and (8), for control predicates. The difference is only that now the sentential complement of the attitude predicate is always taken to be something that expresses a proposition rather than a property. In other words, the type <s, et> now corresponds to the intension of a sentential (type t) expression rather than the intension of a set-denoting (type <e, t>) expression. The compositional rules needed for the centred worlds system are given in (35) and (36). Note that only the intensional rule needs to be changed from the version given in section 2.2. (35) Functional Application (FA): If a is a complex expression formed by combining two expressions b and c, and ½½cw,j is in the domain of ½½bw,j, then ½½aw,j ¼ ½½bw,j (½½cw,j). (36) Intensional Functional Application (IFA): If a is a complex expression formed by combining two expressions b and c, and [kw#s . [kj#e . ½½cw#,j#] ] is in the domain of ½½bw,j, then ½½aw,j ¼ ½½bw,j ([kw#s . [kj#e . ½½cw#,j#] ]).

3.4 Taste predicates in attitude reports A crucial property of this analysis is the way it interacts with the centredependent semantics for taste predicates from section 3.2 above. Consider sentences like (37) and (38), which contain a predicate of personal taste with implicit argument PROJ.


This says that ‘z thinks that p’ is true iff z’s doxastic alternatives are a subset of p—in other words, if p is true at all of z’s doxastic alternatives. Similarly, ‘z wants p’ is true iff z’s ‘want’ alternatives are a subset of p. I have used set notation in (31) and (32), but note that these meanings are equivalent to (33) and (34).


(37) Sue thinks the cake is tasty PROJ. (38) Sue wants the cake to be tasty PROJ. The predicted meanings for (37) and (38) are given in (39) and (40).

According to these meanings, (37) is true iff the cake is tasty at all of Sue’s doxastic alternatives—that is if Sue believes that the cake tastes good to Sue herself. Similarly, (38) is true iff Sue wants the cake to taste good to Sue herself. This seems to be correct.4 Notice that, roughly speaking, this means that attitude predicates effectively ‘bind’ the world centre by linking it to the attitude holder. The meanings in (39) and (40) also predict that PROJ will be interpreted de se under attitude predicates since doxastic alternatives and ‘want’ alternatives crucially involve a de se counterpart. To test this prediction, we need to set up a context where for example Sue does not find something tasty but thinks that a particular person does find it tasty, unaware that that person is Sue herself. Consider the context in (41), for instance: (41) [Context: Sue works as an actress in food commercials. Generally, of course, she is willing to pretend to like foods she dislikes. There’s only one thing she really can’t stand, which is tomato soup, and in the past she has absolutely refused to do commercials for it. Recently, however, she was in particularly dire financial need, and finally agreed to do a commercial for tomato soup. The filming went off without a hitch, but she was so disgusted that she immediately went home and drank several mint juleps just to get the tomato taste out of her mouth. She turned on her favorite cooking show and promptly fell asleep on her living room couch. She later happened to wake up in the middle of the night right when her own tomato soup commercial was airing for the first 4

Example (38) also has a salient reading on which Sue wants the cake to taste good to some other person or people (perhaps the people who are going to eat the cake). This reading arises when tasty takes a silent referential argument instead of PROJ.


(39) ½½(37)w,j ¼ ½½thinkw,j ([kw# . [kj# . ½½the cake is tasty PROJw#,j# ] ]) (Sue) ¼ 1 iff "<w#, y> 2 Doxw,Sue : the cake tastes good to y in w# (40) ½½(38)w,j ¼ ½½wantw,j ([kw# . [kj# . ½½the cake is tasty PROJw#,j# ] ]) (Sue) ¼ 1 iff "<w#, y> 2 Wantw,Sue : the cake tastes good to y in w#


time. In her sleepiness and drunkenness, she thought that the cooking show was still on and that the actress (Sue herself) was the chef enjoying tomato soup. Sue says to herself:] Tomato soup is disgusting—but obviously it tastes good to that woman on T.V. It seems to me this could not be reported as in (42), suggesting that the prediction is correct and PROJ is in fact interpreted de se. (42) Sue thinks that tomato soup tastes good.

In this section, I present my proposal for the semantics of control. The crucial claim here is that PRO directly refers to the world centre. In sections 4.1 and 4.2, I show how this proposal (like other semantically based accounts of control) captures two key properties of control, namely its obligatory de se interpretation and certain locality phenomena. In section 4.3, I return briefly to the opening observation about sloppy identity readings in ellipsis. In section 4.4, I extend this approach to cases of object control.

4.1 PRO as PROJ Let us look again at a typical control construction such as (43). (43) Sue wants PRO to go on the roller coaster. Suppose that PRO in (43) simply refers directly to the world centre. Then, the embedded clause, (PRO) to go on the roller coaster, has the meaning in (44). Putting this together with the meaning for want from section 3.3, the predicted meaning for (43) is (45). (44) ½½PRO to go on the roller coasterw,j ¼ ½½PROJ to go on the roller coasterw,j ¼ 1 iff j goes on the roller coaster in w (45) ½½Sue wants [PROJ to go on the roller coaster] w,j ¼ ½½wants ([kw# . [kj# . ½½PROJ to go on the roller coasterw#,j#] ]) (Sue) ¼ 1 iff "<w#, y> 2 Wantw,Sue : y goes on the roller coaster in w# This says that (43) is true iff all of the situations compatible with Sue’s desires are such that Sue (herself) goes on the roller coaster. This is correct and captures the obligatory de se interpretation of PRO in essentially the same way as the property view, semantically speaking.


4 PROPOSAL FOR CONTROL


4.2 Doubly embedded cases Now consider an example like (46), where a control construction is embedded within another attitude report. It is well known that in cases like this, the implicit subject of the lowest clause (conventionally PRO; PROJ on my view) must be controlled by the lower, that is closest attitude holder (in this case, Bill) and not the higher one (in this case, Sue). In other words, (46) cannot be understood to mean that Sue thinks that Bill wants her to go to the party. (46) Sue thinks that Bill wants PROJ to go to the party. This requirement follows directly from the compositional semantics on my view. For example, the meaning predicted for (46) is shown in (47). (47) ½½(46)w,j ¼ ½½Sue thinks [Bill wants [PROJ to go to the party] ] w,j ¼ ½½thinkw,j ([kw# . [kj# . ½½Bill wants PROJ to go to the partyw#,j#) (Sue) ¼ 1 iff "<w#, y> 2 Doxw,Sue : "<w$, z> 2 Wantw#,Bill : z goes to the party in w$ According to (47), Sue thinks that Bill wants to go to the party is true iff in all of Sue’s doxastic alternatives, all of Bill’s ‘want’ alternatives <w$, z> are such that z goes to the party in w$—that is iff Sue thinks it is the case that Bill wants to have the property of going to the party. The crucial thing here is that the most embedded clause, PROJ to go to the party, expresses the proposition that is true at a world–individual pair <w, j> iff j goes to the party in w. When this is taken as an argument by want, the implicit subject of go to the party is irreversibly linked to the subject of want.


As I hope I have already made clear, it is no accident that my proposal has the same result as Chierchia’s property view. I treat propositions as sets of world–individual pairs, which is exactly what properties are on standard views. The difference here is that on the centred worlds view, all sentence-like expressions are assigned this type—not just those embedded by control verbs. Moreover, this move is independently motivated by the behaviour of taste predicates and other expressions (as argued by Lasersohn 2005; Stephenson 2007). By the same token, this proposal is mainly about the semantics of control and is not intended to say anything new about the syntactic properties or distribution of PRO.


4.3 Ellipsis This paper began with the observation that in both (48) and (49), only a ‘sloppy identity’ reading is possible. (48) Sam thinks that roller coasters are fun PROJ, and Sue does too. [¼ (1)] (49) Sam wants PRO to be famous, and Sue does too. [¼ (2)]

4.4 Object control The view of PRO as PROJ can easily be extended to the case of object control, as in (50). I will illustrate this with persuade, but similar things can be said about other object control verbs such as tell, defy, ask and so on. (50) Sue persuaded Mary to take Sam to the movies. I assume that (50) has the structure in (51). (51) Sue [VP persuaded [Mary] [S PROJ to take Sam to the movies] ] What object control verbs seem to have in common is that they all in some way involve one individual doing something with the intention of getting another individual to have a particular attitude towards some other proposition or action (see e.g. Comrie 1984; Sag & Pollard 1991). For example, in (51), Sue says something with the intention of getting Mary to intend to take Sam to the movies. Since intending is an attitude in its own right, I will express it in terms of ‘intention alternatives’, defined in (52).


On the centred worlds approach, we can make sense of the lack of ‘strict’ identity readings. In both these cases, the elided VP contains an attitude predicate (think or want) that embeds a phrase containing PRO or PROJ. As we have already seen, this automatically links PRO/PROJ to the attitude holder. Since the attitude holder is the only part that changes in the second conjunct (other than the eliding process itself), PROJ and PRO become automatically linked to Sue in the second conjunct of both (48) and (49). Another way to look at it is this: on the centred worlds approach, PRO (and PROJ) in the first conjuncts of (48) and (49) do not actually pick out Sam as a ‘referent’. What gives rise to their link to Sam is crucially the fact that Sam is the holder of an attitude expressed in the higher clause. In the second conjuncts (with ellipsis) the attitude holder changes to Sue, and so PRO/PROJ are automatically linked to Sue in the same way.


(52) Intention alternatives: Intendw,x: {<w#, y> : it fits with what x intends in w for x to be y in w#} Using this notion, we can then give persuade the lexical entry in (53). (53) ½½persuadew,j ¼ [kxe . [kp<s, et> . [kye . y communicates with x in a way that causes it to be the case that "<w#, z> 2 Intendw,x: p(w#)(z) ¼ 1] ] ]

(54) ½½Sue persuaded Mary to take Sam to the moviesw,j ¼ ½½persuadew,j (Mary) ([kw# . [kj# . ½½PROJ to take Sam to the moviesw#,j# ] ]) (Sue) ¼ 1 iff Sue communicated with Mary in w in a way that caused it to be the case that "<w#, z> 2 Intendw,Mary: z takes Sam to the movies This says that (50) is true iff Sue communicated with Mary in a way that made it the case that in all of Mary’s intention alternatives <w#, z>, z takes Sam to the movies—that is if Sue caused Mary to intend for Mary herself to take Sam to the movies.

5 COMPARISON TO ALTERNATIVE VIEWS Now, I will turn to comparisons between the view I have proposed here and other possible or existing views, starting with a Chierchiatype view. The main difference between the centred worlds approach to control and a Chierchia-style property view involves general considerations of theoretical simplicity. The centred worlds approach allows us to give all sentential expressions the same semantic type: their extensions are type t and their intensions are type <s, et>. This in turn lets us give a unified semantics for attitude predicates in control and non-control contexts. Of course, it is crucial that there is independent motivation for treating propositions as type <s, et> rather than <s, t> in the first place; I take it that the cited work on taste predicates and epistemic modals provides this motivation.


This says, roughly speaking, that ‘y persuades x (to) p’ means that y communicates with x in a way that causes x to intend p. Since p is evaluated with respect to the intention alternatives of the direct object (‘x’), the judge parameter is in effect shifted to the direct object. Thus, the meaning of (50) is predicted to be as shown in (54).


(55) [Amharic] on gna n -nñ˜ y l-all John hero be.PRES-ls says-3sm ‘John says that {I am, he is} a hero.’ [Lit: ‘‘John says that I am a hero.’’] [Schlenker 2003, no. (53)] A typical example of a West African-type logophor is given in (56), from Ewe. Here, the pronoun ye` can only refer to the reported speaker, Kofi. (56) [Ewe] Kofi be ye`-dzo Kofi say LOG-leave ‘Kofi said that he (Kofi) left.’ [Clements 1975, no. (1)] Crucially, it has been claimed that both shifting indexicals (when they have their shifted interpretations) and logophors generally must be 5

Thanks to an anonymous reviewer for reminding me of this. Amharic is a Semitic language spoken in Ethiopia; Zazaki is an Indo-Iranian language spoken by ethnic Kurds in Turkey. 6


I have analysed PRO using machinery (including centred worlds) that is independently motivated by the semantics of taste predicates. However, other kinds of machinery have also been independently motivated by other phenomena, and we can ask whether PRO should instead be analysed using one of them. In particular, in the context of work on shifting indexicals and logophors, Anand & Nevins (2004) suggest that it may be possible to analyse PRO as an indexical that refers to a participant in an embedded context.5 Below, I will discuss some of the differences between that kind of view and the one I have proposed here, after I give a bit of background on shifting indexicals and logophors. The motivation for a system with shifting context parameters comes from the behaviour of shifting indexicals of the kind found in Amharic and Zazaki6 (Schlenker 1999, 2003; Anand & Nevins 2004; Anand 2006) and logophors of the kind found in some West African languages, such as Ewe, Yoruba and Abe (Hage`ge 1974; Clements 1975; Pulleyblank 1986; Koopman & Sportiche 1989). One typical example of a shifting indexical is given in (55), from Amharic. The first-person indexical in (55) can either refer to the speaker of the utterance or to the reported speaker, John.


(57) ½½PROw,j ¼ j A shifting-indexical approach would need to make a distinction between subject and object control. The lexical entries for subject and object PRO would be along the lines of (58) and (59), respectively. (58) ½½PROsubjw,a,b ¼ a (59) ½½PROobjw,a,b ¼ b These say that, evaluated at a world w, author a, and addressee b, the ‘subject’ version of PRO refers to a and the ‘object’ version refers to b. I will illustrate the semantic predictions of the two approaches using the typical subject and object control constructions Sam wants to leave and Sue persuades Sam to leave. On the centred worlds approach, the predicted meanings are given in (60) and (61). 7 This claim is difficult to test in fieldwork and has not been verified for every relevant language and item, but Schlenker (1999) makes the claim for Amharic ‘I’ and discusses the issue for logophors [citing e.g. Kusumoto (1998), for Bafut logophors]. Anand (2006) discusses the issue in more detail. At this point, it at least seems reasonable to take it as a working hypothesis that logophors and shifting indexicals are de se.


interpreted de se.7 That is, a sentence like (55) can only report a situation where John said, ‘I am a hero’, not one where for example he unknowingly saw himself on T.V. and said, ‘that man is a hero’. An influential framework that has been developed for analysing these items is one with context shifting operators (see e.g. Schlenker 2003; Anand 2006). When shifting indexicals appear under these operators, they are evaluated with respect to the shifted context rather than the main context of utterance. Abstracting away from some details and variations, this kind of framework treats propositions as sets of contexts, where a context can be construed as a tuple of a world, author, addressee and other necessary parameters. For present purposes, we can simplify the comparison further by thinking of contexts as world–individual–individual triples (where the individuals are the author and addressee, respectively). In the discussion below, when dealing with a shifting-indexical approach, I will write [[a]]w,a,b for the denotation of a at a context in world w with author a and addressee b. As before, when discussing the centred worlds approach, I will continue to write [[a]]w,j for the denotation of an expression a at world w with centre j. Now let us consider what it would look like if we treat PRO as a shifting indexical. First, the lexical meaning for PRO on the centred worlds approach is repeated in (57).


(60) ½½Sam wants [PRO to leave] w,j ¼ 1 iff in all centred worlds <w#, y> such that it’s compatible with Sam’s desires for him to be y in w#, y leaves. (61) ½½Sam persuades Sue [PRO to leave] w,j ¼ 1 iff Sam communicates with Sue in a way that causes it to be the case that in all centred worlds <w#, y> such that it’s compatible with Sue’s intentions in w for her to be y in w#, y leaves. On a shifting indexical view, the predicted meanings would be along the lines of (62) and (63).

Both approaches seem to give the correct semantics for these basic cases, including the de se interpretation of PRO. Both also make use of extra machinery that is independently motivated by other phenomena: centred worlds are motivated by the behaviour of taste predicates, while author and addressee parameters are motivated by shifting indexicals. There are a few differences, though, which I turn to now. A small but obvious difference between the two approaches is that the shifting-indexical approach needs to treat subject and object controlled PRO differently, whereas the centred worlds approach can give a single meaning for PRO. In terms of overall simplicity, then, this gives a slight advantage to the centred worlds approach. Another difference, closely related to the first one, has to do with predicted generalizations about the semantic role of subject and object PRO. As discussed earlier, the centred worlds approach makes it a key property of PRO—both subject controlled and object controlled—that it is linked to a propositional attitude introduced in the lexical semantics of the control predicate. On the other hand, the shiftingindexical approach makes it a key role of PRO that it is linked to a certain participant in an utterance-like context—subject controlled PRO is linked to an author (which could be an attitude holder) and object controlled PRO is linked to an addressee. Since the notion of ‘author’ is generally taken to include the holder of an attitude, a real difference can only come out with object control predicates. If the


(62) ½½Sam wants [PROSubj to leave] w,a,b ¼ 1 iff in all contexts <w#, a#, b#> (where a# is the author) such that it’s compatible with Sam’s desires in w for him to be a# in w#, a# leaves. (63) ½½Sam persuades Sue [PROObj to leave] w,a,b ¼ 1 iff Sam communicates with Sue in w in a way that causes it to be the case that in all contexts <w#, a#, b#> (where b’ is the addressee) such that it’s compatible with Sue’s intentions in w for Sue to be b# in w#, b# leaves.


centred worlds approach is correct, then we might expect to find object control predicates whose objects are clearly the holder of an attitude but not necessarily the addressee of any speech-like event. If, on the other hand, the shifting-indexical approach is correct, we might expect to find the reverse: object control predicates whose objects are clearly the addressee in a speech-like event but not necessarily the (intended) holder of an attitude. Finding examples of either kind turns out to be tricky, but two examples of the first kind are convince and discourage as used in (64) and (65).

It is fairly clear that these cases do not involve any speech act (certainly the rainy weather is not discouraging or convincing Sue by talking to her), and it is equally clear that they do crucially involve a change in Sue’s attitude towards going for a bike ride and staying home, respectively. Thus, discourage and convince give evidence for the centred worlds view over the shifting indexical view of object control. Now, are there examples of object control predicates of the opposite kind—where the object is an addressee but not an attitude holder? On the face of it, there do seem to be plausible cases, such as ask and order as used in (66) and (67). (66) Sam asked Sue to leave, but she didn’t hear him. (67) Sam ordered Sue to leave, but she didn’t hear him. In these examples, Sue is clearly the addressee of an utterance of Sam’s, but she does not come to hold an attitude towards the proposition that the world centre leaves (i.e. that Sue herself leaves) since she is not aware that the utterance took place. However, Sam does have to intend for Sue to hear him, and to consequently gain the relevant attitude, regardless of whether he succeeds, and so the meaning 8 Thanks to Nicole Palffy-Muhoray for useful discussion of these examples. Many naturally occurring examples similar to (64) and (65) can be found through a simple Google search for ‘the weather convinced me to’ and ‘the weather discouraged me from’. Here are a few: (i) Yeah, the weather convinced me to stay in last night (http://gimpysoft.com/2007/01/13/ok-i-lied-see-you-tonight/, accessed 12 February 2010). (ii) The taste of the foods along with the weather convinced me to establish my roots in California (http://www.hawaiianhabaneroheat.com/, accessed 10 February 2010). (iii) This winter, the weather discouraged me from riding much, so I went back into diet mode . . . (http://science.slashdot.org/science/03/04/12/2357234.shtml?tid¼134, accessed 10 February 2010). (iv) And then the weather discouraged me from knitting anything summery (http://stashqueen.typepad.com/stash_queen/2009/07/index.html, accessed 10 February 2010).


(64) The rainy weather discouraged Sue from going for a bike ride. (65) The rainy weather convinced Sue to stay home.8


of ask or order will still indirectly involve an attitude held by Sue. For example, a meaning for ask could be along the lines of (68). (68) ½½asksw,j ¼ [kxe . [kp<s, et> . [kye . y makes a request of x with the intention of making it the case that "<w#, z> 2 Intendw,x: p(w#)(z) ¼ 1] ] ]

(69) a. Playing baseball is fun. b. [PRO playing baseball] is [fun PROJ] Note that the implicit subject of playing baseball (PRO) is understood to be the same as the person who has the experience of fun—that is (69) cannot be understood as saying that some person A finds it fun when another person B plays baseball. (This observation is due to Epstein 1984.) In particular, notice that (69) gives rise to the same kind of ‘subjective disagreement’ found with taste predicates more generally, which was discussed in section 3.1 above. For instance, Sam’s response in (70) can be understood as expressing the fact that Sam does not find it fun when he (himself) plays baseball. This contrasts as expected with (71), where Sam’s response can only be understood as claiming that Sue does not find it fun when she plays baseball. (70) Sue: Sam: (71) Sue: Sam:

Playing baseball is fun. No it isn’t! Playing baseball is fun for me. No it isn’t!

The main point here is that in (70), the interpretation of PRO (i.e. the implicit subject of playing baseball) co-varies with the experiencer of fun.9 The question, then, is how this covariance arises. On the 9

The same covariance also shows up in ‘Super Equi’ constructions such as (i), where it is captured on my view in a parallel way. (i) Sam thinks that playing baseball is fun.


This says that ‘A asks B to VP’ is true iff A makes a request of B, with the intention of making it the case that B intends to VP. Thus, an attitude of B is still involved, even though it is embedded under an attitude of A’s. In fact, it is a routine observation in pragmatics that communicative acts generally involve the speaker intending to cause the addressee to come to have some attitude or other. Thus, any object control verb that entails a speech act should be amenable to this kind of analysis. There is one more difference between the two approaches, also closely related to the previous ones, which is brought out when we consider sentences like (69a), which I take to have the structure in (69b).


(72) My cake tastes good to Sam. (73) Your cake tastes good to Sam. It seems unlikely that such interpretations are available and have not previously been observed, but I leave this to others to test. 6 REMAINING ISSUES In the previous section, I discussed some advantages of a centred worlds approach. At this point I will turn to some problems and challenges for my proposal.

6.1 A puzzle about manage An anonymous reviewer points out a problem for my view in giving an appropriate semantics for the verb manage. To see it, first look at the simple dialogue in (74), which contains no control verb. (74) Sam: This time, John was charming. Sue: No he wasn’t! As with similar dialogues with other taste predicates, there is a salient reading on which, roughly speaking, Sam is expressing the fact that John charmed him and Sue is expressing the fact that John did not charm her. As discussed in section 3, I assume that this reading arises when the implicit argument of charming is PROJ. In other words, the


centred worlds approach, very little needs to be said: since PRO has the same semantics as PROJ, the implicit subject of playing baseball and the implicit experiencer of fun are for all intents and purposes the same lexical item, and so it is completely expected that their interpretation would co-vary, in the same way that for example the reference of I and myself co-vary in different speakers’ utterances of I see myself. On a shifting-indexical approach, in contrast, it would be crucial that PRO be embedded under a context shifter. If it were not embedded, we would expect it to act like a normal first or second person indexical, which it clearly does not. A context shifting operator could perhaps be built into the taste predicate or into the implicit experiencer argument of the taste predicate; in this case, though, we would expect shifted indexicals to be possible (in languages that have them) in sentences with taste predicates more generally. That is, we would expect to find the equivalent of a sentence like either (72) or (73) in a language like Zazaki or Amharic, with the interpretation ‘Sam’s cake tastes good to Sam.’


proposition that Sue is disagreeing with (namely that John was charming) is the one expressed by the structure in (75a), with the denotation (in set terms) in (75b). (75) a. [ John was charming PROJ] b. {<w, x> : John charmed x in w} Now consider a similar dialogue where manage is added, as in (76). (76) Sam: This time, John managed to be charming. Sue: No he didn’t!

(77) Sam: This time, John managed to charm me. Sue: No he didn’t! In (77), Sue’s response can only be understood as denying that John charmed Sam, not denying that John charmed Sue herself. Now, here is the problem with (76): If manage is a control verb, we would expect on my view for the embedded clause (to be charming) to have the subject PROJ, and for the semantics of manage to introduce a mediating attitude that links this subject to Sam. On the other hand, in order for Sue’s utterance to express the fact that John did not charm her, the implicit argument of charming should also be PROJ, and moreover, this PROJ needs to not be embedded under any attitudes. Put another way, if we think of NP managed to VP as having two components, a presupposition that NP tried to VP and an assertion that x did VP, it does not seem to be possible on my view to give the VP a single meaning and structure for both components. What we seem to need instead is for the presupposition to make reference to a VP something like (78a), while the assertion makes reference to a VP like (78b). (78) a. [PROJ to be charming prox] b. [John was charming PROJ] I leave this as an open problem.

6.2 Partial control Certain control verbs allow a ‘partial’ interpretation, where the implicit subject is not identical to the subject of the higher clause, but rather


There is a salient reading of (76) that is essentially the same as the relevant reading of (75) except with the added requirement (presumably a presupposition) that John made some effort to be charming. We can see this even more clearly if we contrast (76) with (77), where the argument of charming is made explicit and this kind of reading goes away.


is a larger group that is contextually salient and includes that individual (see e.g. Lawler 1972; Martin 1996; Petter 1998; Landau 2000). ‘Partial control’ verbs include want and decide, which are illustrated in (79). (79) a. The chair decided to gather during the strike. b. Mary wants to meet at 6:00.

(80) a. */# The chair gathered during the strike. b. */# John met at 6:00. I have very little to add to the discussion of the phenomenon of partial control and what determines whether a particular control verb allows it or not, but I would at least like to show that in principle it is not an insurmountable problem for the view of PRO as PROJ. To account for partial control, Landau (2000: ch. 2) assumes, among other things, that PRO can carry a feature for semantic plurality. Simplifying somewhat, this means that there is a ‘singular’ PRO and a ‘plural’ PRO. (It is crucial for him that these are semantic features, not syntactic phi-features.) Essentially, partial control occurs when the subject of the higher clause is singular but PRO is plural, which is allowed under certain conditions because of the particular way that agreement relations work between the higher and lower clause. Without going into the details of Landau’s analysis, I will just show that there is a coherent way to posit a plural version of PROJ that will yield the right interpretation for partial control cases. Borrowing an idea of Kratzer (2006, 2009), I assume that the plural version of PROJ (which I’ll call PROJ-PLUR) refers to the unique salient group containing the world centre. A lexical entry for PROJ-PLUR is given in (81). (The extra parameter of interpretation ‘c’ stands for the context of utterance.) (81) ½½PROJ-PLURc; w,j ¼ Gc(j), where Gc(x) ¼ the salient group containing x in context c For example, the partial control structure in (82a), which contains PROJ-PLUR, is predicted to have the meaning in (82b).


[based on Adler 2006, no. (15d-e)] We can tell that the implicit subject of the infinitive is a group in each of these cases because gather and meet are collective predicates, as we can see from the unacceptability of (80a–b).


(82) a. Mary wants [PROJ-PLUR to meet] b. ½½(a)c; w,t,j ¼ ½½wantsw,j ([kw# . [kj# . ½½PROJ-PLUR to meetw#,j# ] ]) (Mary) ¼ 1 iff "<w#, y> 2 Wantw,Mary: Gc(y) meets in w# This says that Mary wants to meet is true iff for all of Mary’s ‘want’ alternatives <w#, y>, the salient group containing y meets in w#, which captures the ‘partial’ nature of the control.

6.3 Extensional adjuncts and non-obligatory control

(83) a. Sam left without saying goodbye. b. Sue walked down the street (while) singing. If the gerunds are taken to have PRO subjects, the structures for (83a–b) should be something like (84a–b), respectively. (84) a. Sam [left [AdvP without PRO saying goodbye] ] b. Sue [walked down the street [AdvP (while) PRO singing] ] The issue here is that the gerundive clauses cannot be plausibly treated as being semantically under an attitude. This means that there is nothing to shift the judge parameter to Sam in (84a) or Sue in (84b). My own inclination is to say that adverbial gerunds are sufficiently different from typical control constructions that they should be given a separate analysis, but it is admittedly difficult to give non-circular arguments for this. (That is, part of the reason they seem different to me is probably that they so clearly do not involve attitudes.) The issue is somewhat trickier for cases like (85). (85) Tom felt sheepish. Pinching those elephants was foolish. [Adler 2006, no. (24a), citing Bresnan 1982] On the one hand, the underlined subjectless clause pinching those elephants is clearly not embedded under any overt attitude predicate; on the other hand, it clearly does in some way express Tom’s perspective and experience—in other words, we understand (85) as saying, more or less, that Tom felt sheepish because he thought that it was foolish of him to pinch the elephants. It seems at least initially plausible, then, that some kind of covert perspective-shifting operator is present that expresses an attitude, though I will not attempt to formalize this here.


There are at least two kinds of constructions that are often treated as containing PRO but which cannot (easily) be captured by the account proposed here. The first includes sentences with adverbial gerunds such as (83a–b) (see e.g. Williams 1992).


Another case that has been called non-obligatory control is given in (86). (86) John said to Mary that it would be easy to prepare herself for the exam.

(87) John said to Mary [that it would be [easy proMary] [PRO to prepare herself for the exam] ] In effect, then, PRO is obligatorily controlled by the implicit argument of easy. In this way, it is similar to the Epstein examples discussed in section 5 [see example (69) and footnote 9]. The real issue with this example, then, is whether ‘being easy’ can plausibly be treated as involving an attitude. It is not at all clear to me that this is the case, and so I leave this counterexample as another open problem. 7 CONCLUSIONS In this paper, I have proposed a new twist on a semantically based view of control. I treat control complements essentially as properties (as in e.g. Chierchia 1989), but bring in the extra individual argument by linking it to Lasersohn’s judge parameter. This makes the same key predictions as the property view with the additional advantage of letting all sentential expressions (including subjectless infinitives) share the same semantic type, <s, et>. This in turn allows us to give a semantics for attitude predicates that fits seamlessly together with formal machinery independently needed for de se attitudes. Acknowledgements Earlier versions of this work appeared in Chapter 4 of my 2007 MIT Ph.D. thesis and in the Proceedings of NELS 38. For discussion and helpful suggestions, I would like to thank Seth Cable, Henry Davis, Ashwini Deo, Kai von Fintel, Danny Fox, Michael Freedman, Irene Heim, Idan Landau, Keir Moulton, Nicole PalffyMuhoray, Orin Percus, Agustin Rayo, Martina Wiltschko, audiences at UBC, NELS 38 and the 2008 LSA Annual Meeting and the editors and reviewers at the Journal of Semantics. Special thanks go to Rose Hurley for proofreading. Any errors are, of course, my own.


[Adler 2006, no. (26)] In this case, I suggest that the non-obligatoriness of the control is an illusion. This is because easy itself has an implicit argument, which in this case is naturally understood as referring to Mary simply because she is salient and can corefer with the female reflexive herself. In other words, the structure of (86) is something like (87).

Tamina Stephenson 435 TAMINA STEPHENSON Yale Department of Philosophy P. O. Box 208306 New Haven, CT 06520-8306, USA e-mail: [email protected]

REFERENCES Egan, Andy. (2007), ‘Epistemic modals, relativism, and assertion’. Philosophical Studies 133:1–22. Epstein, Samuel David. (1984), ‘Quantifier-pro and the LF Representation of PROARB’. Linguistic Inquiry 15:499–505. Hage`ge, Claude. (1974), ‘Les pronoms logophoriques’. Bulletin de la Socie´te´ de Linguistique de Paris 69:287–310. Koopman, Hilda & Dominique Sportiche. (1989), ‘Pronouns, logical variables and logophoricity in Abe’. Linguistic Inquiry 20:555–89. Kratzer, Angelika. (2006), ‘Building a pronoun’. Paper presented at Semantics and Linguistic Theory 16. University of Tokyo, Tokyo, Japan. Kratzer, Angelika. (2009), ‘Making a pronoun: Fake indexicals as windows into the properties of pronouns’. Linguistic Inquiry 40:187–237. Kusumoto, Kiyomi. (1998), Tenses as Logophoric Pronouns. Handout of talk given at the MIT/UConn/UMass Semantics Workshop. University of Connecticut. Storrs, CT. Landau, Idan. (2000), Elements of Control: Structure and Meaning in Infinitival Constructions. Studies in Natural Language and Linguistic Theory, vol. 51. Kluwer. Dordrechtvol. 51. Lasersohn, Peter. (2005), ‘Context dependence, disagreement, and predicates of personal taste’. Linguistics and Philosophy 28:643–86. Lawler, John. (1972), A Problem in Participatory Democracy. Indiana


Adler, Allison. (2006), Syntax and Discourse in the Acquisition of Adjunct Control. Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA. Anand, Pranav. (2006), De De Se. Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA. Anand, Pranav & Andrew Nevins. (2004), ‘Shifty operators in changing contexts: indexicals in Zazaki and Slave’. In R. Young (ed.), Proceedings of Semantics and Linguistic Theory 14. CLC Publications. Ithaca, NY. 20–37. Bresnan, Joan. (1982), ‘Control and complementation’. Linguistic Inquiry 13:343–434. Castan˜eda, Hector-Neri. (1966), ‘‘He’: a study in the logic of self-consciousness’. Ratio 8:130–57. Castan˜eda, Hector-Neri. (1968), ‘On the logic of attributions of self-knowledge to others. Journal of Philosophy 54: 439–56. Chierchia, Gennaro. (1989), ‘Anaphora and attitudes De Se’. In R. Bartsch, J. van Benthem and P. van Emde Boas (eds.), Language in Context. Foris. Dordrecht. 1–31. Clements, George. (1975), ‘The logophoric pronoun in Ewe: its role in discourse’. Journal of West African Languages 10:141–77. Comrie, Bernard. (1984), ‘Subject and object control: syntax, semantics, and pragmatics’. In Proceedings of the Tenth Annual Meeting of the Berkeley Linguistics Society. BLS. Berkeley, CA. 450–64.

436 Control in Centred Worlds Massachusetts Institute of Technology, Cambridge, MA. Schlenker, Philippe. (2003), ‘A plea for monsters’. Linguistics and Philosophy 26:29–120. Stephenson, Tamina. (2007), ‘Judge dependence, epistemic modals, and predicates of personal taste’. Linguistics and Philosophy 30:487–525. Stojanovic, Isidora. (2007), ‘Talking about taste: disagreement, implicit arguments, and relative truth’. Linguistics and Philosophy 30:691–706. von Fintel, Kai & Anthony S. Gillies. (2008), ‘CIA leaks’. Philosophical Review 117:77–98. von Fintel, Kai & Irene Heim. (2009), Lecture Notes on Intensional Semantics. Spring 2009 edition. Massachusetts Institute of Technology, Cambridge, MA (http://tinyurl.com/intensional). Williams, Edwin. (1992), ‘Adjunct control’. In R. Larson, S. Iatridou, U. Lahiri and J. Higginbotham (eds.), Control and Grammar, Studies in Linguistics and Philosophy, vol. 48. Kluwer. Dordrecht. 297–322. First version received: 30.04.2008 Second version received: 23.07.2009 Accepted: 30.03.2010


University Linguistics Club. Bloomington, IN. Lewis, David. (1979), ‘Attitudes De Dicto and De Se’. Philosophical Review 88:513–43. Martin, Roger. (1996), A Minimalist Theory of PRO and Control. Ph.D. thesis, University of Connecticut, Storrs, CT. Morgan, Jerry. (1970), ‘On the criterion of identity for noun phrase deletion’. In Papers from the Sixth Regional Meeting of the Chicago Linguistic Society. CLS. Chicago, IL. 380–389. Perry, John. (1977), ‘Frege on demonstratives’. Philosophical Review 86:474–97. Perry, John. (1979), ‘The problem of the essential indexical’. NOUˆS 13:3–21. Petter, Marga. (1998), Getting PRO under Control, LOT International Series vol. 8. Holland Academic Graphics: The Hague. Pulleyblank, Douglas. (1986), ‘Clitics in Yoruba’. In H. Borer (ed.), The Syntax of Pronominal Clitics, Syntax and Semantic. vol. 19. Academic Press. Orlando, FL. 43–64. Sag, Ivan & Carl Pollard. (1991), ‘An integrated theory of complement control’. Language 67:63–113. Schlenker, Philippe. (1999), Propositional Attitudes and Indexicality. Ph.D. thesis,

Journal of Semantics 27: 437–527 doi:10.1093/jos/ffq008 Advance Access publication July 20, 2010

Decomposing Modal Quantification ADRIAN BRASOVEANU University of California, Santa Cruz

Abstract

1 INTRODUCTION Providing a compositional interpretation procedure for sentences and discourses in which complex descriptions of dependencies between multiple interrelated objects are incrementally built has proved to be a key challenge for formal theories of natural language interpretation. Consider, for example, the following discourse, part of the text of an LSAT logic puzzle.1 (1)

[Preamble] An amusement park roller coaster includes five cars, numbered 1 through 5 from front to back. Each car accommodates up to two riders, seated side by side. Six people—Tom, Gwen, Laurie, Mark, Paul and Jack—are riding the coaster at the same time. Laurie is sharing a car. Mark is not sharing a car and . . .

The first sentence sets up the basic situation we are invited to consider, namely a roller coaster that has five cars. The sentence contains two 1

Available online at http://www.west.net/;stewart/lwsample%5Bp%5D.htm. The Author 2010. Published by Oxford University Press. All rights reserved. For Permissions, please email: [email protected].


Providing a compositional interpretation procedure for discourses in which descriptions of complex dependencies between interrelated objects are incrementally built is a key challenge for natural language semantics. This article focuses on the interactions between the entailment particle therefore, modalized conditionals and modal subordination. It shows that the dependencies between individuals and possibilities that emerge out of such interactions can receive a unified compositional account in a system couched in classical type logic that integrates and simplifies van den Berg’s dynamic plural logic and the classical Lewis–Kratzer analysis of modal quantification. The main proposal is that modal quantification is a composite notion, to be decomposed in terms of discourse reference to quantificational dependencies that is multiply constrained by the various components that make up a modal quantifier. The system captures the truthconditional and anaphoric components of modal quantification in an even-handed way and, unlike previous accounts, makes the propositional contents contributed by modal constructions available for subsequent discourse reference.

438 Decomposing Modal Quantification

(2) a. [Q1] Which of the following groups of riders could occupy the second car? (a) Laurie only. (b) . . . b. [Q2] If Gwen is riding immediately behind Laurie’s car and immediately ahead of Tom’s car, all of the following must be true except: (a) Gwen is riding in the fourth car. (b) . . . c. [Q3] Which one of the following statements cannot be true? ... d. [Q4] If Paul is riding in the second car, how many different combinations of riders are possible for the third car? These questions invite us to consider alternative scenarios featuring the previously mentioned entities. Q1 above focuses on the second car and the hypothetical scenarios featuring different people (from our set of six) that ride in that car. Q2 invites us to consider a scenario in which three of the six people ride in consecutive cars. And so on. That is, our description relating a roller coaster, its five cars and its six riders (at a particular time) is enriched now by the fact that we consider


quantificational expressions—the singular indefinite a roller coaster and the cardinal indefinite five cars, the first of which takes scope over the second. The second sentence elaborates on these objects. The quantifier each car refers back to the five cars and further constrains the information we have about them: any one of these five cars can accommodate up to two riders. Yet again, the first quantifier (the distributive universal each car) takes scope over the second one (the modified cardinal indefinite up to two riders). Against the background information provided by the first two sentences, the third sentence invites us to consider a more specific situation: six people are riding the coaster (which was introduced in the first sentence) at the same time. Ignoring the apposition that enumerates the names of the just mentioned six people, this sentence relates three sets of objects, contributed by the three nominal expressions in the sentence: six people, the anaphorically retrieved roller coaster and the six periods of time that each person rides the coaster. The non-anaphoric definite the same time has narrow scope with respect to the indefinite six people and, thereby, requires these six periods of time to be identical. The remaining sentences of the preamble provide additional information about how the six people and the five cars in our scenario are related. The preamble is then further elaborated upon by questions like (2a) through (2d) below.

Adrian Brasoveanu 439


various possibilities (i.e. hypothetical scenarios) and how these possibilities relate to the previously mentioned objects. Moreover, the propositional contents of the sentences in the preamble must also be available in subsequent discourse. We need to be able to pool them together in a modal base (to use the terminology of Kratzer 1981) relative to which the modal verb cannot in Q3 above is interpreted. Furthermore, this discourse-contributed modal base can be subsequently updated with additional contents. For example, in Q4, the content of the conditional antecedent if Paul is riding in the second car is temporarily added and we are asked to identify certain possibilities compatible with the resulting modal base. To successfully solve logic puzzles like this one, that is, to correctly answer their questions, we need to have a precise understanding of the sets of objects and the relations between them that are incrementally described by the quantifiers, modals, pronouns etc. occurring in the text of the puzzle. That is, we need to be able to associate such naturally-occurring texts with precisely specified meanings, which, in turn, can form the basis for subsequent logical reasoning. As Lev (2007: 10) observes, ‘whereas for humans the language understanding part of logic puzzles is trivial but the reasoning is difficult, for computers it is clearly the reverse’. The goal of this article is to argue that we can make good progress on the first front—that is, formally specifying precise meanings for discourses in which intricate descriptions of interrelated objects are incrementally constructed—if we generalize the classical Tarskian semantics for first-order logic in two ways. First, we will take our contexts of evaluation to be modelled by a set of assignments G instead of a single assignment g. In the Montagovian tradition, the variable assignment is an essential part of the context of evaluation, storing the referents of anaphoric pronouns, past tense and so on. Given that we want to elaborate on sets of referents and relations between them, we take our context of evaluation to consist of a set of assignments. In this way, we will be able to elaborate on the relations between the sets of values associated with variables over individuals x, y, . . . and the set of possibilities associated with variables over possible worlds w, . . . Such a set of assignments G can be represented as a matrix, exemplified in (3) below. The rows of the matrix represent variable assignments g1, g2, g3, . . . . The columns represent variables x, y, w, . . . . The objects in the cells of the matrix are values that assignments assign to variables: car1 ¼ g1(x), car2 ¼ g2(x), rider1 ¼ g1(y), rider2 ¼ g2(y), v1 ¼ g1(w), v2 ¼ g2(w) and so on.


(3)


The second generalization is going from a static semantics, where expressions are interpreted relative to a single context of evaluation G, to a dynamic semantics, where expressions are interpreted relative to a pair of contexts of evaluation ÆG, Hæ—see, for example, Discourse Representation Theory (DRT; Kamp 1981; Kamp & Reyle 1993), File Change Semantics (FCS; Heim 1982) and Dynamic Predicate Logic (DPL; Groenendijk & Stokhof 1991). The first member of the pair, that is, G, is the input context relative to which natural language expressions are interpreted. This part is exactly as in static semantics. The second member of the pair, that is, H, is the output context, which is the context that results after natural language expressions are interpreted. Interpreting natural language expressions relative to such pairs of contexts—that is, as programs that incrementally update the discourse context—enables us to incrementally build the complex descriptions of interrelated objects needed for the interpretation of logic puzzles (among other things). The present article develops a formal semantics along these lines, building on van den Berg (1996) (see also Krifka 1996; Nouwen 2003), and shows how discourses involving quantifiers, indefinites, modal verbs and pronouns can be compositionally interpreted, where composition is understood in the classical Fregean/Montagovian sense. The focus is on modal expressions and their interactions with each other and with individual-level anaphora in discourse. The main proposal is that quantifiers over individuals and possible worlds should be decomposed into smaller atomic components that manipulate


1.1 Relating variables/discourse referents and variable assignments We can think of variables, also known as (a.k.a.) discourse referents (drefs), and variable assignments in two ways. Classical static and dynamic semantics takes variables to be basic entities and variable assignments to be composite objects, namely functions from variables to appropriate values. Taking variables to be the basic building blocks is pretheoretically appealing: as Karttunen (1976) and Webber (1978) first argued, natural language interpretation involves an irreducible notion of discourse-level reference and the referents that are introduced, constrained and related to each other in discourse are distinct from the actual referents. However, we want to make our discourse interpretation procedure compositional at the sub-clausal level—and we can preserve the Montagovian solution to the problem of compositionality if we change our perspective on the relationship between variables and assignments and take assignments to be the basic building blocks and variables to be the composite functional objects. The idea is to think of variables as projection functions over assignments (following Landman 1986): instead of a variable assignment g taking the variables x, y, w and so on as arguments and assigning them an individual or a possible world as values, we ‘type-lift’ variables and think of them as projection functions that take assignments/sequences of objects as arguments and return individuals or possible worlds as values.2 To reflect this change in perspective, we will use u1, u2, u, u#, . . . to denote ‘type-lifted’ variables/drefs for individuals and p1, p2, p, p#, . . . to denote ‘type-lifted’ variables/drefs for possible worlds. Also, we will 2 For more discussion of these issues, see Groenendijk and Stokhof (1990), Chierchia (1995), Muskens (1996), Sternefeld (2001), Szabolcsi (2003) and Brasoveanu (2008) among others.


contexts of evaluation in simple ways—and which together conspire to associate quantifiers, modal verbs, conditionals and so on with their intuitively correct truth conditions and anaphoric potential. Thus, the intra- and cross-sentential interactions between quantification and anaphora in the modal and individual domains receive a unified compositional account in a system couched in classical type logic that integrates and simplifies van den Berg’s Dynamic Plural Logic and the classical Lewis–Kratzer analysis of modal quantification. The system captures the truth-conditional and anaphoric components of modal quantification in an even-handed way and, unlike previous accounts, makes the propositional contents contributed by modal constructions available for subsequent discourse reference.


(4)

A dref stores a set of values relative to a set of assignments I—or, as we will call it following the dynamic semantics tradition, relative to a plural info state I. These sets of values are represented in the columns of


use i, j, i1, i2, i#, i$, . . . to denote variable assignments. The value of a dref u1 at an assignment i is obtained by applying the function denoted by the dref to the atomic entity denoted by the assignment: u1(i)—or u1i for short. A suitable set of axioms ensures that the atomic entities i, j and so on behave as variable assignments; see Muskens (1996) and Brasoveanu (2008) among others for more discussion. Viewed in this way, that is, as functions from variable assignments to individuals, variables become parallel to Montagovian individual concepts—and open the way for defining a compositional dynamic system in the tradition of Montague semantics. For example, the individual u1i is the individual that the dref u1 denotes relative to the assignment i and the possible world p1i is the world that the dref p denotes relative to i, much like the individual concept fchair denoted by the definite description the chair of the linguistics department associates different individuals fchair(t), fchair(t#), . . . with different times of evaluation t, t#, . . .. The values, that is, the objects in the cells of a matrix, remain the same, only this time they are the actual referents that drefs have relative to different variable assignments: car1 ¼ u1i1, car2 ¼ u1i2, rider1 ¼ u2i1, rider2 ¼ u2i2, v1 ¼ p1i1, v2 ¼ p1i2 and so on. This is shown in (4) below, which is identical to (3) above except for the notational changes we just introduced.


1.2 Quantificational and modal subordination Quantifiers like every convention in (5a/6a) below (from Karttunen 1976) are typical examples of expressions that introduce—and elaborate on previously introduced—dependencies. In all examples, subscripts indicate the anaphors and superscripts their antecedents, following the notational convention in Barwise (1987). (5)

a. b. (6) a. b. c.

Harvey courts au woman at every convention. Sheu is very pretty. Harvey courts au woman at every convention. Sheu always comes to the banquet with him. [Theu woman is usually also very pretty.]

Consider, for example, the initial sentence (5a/6a) in the two discourses above. This sentence is ambiguous between two quantifier


matrices like (4) above. For example, the set of individuals u1[I ] :¼ {u1i : i 2 I} is the u1 column of matrix I above and the set of possible worlds (i.e. the proposition) p1[I ] :¼ {p1i : i 2 I} is the p1 column. Thus, columns associated with drefs for possible worlds encode propositional contents, that is, classical truth conditions—and the rows encode anaphoric information about values and about dependencies between values that determine these truth conditions. Under this view, natural language sentences and discourses denote programs incrementally updating such plural info states. The semantic values of sentences and discourses are, therefore, binary relations between an input plural info state I—the info state that is updated—and an output plural info state J—the info state that is the result of the update. Quantification over individuals and possible worlds is defined in terms of matrices instead of single assignments and the semantics of the non-quantificational part (lexical items like car, ride etc.) consists of rules for how to fill out a matrix. This article is dedicated to the detailed analysis of several discourses involving quantifiers, modals and anaphora that exemplify the ways in which these expressions interact to incrementally build complex descriptions of relations between sets of objects. These (mostly constructed) discourses will perforce be shorter and sketchier than the naturally occurring logic puzzle texts. This will enable us to focus exclusively on the analysis of modals, quantifiers and pronouns. The remainder of this section introduces these discourses and briefly discusses them.


(7) a. Harvey courts au woman at every convention. b. Theyu are very pretty. We can see that it is indeed quantifier scopings that are disambiguated if we replace the indefinite au woman in (5a) with exactly oneu woman. This yields two truth-conditionally independent scopings: (i) exactly oneu woman >> every convention, which is true in a situation in which Harvey courts more than one woman per convention as long as there is exactly one that he never fails to court, and (ii) every convention >> exactly oneu woman, where Harvey courts exactly one woman per convention, but the woman can be different from convention to convention. Discourse (6) raises the following questions. First, why is it that adding an adverb of quantification, that is, always/usually, preserves both readings of sentence (6a) and makes them available for the discourse as whole? Moreover, on the newly available reading of sentence (6a), that is, the every convention >> au woman scoping, how can we capture the intuition that the singular pronoun sheu and the adverb always in sentence (6b) elaborate on the quantificational dependency between conventions and women introduced in sentence (6a), that is, how can we capture the intuition that we seem to have simultaneous anaphora to the two quantifier domains and the quantificational dependency between them? Thus, quantifiers are not the only kind of expressions that can introduce and elaborate on dependencies. Pronouns, for example, sheu in (5b/6b), and indefinites, for example, au woman in (5a/6a), can also do this and interact with the dependencies introduced by quantificational expressions.


scopings: it ‘can mean that, at every convention, there is some woman that Harvey courts or that there is some woman that Harvey courts at every convention. [. . .] Harvey always courts the same [woman] [. . .] [or] it may be a different [woman] each time’ (Karttunen 1976: 377). The contrast between (5b) and (6b) is that the former allows only for the ‘same woman’ reading of sentence (5a/6a), while the latter is also compatible with the ‘possibly different women’ reading. Discourse (5) raises the following question: how can we capture the fact that a singular pronoun in sentence (5b) can interact with and disambiguate quantifier scopings in sentence (5a)? The fact that number morphology on the pronoun sheu is crucial is shown by the discourse in (7) below, where the (preferred) relative scoping of every convention and au woman is the opposite of the one in discourse (5).


The kind of interaction between quantifiers, indefinites and morphologically singular anaphora exemplified in discourses (5) and (6) above has become known under the label of quantificational subordination (see Heim 1990: 139(2)). Quantificational subordination phenomena suggest that the notion of generalized quantification involved in natural language interpretation should in fact be decomposed into at least two components:

Decomposing quantification along these lines enables us to account for the contrast between discourses (5) and (6) while preserving the Montagovian solution to the compositionality problem. The basic idea is that plural info states enable us to store both quantifier domains (in the columns of the matrix) and quantificational dependencies (in the rows of the matrix), pass them across sentential boundaries and further elaborate on them—for example, by letting a singular pronoun like she constrain the cardinality of a previously introduced quantifier domain. This account of quantificational subordination generalizes to modal subordination. The resulting analysis of the modal subordination discourse in (8) below (based on Roberts 1989) is point-for-point parallel to the analysis of the quantificational subordination discourse in (6) above. We are, therefore, able to capture the anaphoric and quantificational parallels between the individual and modal domains argued for in Geurts (1995/1999), Frank (1996), van Rooy (1998), Stone (1999), Bittner (2001) and Schlenker (2005) among others (building on Partee 1973, 1984). (8)

a. Au wolf might come in. b. Itu would eat Harvey first.

1.3 Entailment particles In addition, we want to be able to analyse the more complex interactions between modal and individual-level anaphora exhibited by discourses like (9) below (attributed to Thomas Aquinas). (9)

a. [A] man cannot live without joy. b. Therefore, when he is deprived of true spiritual joys, it is necessary that he become addicted to carnal pleasures.


(i) a static generalized quantifier component relating sets of individuals (as in Barwise & Cooper 1981 among many others) and (ii) one or more components operating over plural info states that regulate the dynamics of dependencies.


(10) a. If au1 man is alive, heu1 must find somethingu2 pleasurable/heu1 must have au2 pleasure. b. Therefore, if heu1 doesn’t have anyu3 spiritual pleasure, heu1 must have au4 carnal pleasure.

3 Modelling the entailment relation expressed by therefore as a truth-conditional relation, that is, as requiring inclusion between two sets of possible worlds, cannot account for the fact that the discourse p is an irrational number, therefore Fermat’s last theorem is true is not intuitively acceptable as a valid entailment and it cannot be accepted as a mathematical proof despite the fact that both sentences are necessary truths (i.e. they are true in every possible world). For expository simplicity, we will ignore hyper-intensionality throughout the article but nothing in the proposed account prevents us from replacing sets of worlds with a suitably finer-grained notion of content.


We will focus on only one of the meaning dimensions of this discourse, namely the entailment relation established by therefore between the modal premise (9a) and the modal conclusion (9b). First, we want to capture the meaning of the entailment particle therefore, which relates the content of the premise (9a) and the content of the conclusion (9b) and requires the latter to be entailed by the former. We will take the content of a sentence to be truth-conditional in nature, that is, to be the set of possible worlds in which the sentence is true, and entailment to be content inclusion, that is, (9a) entails (9b) iff for any world w, if (9a) is true in w, so is (9b).3 Second, we are interested in the meanings of (9a) and (9b). We will take meaning to be context change potential, that is, to encode both content (truth conditions) and anaphoric potential. Thus, on one hand, we are interested in the contents of (9a) and (9b). They are both modal quantifications. Sentence (9a) involves a circumstantial modal base (to use the terminology introduced in Kratzer 1981) and says that, in view of the circumstances, that is, given that God created man in a particular way, as long as a man is alive, he must find something or other pleasurable. Sentence (9b) involves the same modal base and elaborates on the preceding modal quantification: in view of the circumstances, if a man is alive and has no spiritual pleasure, he must have a carnal pleasure. Importantly, we need to make the contents of (9a) and (9b) accessible in discourse so that the entailment particle therefore can cross-sententially relate them. On the other hand, we are interested in the anaphoric potential of (9a) and (9b), that is, in the anaphoric connections between them. These connections are explicitly represented in discourse (10) below, which is intuitively equivalent to (9), albeit more awkwardly phrased.


(i) the modalized conditional in (10a), that is, the premise; (ii) the modalized conditional in (10b), that is, the conclusion; and (iii) the entailment particle therefore, which relates the premise and the conclusion. Plural info states enable us to analyse discourse (9/10) as a network of interrelated anaphoric connections—and the validity of the Aquinas argument will emerge as a consequence of the intertwined individuallevel and modal anaphora. The analysis brings further support to the idea that the dynamic turn in natural language semantics should explicitly preserve and incorporate the classical static approach to meaning and reference. In fact, to analyse the Aquinas argument in (9/10), we use propositional drefs p1, p2 and so on to make classical static propositional contents available for subsequent discourse reference—that is, not merely available in the meta-language as part of the recursive definition of truth and satisfaction but available in the representation/object language, which in turn enables us to analyse the argument as relating drefs storing the propositional contents of its premise and conclusion. The article is structured as follows. Section 2 discusses the simpler case of quantification over individuals, its decomposition in a dynamic system based on plural info states and the resulting account of quantificational subordination. A good part of the material is not new, so the discussion will be fairly compressed (see Brasoveanu 2010 for more details). Working knowledge of DPL (Groenendijk & Stokhof


The indefinite au1 man in the antecedent of the conditional in (10a) introduces the dref u1, which is anaphorically retrieved by the pronoun heu1 in the antecedent of the conditional in (10b). This is an instance of modal subordination, that is, an instance of simultaneous modal and individual-level anaphora: the interpretation of the conditional in (10b) is such that we seem to covertly duplicate the antecedent of the conditional in (10a)—if a man is alive and he does not have any spiritual pleasure, he must have a carnal one. We will henceforth discuss the more transparent discourse in (10) instead of the naturally occurring one in (9). The challenge posed by (10) is that we need to compositionally assign meanings to the three discourse segments listed below—and we need to do that in such a way that we capture both the intuitively correct truth conditions of the whole discourse and the modal and individual-level anaphoric connections between the two conditionals and within each one of them.


1991) and compositional DRT (CDRT; Muskens 1996) is probably a prerequisite for section 2 and the rest of the article (for a review, see Brasoveanu 2007: ch. 2, 3 among many others). Section 3 tackles the more complex case of modal quantification and introduces the intensional dynamic system within which modal and individual-level quantification, as well as modal and quantificational subordination, receive a parallel decompositional analysis. Section 4 shows that the account of entailment particles and of the Aquinas discourse follows in this system. Finally, section 5 briefly compares this account with previous analyses of modal quantification and modal subordination.

The goal of this section is to introduce the basic dynamic system that enables us to account for quantificational subordination. By simply adding possible-world drefs in the following section, we will be able to account for modal subordination in a way that explicitly captures the anaphoric and quantificational parallels between the individual and the modal domains. The knowledgeable reader eager to get to the heart of the matter, namely modal quantification and modal subordination, should feel free to skim this section and start reading in earnest only the next one. The less eager reader will find that I have repeatedly highlighted the parts of this section that will be more or less directly imported in the next section (and these parts make up the bulk of this section). Moreover, the dynamic perspective taken on individual-level quantification in this section is, in fact, a modal perspective:4 variable assignments are conceptualized as atomic, basic entities, that is, points/states/worlds in a modal model, and operations on variable assignments are ultimately conceptualized as modal operations over such points, in the spirit of van Benthem (1997; see also Ben-Shalom 1996; Marx & Venema 1997 among others). Thus, in this section, we want to capture the fact that discourse (5) above allows for only one of the two quantifier scopings of sentence (5a/6a), while discourse (6) allows for both scopings. Informally, the analysis proceeds as follows. First, sentence (5a) updates the discourse-initial info state ;—which stores no discourse information whatsoever—by introducing the dref u1 that stores the (possibly singleton) set of women that Harvey courts at some convention or other and the dref u2 that stores all the conventions. This update can happen in two ways, depending on whether the indefinite scopes over the universal quantifier or vice versa, as shown in (11) and (12). 4

As Paul Dekker graciously reminded me (p.c.).


2 DECOMPOSING QUANTIFICATION OVER INDIVIDUALS


(11)

(12)

(13)


Irrespective of which quantifier scoping we choose for sentence (5a), the singular pronoun sheu1 in sentence (5b) constrains the set of u1-women to be a singleton set. This is easily satisfied in (11), where the indefinite takes scope over the universal quantifier. In the case of (12), however, the singleton requirement contributed by the singular number morphology on the pronoun sheu1 makes a non-trivial contribution: it requires all the cells in the u1-column to store the same entity, as shown in (13) below. Thus, irrespective of which quantifier scoping we choose for sentence (5a), the only available reading for discourse (5) as a whole is the widescope indefinite reading.


(14)

Note that we allow for models in which Harvey courts more than one woman at a convention. The singleton requirement contributed by singular number morphology on anaphoric pronouns requires uniqueness relative to the local plural info state and not globally, relative to the entire model—as Russellian (non-anaphoric) definite descriptions would. Moreover, we allow for models in which Harvey courts more than one woman at a convention and not every woman courted by Harvey comes to the banquet with him—we only require one of the women he courts at a convention to come to the banquet of that convention with him. We will further discuss this matter in due course, as well as the related issue of weak v. strong readings for singular donkey anaphora.


The fact that discourse (6)—in contrast to (5)—is also compatible with the narrow-scope indefinite reading is due to the fact that the quantificational adverb alwaysu2 in (6b) can take scope over the singular pronoun sheu1 and neutralize the effect that singular number morphology has on the cardinality of the previously introduced set of women. This neutralization is a consequence of the discourse-level distributivity operator dist that quantificational expressions contribute. The dist operator distributes over plural info states in the sense that it requires the update in its scope to be interpreted relative to singleton subsets of the input plural info state, as shown in (14) below. So, the singleton requirement contributed by the singular pronoun sheu1 is interpreted relative to single rows and is trivially satisfied.


The analysis of the modal subordination discourse in (8) above will proceed in a way that is strictly parallel to the analysis of the quantificational subordination discourse in (6)—as shown by the sequence of updates depicted in (15) below. The only difference is that the modal verbs might and would quantify over possible worlds as opposed to individuals. (15) Downloaded from jos.oxfordjournals.org by guest on December 31, 2010

2.1 The basics: plural info states, discourse representation structures, conditions and compositionality The main formal innovation relative to classical DRT/FCS/DPL is that, just as in Dynamic Plural Logic (van den Berg 1996), information states I, J and so on are modelled as sets of variable assignments i, j and so on. Plural info states enable us to encode discourse reference to both quantifier domains and quantificational dependencies and pass this anaphoric information across sentential boundaries, which is exactly what we need to account for the interpretation of discourses (5), (6) and (8).


More precisely, we need the following two ingredients. First, we need a suitable meaning for generalized determiners (over individuals) that will store two things in the output plural info state: (i) the restrictor and nuclear scope sets of individuals that are introduced by the determiner and (ii) the quantificational dependencies between these sets and any other quantifiers/indefinites.


For example, we store the sets of individuals and the dependencies between them introduced by the universal every convention in (6a) and the indefinite a woman in its nuclear scope. These sets and dependencies are available for subsequent anaphoric retrieval—for example, always and she in (6b) are simultaneously anaphoric both to the two sets of conventions and women and to the dependency between these sets introduced in (6a). Second, we need a suitable meaning for singular number morphology on pronouns like she above that requires the dref anaphorically retrieved by the pronoun to store a singleton set of individuals. Plural info states are, once again, crucial: they store and pass on structured sets (i.e. sets of values plus their associated dependencies/ structure), so we can constrain their cardinality by subsequent syntactically non-local anaphoric elements. Modal verbs will be analysed as the modal counterparts of generalized determiners and verbal moods (e.g. indicative) as the modal counterparts of pronouns. To formalize these meanings for generalized determiners and singular anaphors, we work with a Dynamic Ty2 logic, that is, with the logic of change in Muskens (1996) that reformulates dynamic semantics (Kamp 1981; Heim 1982; Groenendijk & Stokhof 1991) in Gallin’s (1975) Ty2. We have three basic types: type t (truth values), type e (individuals; variables: x, y, . . .) and type s (variable assignments; variables: i, j, . . .). A suitable set of axioms ensures that the entities of type s behave as variable assignments (see Muskens 1996; Brasoveanu 2008 for more details). A dref for individuals u is a function of type se from assignments is to individuals xe (subscripts on terms indicate their type). Intuitively, the individual useis is the individual that the assignment i assigns to the dref u. Dynamic info states I, J, . . . are plural: they are sets of variable assignments, that is, terms of type st. An individual dref u stores a set of individuals relative to a plural info state I: u[I] is the image of the set of assignments I under the function u.


(16) u[I]: ¼ {useis : i 2 I} A sentence is interpreted as a discourse representation structure (DRS), which is a binary relation of type (st)((st)t) between an input state Ist and an output state Jst, as shown in (17). (17) [newdrefs j conditions] :¼ kIst.kJst. I[newdrefs] J ^ conditions J A DRS requires:

The definition of dref introduction is given in (18) below. This definition is based on the familiar notion of dref introduction i[u]j in DPL and CDRT, which relates single variable assignments i and j. Intuitively, the DPL/CDRT notion of dref introduction i[u] j—a.k.a. random (re)assignment of value to a variable u— is interpreted as follows: the output assignment j differs from the input assignment i at most with respect to the value it assigns to u (see Groenendijk & Stokhof 1991; Muskens 1996; Brasoveanu 2008 among others for more discussion and the exact definition of this notion). The binary relation i[u]j is an equivalence relation over total variable assignments. We need to generalize this binary relation i[u]j between single assignments i and j to a binary relation I[u]J between sets of assignments I and J—that is, we need to generalize i[u]j to a relation between plural info states. We do this cumulative-quantification style, as shown in (18): I[u]J requires any input assignment i 2 I to have a [u]-successor assignment j 2 J and, vice versa, any output assignment j 2 J should have a [u]-predecessor assignment i 2 I. The binary relation I[u]J is an equivalence relation over sets of total variable assignments. (18) [u] :¼ kIst.kJst."is 2 I($js 2 J(i[u] j)) ^ "js 2 J($is 2 I(i[u]j)) Multiple dref introduction is defined in terms of dynamic conjunction ‘;’, which in turn is defined as DRS composition (i.e. binary relation composition), as shown in (19) below. Note the difference between dynamic conjunction and classical static conjunction ‘^’: the former is an abbreviation, while the latter is part of the Dynamic Ty2 logic. An example is provided in (21). (19) D; D# :¼ kIst.kJst. $Hst(DIH ^ D#HJ)


(i) the input info state I to differ from the output state J at most with respect to the new drefs and (ii) all the conditions to be satisfied relative to the output state J.


(20) [u1 ; . . . ; un ] :¼ [u1 ]; . . . ; [un ] (21) [u1, u2 j WOMAN{u1}, CONVENTION{u2}, COURTED-AT{u1, u2}] : ¼ kIst.kJst. I[u1, u2] J ^ WOMAN{u1}J ^ CONVENTION{u2}J ^ COURTED-AT{u1, u2}J DRSs of the form shown in (22) are tests. An example is provided in (23). (22) [conditions] :¼ kIst.kJst. I ¼ J ^ conditionsJ (23) [COURTED-AT{u1, u2}] :¼ kIst.kJst. I ¼ J ^ COURTED-AT{u1, u2}J

(24) [u1, u2 j WOMAN{u1}, CONVENTION{u2}, COURTED-AT{u1, u2}] ¼ [u1, u2]; [WOMAN{u1}, CONVENTION{u2}, COURTED-AT{u1, u2}] Conditions denote sets of info states, that is, they are terms of type (st)t, and they are interpreted distributively relative to a plural info state. For example, COURTED-AT{u1, u2} is a dynamic condition based on the static relation between individuals COURTED-AT of type e(et) and a plural info state I is in the set denoted by this condition iff "is 2 I(COURTEDAT(u1i, u2i)), as shown in (25). (25)

u2} :¼ kIst. I 6¼ ; ^ "is 2 I(COURTED-AT(u1i, u2i)) (prelim. version)

COURTED-AT{u1,


Note that DRSs like (21) above are simply a conjunction of an update introducing the new drefs followed by a test containing all the conditions, as shown below.


(26) woman , kve. [WOMANet{v}] Later on, we will be able to intensionalize this extensional system by simply adding a basic type for possible worlds: we will build intensions by relativizing the corresponding extensions to possible-world drefs.

2.2 Indefinites and pronouns This subsection is dedicated to the analysis of the simple discourse in (27) below. The goal is to see the formal system in action and to show how indefinites, pronouns and basic patterns of cross-sentential anaphora are analysed in this system. (27) a. Au wolf came in. b. Itu ate Harveyu#. To model the fact that the discourse-initial info state does not contain any information, we introduce the dummy individual w. This individual is the universal falsifier, that is, any lexical relation that has w as one of its arguments, for example, WOLF(w) or EAT(w, a1), is false.5 The dummy assignment iw assigns the dummy individual w to every We ensure that any lexical relation R of arity n—that is, of type ent, defined as in Muskens (1996: 157–58): e0t :¼ t and em+1t :¼ e(emt)—yields falsity whenever w is one of its arguments by letting R (DeM\{w})n. 5


Given the underlying type logic, Montague-style (Montague 1974) compositionality at sub-clausal level follows in the usual way. More precisely, the compositional aspect of interpretation in an extensional Fregean/Montagovian framework is largely determined by the types for the (extensions of the) saturated expressions, that is, names and sentences. Let us abbreviate them as e and t. An extensional static logic, for example, identifies e with e and t with t. The translation of the English noun woman is of type et, that is, et: woman , kxe. WOMANet(x). The determiner every is of type (et)((et)t), that is, (et)((et)t): every , kXet : kXet0 : 8xe (X(x) ! X 0 (x)): For our dynamic system based on plural info states, we only need to change the abbreviations for e and t. We let t abbreviate (st)((st)t), that is, a sentence is interpreted as a DRS, and we let e abbreviate se, that is, a name is interpreted as a dref. The denotation of the noun woman is still of type et, as shown in (26) below. Moreover, the determiner every is still of type (et)((et)t)—and its dynamic interpretation will be discussed later in this section.


dref. The discourse-initial info state that contains no anaphoric information is the plural info state containing only the dummy assignment Iw ¼ {iw}. (28)

(29) Iu6¼w :¼ {is 2 I : ui 6¼ w} (30) WOLF{u} :¼ kIst. Iu6¼w 6¼ ; ^ "is 2 Iu6¼w (WOLF(ui)) (31) Iu6¼w,u#6¼w :¼ {is 2 I : ui 6¼ w ^ u#i 6¼ w} (32) EAT{u, u#} :¼ kIst. Iu6¼w,u#6¼w 6¼ ; ^ "is 2 Iu6¼w,u#6¼w(EAT(ui, u#i)) (33) Iu1 6¼w;...;un 6¼w :¼ fis 2 I : u1 i 6¼ w ^ . . . ^ un i 6¼ wg (34) Rfu1 ; . . . ; un g :¼ kIst : Iu1 6¼w;...;un 6¼w 6¼ ; ^ 8is 2 Iu1 6¼w;...;un 6¼w (R(u1 i; . . . ; un i)) The translation of any sentence or discourse, hence also the translation of (27) above, will be a DRS D. This DRS is true relative to an input info state I, in particular, the dummy info state Iw ¼ {iw}, iff there is an output state J such that D relates I and J. In other words, a DRS D is true relative to I iff there is at least one way to successfully update I with D. (35) A DRS D of type t is true with respect to an input info state Ist iff $Jst(DIJ). We capture cross-sentential anaphora between the indefinite au wolf and the pronoun itu in (27) in very much the same way as classical


The dummy info state Iw enables us to capture the fact that using pronouns out of the blue is infelicitous. Classical DRT/FCS captures this by using partial—instead of total—variable assignments. The dummy individual enables us to keep the underlying logic as simple/ classical as possible: we work with total, not partial, assignments and we work with a total two-valued logic—in contrast to the partial logic in van den Berg (1996). Given the introduction of the universal falsifier w, we need to interpret lexical relations (i.e. atomic conditions) distributively relative to the non-dummy substate of the input plural info state I, as shown below.


(36) (37) (38) (39) (40) (41)

au , kPet.kP#et. [u j sing(u)]; P(u); P#(u) itu , kPet. [sing(u)]; P(u) uI :¼ {ui : is 2 Iu6¼w} sing(u) :¼ kIst. juIj ¼ 1 theyu , kPet. [u 6¼ ;]; P(u) u 6¼ ; :¼ kIst. uI 6¼ ;

The proper name Harveyu# introduces a new dref u# and constrains it to pick out the individual denoted by the non-logical constant HARVEY (of type e) relative to any assignment i 2 I. (42) Harveyu# , kPet. [u# j u# ¼ HARVEY]; P(u#) (43) u# ¼ HARVEY :¼ kIst. u#I ¼ {HARVEY} The two sentences of discourse (27) are compositionally translated as shown in (44) and (45) below. (44) a. b. c. d. (45) a. b. 6

wolf , kve. [WOLF{v}] au wolf , kP#et. [u j sing(u)]; [WOLF{u}]; P#(u) came in , kve. [COME-IN{v}] au wolf came in , [u j sing(u)]; [WOLF{u}]; [COME-IN{u}] ate , kQ(et)t.kve. Q(kv#e. [EAT{v, v#}]) ate Harveyu#, kve. [u# j u# ¼ HARVEY]; [EAT{v, u#}]

See Nouwen (2007) for a similar proposal in a closely related framework.


DRT/FCS/DPL: the indefinite introduces a dref u that the pronoun later retrieves. The translations for the singular indefinite and the singular pronoun are provided in (36) and (37) below. The translations have the expected Montagovian form: the indefinite takes as arguments a restrictor property P and a nuclear scope property P#, introduces a new dref u and predicates the two properties of this dref; the pronoun is the Montagovian type-lift of the anaphorically retrieved dref u. In both translations, singular number morphology contributes a condition sing(u) that requires uniqueness of the non-dummy value of the dref u relative to the plural info state I; juIj denotes the cardinality of the set uI.6 In contrast, plural pronouns do not require uniqueness, as shown in (40). Recall that drefs are assigned only atomic (i.e. semantically singular) entities as values; for a version of Dynamic Ty2 that countenances non-atomic individuals in addition to plural info states (i.e. both domain-level and discourse-level plurality), see Brasoveanu (2008).


c. itu ate Harveyu# , [sing(u)]; [u# j u# ¼

HARVEY]; [EAT{u,

u#}]

Conjoining the translations of the two sentences gives us the translation for the entire discourse in (27), provided in (46) below. The DRSs in (47) and (48) are equivalent ways of representing this discourse: (47) has the same format as classical DRT boxes (represented in a linearized way), while (48) is completely explicit about each atomic update contributed by discourse (27).

While the DRT-style representation in (47) is the most readable, the representation in (48) provides insight into the internal workings of the update procedure. This is graphically depicted in (49) below. We start with the dummy info state Iw that contains no anaphoric information. Then, we introduce a new dref [u]. The result is many plural info states, some containing only one row, some containing two rows and so on and assigning all possible individuals or combinations thereof to the newly introduced dref u. That is, we now have a graph with many paths. This is the result of the fact that our DRSs are relations between info states and not functions, that is, they are nondeterministic updates. The test [sing(u)] eliminates some of the paths in the graph, namely all those paths that end in an info state assigning more than one entity to the dref u. The test [WOLF{u}] eliminates further paths in the graph—namely all those that end in an info state where u is not assigned a wolf. The test [COME-IN{u}] eliminates all the wolves that did not come in. The test [sing(u)] contributed by the pronoun is vacuously satisfied, so it does not eliminate any more paths in the graph. We now introduce another dref u# that extends the graph in many different ways. The subsequent test [u# ¼ HARVEY] prunes down the graph by eliminating all info states that do not assign the individual harvey to u#. Finally, the test [EAT{u, u#}] keeps only the info states such that, for any row i in those info states, the individual ui ate the individual u#i.


(46) [u j sing(u)]; [WOLF{u}]; [COME-IN{u}]; [sing(u)]; [u# j u# ¼ HARVEY]; [EAT{u, u#}] (47) [u, u# j sing(u), WOLF{u}, COME-IN{u}, u# ¼ HARVEY, EAT{u, u#}] (48) [u]; [sing(u)]; [WOLF{u}]; [COME-IN{u}]; [sing(u)]; [u#]; [u# ¼ HARVEY]; [EAT{u, u#}]


(49) Downloaded from jos.oxfordjournals.org by guest on December 31, 2010

The picture in (49) above might seem overwhelming at first. However, except for the fact that we allow plural info states (i.e. matrices with multiple rows), this is in no way different from the way interpretation proceeds in classical first-order logic or in classical DRT/FCS. Such


graphs are implicit in their recursive definitions of truth and satisfaction. We will follow their lead and keep the graphs implicit, that is, from now on, we will depict updates by choosing a single typical path through the graph. For example, the update contributed by discourse (27) will be represented as shown in (50) below—or in abbreviated form, as shown in (51). (50)

The definition of truth in (35) above basically says that a DRS D is true if there is at least one path through the graph denoted by D. Again, this is just as in classical first-order logic or in classical DRT/ FCS, except this is implicit in their definitions of truth and satisfaction. We end this subsection with the definition of dynamic negation, provided in (52) below, which derives the intuitively correct truth conditions for examples like Linus didn’t bring an umbrella, and with the translations for the anaphoric readings of singular and plural definite articles, which are parallel to the translations for singular and plural pronouns in (37) and (40) above.7 Later on, we will analyse verbal moods as the modal counterparts of anaphoric pronouns. (52) ;D :¼ kIst : I 6¼ ; ^ 8Hst 6¼ ;(H I ! :9Kst (DHK)) 0 : [sing(u)]; P(u); P0 (u) (53) thesg:u ,kPet :kPet 0 : [u 6¼ ;]; P(u); P0 (u) (54) thepl:u ,kPet :kPet 7

Semantically distinguishing between singular and plural definite articles is supported by the fact that other languages, for example, Romance languages, have overt number morphology on definite articles.


(51)


2.3 Desiderata for dynamic generalized quantification A definition of dynamic generalized quantification, in both the individual and the modal domain, should satisfy several desiderata. We will discuss these desiderata here with respect to quantification over individuals, but the same considerations apply to quantification over possible worlds. First, we want our notion of dynamic quantification to account for donkey anaphora, exemplified in (55) below.

Second, we want to avoid the proportion problem that unselective quantification (‘unselective’ in the sense of Lewis 1975) runs into. The sentence in (56) below exemplifies this problem. Intuitively, (56) is false in a situation in which there are 10 farmers, 9 have a single donkey each and they do not beat it, while the 10th has 20 donkeys and he is busy beating them all. The unselective interpretation of the mostquantification, however, incorrectly predicts that the sentence is true in such a situation because more than half of the Æfarmer, donkeyæ -pairs (20 out of 29) are such that the farmer beats the donkey. Thus, dynamic generalized determiners should relate sets of individuals (of type et) and not sets of assignments (of type st). (56) Mostu farmers who own au# donkey beat itu#. Third, generalized quantification should be compatible with both strong and weak donkey readings. That is, we want to allow for the different interpretations associated with the donkey anaphora in (57) (Heim 1990) and (58) (Pelletier & Schubert 1989) below. The interpretation of (57) is as follows: most slave owners were such that, for every (strong reading) slave they owned, they also owned her/his offspring. The interpretation of (58) is as follows: every dime-owner will put some (weak reading) dime of her/his in the meter. (57) Mostu people that owned au# slave also owned hisu# offspring. (58) Everyu person who has au# dime will put itu# in the meter. Finally, as the discourses in (5) and (6) above indicate, dynamic quantification should be defined in such a way that we make available the restrictor and nuclear scope sets of individuals for subsequent anaphoric take-up. In addition, the quantificational dependencies


(55) Everyu farmer who owns au# donkey beats itu#.


between different quantifiers/indefinites should also be anaphorically available. More precisely, generalized quantification supports anaphora to two sets: (i) the maximal set of individuals satisfying the restrictor update and (ii) the maximal set of individuals satisfying both the restrictor update and the nuclear scope update8 (i.e we build conservativity into our representation of generalized quantification; this is needed for, e.g. donkey anaphora).

(59) a. Mostu# students left the party after 5 a.m. b. Theyu# went directly to the beach. The discourses in (60) and (61) exemplify anaphora to restrictor sets. Using downward monotonic quantifiers like nou student and very fewu people is important for this. Consider (60) first: any successful update with a nou-quantification ensures that the nuclear scope set is empty (given that we build conservativity into our representation of generalized quantification)—and anaphora to it is therefore infelicitous. The only possible anaphora in (60) is restrictor-set anaphora. (60) a. Nou student left the party later than 10 p.m. b. Theyu had classes early in the morning. Restrictor set anaphora is the only possible one in (61) too. This is because nuclear scope anaphora would yield a contradictory interpretation for (61b), namely: most of the people with a rich uncle that inherit his fortune do not inherit his fortune. (61) a. Very fewu people with a rich uncle inherit his fortune. b. Most of themu don’t. Given these four desiderata, we translate dynamic generalized determiners as shown in (62). 8 We ignore anaphora to complement sets, that is, sets obtained by taking the complement of the nuclear scope relative to the restrictor, for example, Few students were paying attention in class. They were tired.; see Nouwen (2003) for arguments that complement-set anaphora is a pragmatic, not semantic, phenomenon (I am indebted to an anonymous reviewer for bringing this point to my attention).


The discourse in (59) below exemplifies anaphora to nuclear scope sets. Sentence (59b) is interpreted as follows: the people that went to the beach are the students that left the party after 5 a.m.—which, in addition, formed a majority of the students at the party.


(62) detu,u#vu , kPet.kP#et. maxu(Æuæ(P(u))); maxu#vu(Æu#æ(P#(u#))); [DET{u, u#}]

(i) two operators over plural info states, namely a maximization operator maxu(. . .) and a distributivity operator Æuæ(. . .) and (ii) a notion of structured inclusion u#vu that requires the subset to preserve the quantificational dependencies, that is, the structure, associated with the individuals in the superset. The following subsections introduce dynamic quantification over individuals and the resulting analysis of quantificational subordination. The reader should take heart in the fact that, once this work is done, the analysis of modal quantification and modal subordination will follow by


This translation is in the spirit of van den Berg (1996) (cf. van den Berg 1996: 149(4.1)). Let us examine it in detail. First, a determiner detu,u#vu introduces two drefs u and u#: u is the restrictor dref and u# is the nuclear scope dref. Given the conservativity of natural language determiners, the nuclear scope dref is a subset of the restrictor dref: u#vu. Second, determiners relate a restrictor dynamic property Pet and a nuclear scope dynamic property P#et. When these dynamic properties are applied to their respective drefs, we obtain a restrictor DRS P(u) of type t and a nuclear scope DRS P#(u#), also of type t. The drefs u and u# and the properties P and P# are the basic building blocks of the three updates in (62). The first update, namely maxu(Æuæ(P(u))), has three components: the operator maxu(. . .), the distributivity operator Æuæ(. . .) and the DRS P(u). This update ensures that u stores the maximal set of individuals, that is, maxu(. . .), such that, when we take each u-individual separately, that is, Æuæ(. . .), this individual satisfies the restrictor dynamic property, that is, P(u). Once again, recall that the values assigned to the dref u are atomic, that is, semantically singular, but plural info states store collections of such singular values. The second update, namely maxu#vu(Æu#æ(P#(u#))), ensures that the nuclear scope set u# is obtained in much the same way as the restrictor set u, except for the requirement that u# is the maximal structured subset of u, that is, maxu#vu(. . .). Finally, the third update, namely [DET{u, u#}], is a test: we test that the restrictor set u and the nuclear scope set u# stand in the relation denoted by the corresponding static determiner DET. To formally spell out the meaning for generalized determiners in (62) above, we need:


transferring all the developed notions from the domain of individuals to the domain of possible worlds.

2.4 Structured inclusion, maximization and distributivity

(63) a. Harvey courts au2 woman at everyu1 convention. b. Sheu2 usuallyu3u1 comes to the banquet with him. (64) Two possible ways to introduce the subset dref u3:

(65) u3u1: ¼ kIst. u3[I]u1[I] (66) u36u1: ¼ kIst. "is 2 I(u3i ¼ u1i _ u3i ¼ w) Intuitively, the adverb usually in (63b) is anaphoric to the set of conventions introduced in (63a)—and sentence (63b) is interpreted as follows: at most conventions, the woman courted by Harvey at that convention comes to the banquet with him. Thus, we want to select a set that consists of a majority of conventions, that is, we want to select a most-subset of the u1-column in matrix (64) above. At the same time, we want to preserve the dependencies associated with the entities in this subset—which dependencies are encoded in the rows of the matrix. The simplest notion of inclusion is the one defined in (65) above and symbolized by (the customary symbol). This is a notion of valueinclusion because it is concerned exclusively with sets of values. That is, it is concerned with the information stored in the columns of a matrix and completely disregards structure, i.e. the information stored in the rows of a matrix.


We start with the notion of structured inclusion. Consider, for example, the discourse in (63) below, where u1 stores the set of conventions and u2 stores the set of corresponding women. Assume that, in (63a), everyu1 convention takes scope over au2 woman and the correlation between u1-conventions and u2-women is the one represented in (64) below. That is, the correlation/dependency between conventions and women is the binary relation {Æa1, b1æ, Æa2, b2æ, Æa3, b3æ, Æa4, b4æ}.


(67) Mostu1,u3u1 farmers who own au2 donkey beat itu2. So, to capture the intra-sentential and cross-sentential interaction between anaphora and quantification, we need the notion of structured inclusion defined in (66) above, whereby we go from a superset to a subset by discarding rows in the matrix. The subset is then guaranteed to contain only the dependencies associated with the superset (but not necessarily all dependencies—see below). To formalize this, we follow van den Berg (1996) and use the dummy individual w as a tag for the cells in the matrix that should be discarded in order to obtain a structured subset u3 of a superset u1—as shown by the rightmost u3 column in (64) above. However, unlike van den Berg (1996), we will not take the dummy individual w to require making the underlying logic partial. The notion of structured inclusion 6 in (66) above ensures that the subset inherits only the superset structure—but we also need it to inherit all the superset structure. We achieve this by means of the second conjunct in definition (68) below. This conjunct is needed to account for the strong donkey sentence in (57) above (among other things), which is interpreted as talking about every slave owned by any given person. That is, the nuclear scope set in (57), which is a most-subset of the restrictor set, needs to inherit all the superset


For example, the leftmost u3 column in matrix (64) above satisfies the condition u3u1: the dref u3 is a value-subset of the dref u1 because u3[I] ¼ {a1, a2, a3} u1[I] ¼ {a1, a2, a3, a4}. We correctly store in u3 most u1-conventions (three out of four), but we fail to preserve the dependency between u1-conventions and u2-women established in (63a), that is, the relation {Æa1, b1æ, Æa2, b2æ, Æa3, b3æ, Æa4, b4æ}: as far as u3 and u2 are concerned, a1 is still correlated with b1, but it is now also correlated with b3, a2 is now correlated with b4 (not b2) and a3 with b2 (not b3). We therefore fail to derive the intuitively correct interpretation for sentence (63b)—and for discourse (63) as a whole. We obtain similarly incorrect results for donkey sentences like the one in (67) below. The restrictor of the quantification introduces a dependency between all the donkey-owning u1-farmers and the u2donkeys that they own. The nuclear scope set u3 needs to contain most u1-farmers, but in such a way that the correlated u2-donkeys remain the same. That is, the nuclear scope set contains a most-subset of donkeyowning farmers that beat their respective donkey(s). The notion of valueonly inclusion in (65) is, yet again, inadequate.


structure: each slave owner in the nuclear scope set needs to be associated with every slave that s/he owned. (68) u0 v u :¼ kIst : (u0 6u)I ^ 8is 2 I(ui 2 u0 I ! ui ¼ u0 i)

(69) maxu(D): ¼ kIst.kJst. ([u]; D)IJ ^ :$Kst(([u]; D)IK ^ Ju6¼w=Ku6¼w) The definition of maximization is given in terms of local maxima, that is, :$Kst(([u]; D)IK ^ Ju6¼w=Ku6¼w), and not in terms of a global supremum, that is, 8Kst (([u]; D)IK ! Ku6¼w Ju6¼w ); to allow for the fact that the DRS D could contain a singular indefinite—that is, a nondeterministic update of the form [u# j sing(u#)]—that could in principle be satisfied by multiple single individuals. Maximal structured subsets can now be defined as shown in (70). (70) maxu#vu(D) :¼ maxu#([u#vu]; D) The definition of distributivity in (72) below—depicted in (73)—states that updating an info state I with a DRS D distributively over a dref u means: (i) generating the u-partition of I, namely {Iu¼x : x 2 uI} [a partition cell Iu¼x is defined as shown in (71) below]; (ii) updating each cell Iu¼x in the partition with the DRS D; and (iii) taking the union of the resulting output info states. (71) Iu¼x :¼ {i 2 I : ui ¼ x}


We turn now to the maximization and distributivity operators maxu and distu, defined in the spirit of van den Berg (1996). Together, maximization and distributivity enable us to dynamize k-abstraction over both values (i.e. quantifier domains) and structure (i.e. quantificational dependencies). That is, maxu and distu enable us to extract and store the restrictor and nuclear scope structured sets needed to define dynamic generalized quantification. Consider the definition of maxu in (69) below first. The first conjunct ([u]; D)IJ introduces u as a new dref and makes sure that each u-individual stored in the output state J satisfies D. So, we ensure that u stores only individuals that satisfy D. The second conjunct enforces maximality: there is no output state K that stores u-individuals satisfying D and that is a strict superset of J. So, we ensure that u stores all individuals that satisfy D relative to J.


(72) distu(D) :¼ kIst.kJst. uI ¼ uJ ^ "xe 2 uI(DIu¼x Ju¼x) (73) Updating the info state I with the DRS D distributively over the dref u:

2.5 Dynamic generalized quantifiers The translation for generalized determiners is provided in (77) below. The justification for the fact that we use the distributivity operators Æuæ ( . . . ) and Æu0 æ ( . . . ) in the translation of generalized determiners has to do with the existential commitment customarily associated with new dref introduction. (74) u(D) :¼ kIst.kJst. Iu¼w ¼ Ju¼w ^ uI 6¼ ; ^ distu(D)Iu6¼w Ju6¼w (75) Æuæ (D) :¼ kIst :kJst : Iu¼w ¼ Ju¼w ^ (uI ¼ ; ! I ¼ J) ^ (uI 6¼ ; ! distu (D)Iu6¼w Ju6¼w ) (76) DET{u, u#} :¼ kIst. DET(uI, u#I), where DET is a static determiner. (77) det u,u#vu , kPet.kP#et. maxu(Æuæ(P(u))); maxu#vu(Æu#æ(P#(u#))); [DET{u, u#}] 9 Nouwen (2003: 87) was the first to observe that we need to add the first conjunct in (72) to the original definition of distributivity in van den Berg (1996: 145(18)).


The first conjunct in (72) is required to ensure that there is a bijection between the partition induced by the dref u over the input state I and the one induced over the output state J. Without this conjunct, we could introduce arbitrary new values for u in the output state J, that is, arbitrary new partition cells.9 The second conjunct in (72) is the one that actually defines the distributive update: the DRS D relates every partition cell in the input state I to the corresponding partition cell in the output state J, as shown in (73) above.


The existential commitment associated with new dref introduction is built into: (i)

the definition of lexical relations–see the conjunct Iu1 6¼w;...;un 6¼w 6¼ ; in (34) above and (ii) the definition of the operator u(. . .)–see the conjunct uI 6¼ ; in (74) above.

10

Even if definition (77) allows for empty restrictor and nuclear scope sets, we still capture the fact that subsequent anaphora to such empty sets is infelicitous [e.g. anaphora to the nuclear scope sets in (60) and (61) above] because pronouns contribute non-emptiness requirements—see the sing(u) condition contributed by it in (37) above and the u 6¼ ; condition contributed by they in (40). Moreover, the fact that the second conjunct in (75) requires the identity of the input and output states I and J correctly predicts that anaphora to both empty restrictor/nuclear scope sets and indefinites in restrictor/nuclear scope DRSs associated with such empty sets is infelicitous. For example, the nuclear scope DRS of a successful nou,u#vu-quantification, that is, maxu#vuðÆu0 æ (P#(u#))), will always be a test. Hence, we correctly predict that anaphora to any indefinites in the nuclear scope of a no-quantification is infelicitous, for example, Harvey courts au$ woman at nou,u#vu convention. #Sheu$ is very pretty/#Theyu$ are very pretty (on the narrow-scope indefinite reading).


We need these non-emptiness requirements because the pair of empty info states Æ;st, ;stæ is, on one hand, in the denotation of [u] for any dref u [see definition (18) above] and, on the other hand, in the denotation of distu(D) for any dref u and DRS D [see definition (72) above]. Crucially, however, there is no existential commitment in the translation of detu,u#vu, which employs the distributivity operators Æuæ(. . .) and Æu#æ(. . .) defined in (75) above. The fact that we use these distributivity operators enables us to capture the meaning of both upward and downward monotonic quantifiers by means of the same translation. The problem posed by downward monotonic quantifiers is that their nuclear scope set can or has to be empty. For example, after a successful update with a nou,u#vu-quantification, the nuclear scope set u# is necessarily empty, that is, the dref u# always stores only the dummy individual w relative to the output info state. This, in turn, means that no lexical relation in the nuclear scope DRS that has u# as an argument can be satisfied. The second conjunct uI ¼ ; ! I ¼ J in (75) resolves the conflict between the emptiness requirement enforced by a no-quantification and the non-emptiness requirement enforced by lexical relations.10 Another important feature of the translation in (77) above is the fact that it uses maximization operators to extract both the restrictor and the nuclear scope set of individuals. These max operators (and the nuclear scope one in particular) are essential for the derivation of


(78) thesg:u , kPet.kP#et . maxu(P(u)); [sing(u)]; P#(u) 0 . maxu(u(P(u))); [u 6¼ ;]; u(P#(u)) (79) thepl:u , kPet.kPet

2.6 Quantificational subordination We can now analyse discourses (5) and (6). We start with the two quantifier scopings that are possible for the discourse-initial sentence (5a/6a). For simplicity, we assume that the two scopings are due to the two different lexical entries for the ditransitive verb court-at provided in (80) and (81) below: court-at1 assigns the indefinite a woman wide scope relative to every convention, while court-at2 assigns it narrow scope. This quantifier scoping mechanism is just a matter of presentational convenience; any other one (quantifier raising, Cooper storage, typeshifting etc.) would be equally suitable. The basic syntactic structure of sentence (5a/6a) is given in (82). (80) court-at1 , kQ#(et)t.kQ$(et)t.kve. Q#(kv#e. Q$(kv$e. [COURT-AT{v, v#, v$}]))

11 Recall the Evans examples Few senators admire Kennedy and they are very junior and Harry bought some sheep. Bill vaccinated them (see Evans 1977, 1980) —in addition to (59), (60) and (61) above.


the correct truth conditions associated generalized quantifiers—and downward monotonic quantifiers in particular. The max-based definition of generalized quantification makes an independent—and correct—prediction: it predicts that anaphora to restrictor/nuclear scope sets is always anaphora to maximal sets, that is, E-type anaphora.11 Thus, the maximality of anaphora to quantifier sets is an automatic consequence of the fact that we independently need max-operators to formulate truth-conditionally correct dynamic meanings for quantifiers. This is one of the major results in van den Berg (1996), preserved here. We end this subsection with the observation that maximization and distributivity enable us to give appropriate translations for nonanaphoric definites. Russellian definites are translated by combining the maxu operator and the sing(u) condition, as shown in (78) below. This is needed to interpret the DP the banquet in (6b) above. Link-style plural definites (under their distributive reading; see Link 1983) are translated as shown in (79).


(81) court-at2 , kQ#(et)t.kQ$(et)t.kve. Q$(kv$e. Q#(kv#e. [COURT-AT{v, v#, v$}])) (82) Harveyu1 [[court-at1=2 [au4 woman]][everyu2 ;u3 v u2 convention]] We will assume that the restrictor set of the every-quantification is nonempty, so we can safely replace the distributivity operators Æu2æ(. . .) and Æu3æ(. . .) with the simpler distributivity operators u2(. . .) and u3(. . .). The representations of the two quantifier scopings for sentence (5a/6a) are provided in (85) and (86) below (redundant distributivity operators are omitted).12

(84) everyu2 ;u3 vu2 convention, 0 : maxu2 ([conventionfu2 g]); maxu3 vu2 (u3 (P0 (u3 ))); kPet

[EVERYfu2 ; u3 g] (85) au4 woman >> everyu2 ;u3 vu2 convention, [u1 j u1 ¼ harvey]; [u4 j sing(u4 ); womanfu4 g]; maxu2 ([conventionfu2 g]); maxu3 vu2 ([court-atfu1 ; u4 ; u3 g]); [EVERYfu2 ; u3 g] (86) everyu2 ;u3 v u2 convention>>au4 woman, [u1 j u1 ¼ harvey]; maxu2 ð[conventionfu2 g]); maxu3 vu2 (u3 ([u4 j sing(u4 ); womanfu4 g; court-atfu1 ; u4 ; u3 g])); [EVERYfu2 ; u3 g]

12 I assume that the following constraint (possibly pragmatic in nature—e.g. manner/relevance based) is satisfied by every new dref introduction update: the dummy individual w is not assigned as a value for any newly introduced dref unless this is absolutely necessary, that is, required for the satisfaction of subsequent updates. For example, in (85), the dref u1 will only store harvey in the output info state (and not harvey and the dummy individual w), the dref u4 will only store a woman in the output state and u2 will only store conventions (all of them). Given the fact that u3 is a structured subset of u2, u3 is the only dref that could conceivably store the dummy individual w in (part of) the output state—but even this is not possible in (85) because of the final condition EVERY{u2, u3}.


(83) everyu2 ;u3 vu2 , 0 : maxu2 (u2 (P(u2 ))); maxu3 vu2 (u3 (P0 (u3 ))); kPet :kPet [EVERY fu2 ; u3 g]


(87)

The representation in (86) updates the discourse-initial info state Iw as follows. First, we store Harvey in u1. Then, we introduce the set of all conventions relative to the dref u2. Then, we store in u3 the set of conventions such that, when we take each convention one at a time, we can introduce one u4-woman relative to it such that Harvey courts this woman at the convention under consideration. The distributive operator u3(. . .) ensures that the u4-women are introduced relative to one u3-convention at a time and, at the end of this distributive update, they are collected together in the output info state in such a way that, for every row, the u4 woman in that row was courted at the u3 convention in that row. Importantly, the women may be different from convention to convention. Finally, we


The representation in (85) updates the discourse-initial info state Iw as follows. First, we store Harvey in u1 and one woman in u4. Then, we store the set of all conventions in u2 in a pointwise manner, that is, one convention per row in the matrix. This is tantamount to associating Harvey and the u4-woman with each and every convention in the resulting plural info state. The next update introduces u3 and stores in it the set of all conventions at which Harvey courts the u4-woman. Finally, we test that the set of u2-conventions, that is, all of them, and the set of u3-conventions, that is, the conventions where Harvey courts the u4-woman, stand in the EVERY relation, that is, we have that u2Iu3I. If this final test is satisfied, the update in (85) is true relative to the input state Iw —and this can happen iff there is a woman such that Harvey courts her at every convention, as depicted in (87) below.


test that the set of u2-conventions, that is, all of them, and the set of u3-conventions, that is, the conventions where Harvey courts the corresponding u4-woman, stand in the EVERY relation. If this final test is satisfied, the update in (86) is true relative to the input state Iw —and this can happen iff every convention is such that Harvey courts some woman or other at that convention, as depicted in (88) below. (88)


We can now see how sentence (5b)—in particular, the singular morphology on the pronoun sheu4—forces the wide-scope indefinite reading: the condition sing(u4) in (89) below effectively conflates the two scopings by requiring the set of u4-women obtained after updating with (85) or (86) to be a singleton. This requirement leaves the truth conditions derived on the basis of (85) untouched but makes the truth conditions associated with (86) strictly stronger. This is because


sing(u4) requires the set of women {woman1, woman2, woman3} stored in the final output state in (88) above to be a singleton set, that is, it requires that woman1 ¼ woman2 ¼ woman3. (89) sheu4 is very pretty , [sing(u4 ); very-prettyfu4 g]

(90) alwaysu5 v u3 ,kPet : max u5 vu3 (u5 (P(u5 ))); [EVERYfu3 ; u5 g] (91) detu#vu , kPet. maxu#vu(Æu0 æ (P(u#))); [DET{u, u#}] The definite description the banquet in (6b) is a Russellian definite description [see (78) above], which contributes existence and modellevel uniqueness (relativized to conventions: there is a unique banquet per convention13). However, for simplicity, we will assume that sentence (6b) contributes a transitive predication of the form COMEWITH-HARVEY-TO-BANQUET-OF, abbreviated as COME, that relates women and conventions and that can be translated in two different ways corresponding to the two possible relative scopes of sheu4 and alwaysu5 vu3 ; as shown in (92) and (93) below. That is, the scoping technique is the same as in (80) and (81) above. The translation in (92) gives the pronoun sheu4 wide scope relative to the adverb alwaysu5 vu3 ; while the translation in (93) gives the pronoun narrow scope relative to the adverb.

13 The existence and uniqueness are contributed by the Russellian definite article, translated as 0 follows: theu6 , kPet : kPet : maxu6 ðPðu6 ÞÞ; ½singðu6 Þ; P0 ðu6 Þ: The relational noun banquet is anaphoric to u3-conventions and is translated as: banquetu3 ,kve : ½banquet fv; u3 g (this is the set of banquets v organized at convention u3). Putting the two translations together, we obtain the following representation for our Russellian definite description: theu6 banquetu3 , kPet : maxu6 ð½banquetfu6 ; u3 gÞ; ½singðu6 Þ; P0 ðu6 Þ: The relativized uniqueness effect, i.e. the intuition that the banquet is unique per u3-convention, is due to the fact that the definite description is in the scope of the adverb alwaysu5 vu3 and, therefore, in the scope of the distributivity operator u 5(. . .) contributed by the adverb.


In contrast, sentence (6b) contains the adverb of quantification alwaysu5 vu3 ; which can take scope above or below the singular pronoun sheu4. In the former case, the u4-uniqueness requirement is weakened by being relativized to u3-conventions. As shown in (90) below, we take the meaning of alwaysu5 vu3 to be a universal quantification over an anaphorically retrieved restrictor, which is none other than the nuclear scope dref introduced by the quantifier everyu2 ;u3 vu2 convention in the preceding sentence. The general format for the interpretation of quantificational expressions that anaphorically retrieve their restrictors is provided in (91).


(92) come-to-banquet-of 1 , kQ(et)t.kQ#(et)t. Q#(kv#e. Q(kve. [COME{v#, v}])) (93) come-to-banquet-of 2, kQ(et)t.kQ#(et)t. Q(kve. Q#(kv#e. [COME{v#, v}])) (94) sheu4 [[alwaysu5 vu3 ] come-to-banquet-of 1=2 ] The two translations for sentence (6b), obtained on the basis of the syntactic structure in (94) above, are provided in (95) and (96) below (redundant distributivity operators are omitted).

[sing(u4 )]; maxu5 vu3 ([comefu4 ; u5 g]); [EVERYfu3 ; u5 g] (96) alwaysu5 v u3 >>sheu4 , maxu5 v u3 (u5 ([sing(u4 ); comefu4 ; u5 g])); [EVERYfu3 ; u5 g] Thus, there are two possible representations for sentence (6a), that is, (85) and (86), and two possible representations for sentence (6b), that is, (95) and (96). Out of the four combinations, three end up effectively requiring the indefinite au4 woman to have wide scope relative to everyu2 ;u3 v u2 convention. The fourth combination (86 + 96), provided in (97) below, encodes the ‘narrow-scope indefinite’ reading that is intuitively available for discourse (6) but not for (5). (97) [u1 j u1 ¼ harvey]; maxu2 ([conventionfu2 g]); maxu3 vu2 (u3 ([u4 j sing(u4 ); womanfu4 g; court-atfu1 ; u4 ; u3 g])); [EVERYfu2 ; u3 g]; _ maxu5 v u3 (u5 (½sing(u4 ); comefu4 ; u5 g])); [EVERYfu3 ; u5 g


(95) sheu4 >>alwaysu5 vu3 ,


(98)



2.7 Donkey anaphora Our current meanings for generalized determiners, indefinites and pronouns derive weak donkey readings. Consider again the typical weak donkey sentence in (58) above. Its PCDRT translation, which derives the intuitively correct interpretation, is provided in (99) below. (99) maxu(u([PERSON{u}]; [u# j sing(u#),

DIME{u#}, HAVE{u,

u#}]));

u$vu

max (u$([sing(u#), PUT-IN-METER{u$, u#}])); [EVERY{u, u$}] As the PCDRT system currently stands, it cannot derive the intuitively correct interpretation for strong donkey sentences like (55) above. However, in the spirit of Dekker (1993; see also Schwarzschild 1989), we can import the co-indexation mechanism in Heim (1982) and capture strong donkey readings. Moreover, we will preserve our solution to the proportion problem and the account will automatically generalize to mixed weak and strong donkey sentences of the kind discussed in Brasoveanu (2008). The main proposal is as follows: we let the indefinites that intuitively receive a strong reading behave as open formulas, very much along the lines of classical DRT and FCS. Thus, strong indefinites are exactly like ordinary weak indefinites except they do not introduce their own dref,


As depicted in (98) above, the narrow-scope indefinite reading is available because the two occurrences of the condition sing(u4) are in the scope of two distributivity operators over conventions u3 ( . . . ) and u5 ( . . . ): Note that we allow for models in which Harvey courts more than one woman at a convention and, in addition, not every woman courted by Harvey comes to the banquet with him. We only require one of the women he courts at a convention to come to the banquet of that convention with him. That is, singular indefinites—and subsequent singular anaphora to them—have a weak reading. This issue is the main focus of the next subsection. In sum, the present dynamic system—dubbed Plural CDRT (PCDRT)—enables us to formulate in classical type logic a compositional account of the intra- and cross-sentential interactions between quantifiers, anaphora and number morphology exhibited by the quantificational subordination discourses in (5) and (6) above. The dynamics of plural info states and the static meaning for generalized determiners are integrated in an even-handed way, which enables us to provide an analysis of quantificational subordination as structured anaphora to quantifier domains.


(100) Everyu,u$vu,u# farmer who owns au# donkey beats itu#. This co-indexation mechanism is just a way to represent the contextual pragmatically determined coercion of the meaning of dynamic generalized determiners that Kanazawa (1994) argues for. Taking coindexation to be the representation of this kind of coercion/quantifier domain manipulation correctly restricts the availability of strong readings to quantificational environments and predicts that the indefinite can be ‘reinterpreted’ as a definite only in this kind of configurations. The translation for multiply selective generalized determiners is given in terms of multiply selective maximization and distributivity operators. These are a straightforward generalization of the singly selective operators we have already defined, as shown below. (101) maxu,u#(D) :¼ kIst.kJst. ([u, u#]; D)IJ ^ :$Kst(([u, u#]; D)IK ^ Ju6¼w,u#6¼w=Ku6¼w,u#6¼w)14 (102) distu;u0 (D) :¼ kIst :kJst : 8x8x0 (Iu¼x;u0 ¼x0 6¼ ; 4 Ju¼x;u0 ¼x0 6¼ ;) ^ 8x8x0 (Iu¼x;u0 ¼x0 6¼ ; ! DIu¼x;u0 ¼x0 Ju¼x;u0 ¼x0 )15 (103) u,u#(D) :¼ kIst.kJst. (Iu¼w ¼ Ju¼w ^ Iu#¼w ¼ Ju#¼w) ^ Iu6¼w,u#6¼w 6¼ ; ^ distu,u#(D)Iu6¼w,u#6¼w Ju6¼w,u#6¼w16 14 maxu1 ;...;un ðDÞ :¼ kIst :k Jst : ð½u1 ; . . . ; un ; DÞIJ^ :9Kst ðð½u1 ; . . . ; un ; DÞIK ^ Ju1 6¼w;...;un 6¼w =Ku1 6¼w;...;un 6¼w Þ: 15 distu1 ;...;un ðDÞ :¼ k Ist :k Jst :8x1 . . . 8xn ðIu1 ¼x1 ;...;un ¼xn 6¼ ;4Ju1 ¼x1 ;...;un ¼xn 6¼ ;Þ ^ 8x1 . . . 8xn ðIu1 ¼x1 ;...;un ¼xn 6¼ ; ! DIu1 ¼x1 ;...;un ¼xn Ju1 ¼x1 ...;un ¼xn Þ: 16 u1 ;...;un ðDÞ :¼ k Ist :k Jst :ðIu1 ¼w ¼ Ju1 ¼w ^ . . . ^ Iun ¼w ¼ Jun ¼w Þ^ Iu1 6¼w;...;un 6¼w 6¼ ; ^ distu1 ;...;un ðDÞIu1 6¼w;...;un 6¼w Ju1 6¼w;...;un 6¼w :


which is instead introduced by the main generalized determiner of the donkey sentence. In other words, we allow generalized determiners to be multiply selective instead of singly selective. Importantly, we do not run into the proportion problem because we have decomposed quantification and separated the static DET condition from the maximization and distributivity operators that regulate the dynamics of dependencies. The resulting indexation of the paradigmatic example of strong donkey sentences is provided in (100) below. The universal determiner introduces its restrictor dref u, its nuclear scope dref u$ and the strong donkey dref u#. The indefinite is basically anaphoric to this dref (just as the donkey pronoun is) and its translation is identical to the one for singular anaphoric definites in (53) above.


(104) Æu;u0 æ (D) :¼ kIst :kJst : (Iu¼w ¼ Ju¼w ^ Iu0 ¼w ¼ Ju0 ¼w )^ (Iu6¼w;u0 6¼w ¼ ; ! I ¼ J)^ (Iu6¼w;u0 6¼w 6¼ ; ! distu;u0 (D)Iu6¼w;u0 6¼w Ju6¼w;u0 6¼w )17 (105) detu,u$vu,u#, kPet.kP#et. maxu,u#(Æu;u0 æ (P(u))); maxu$vu(Æu00 ;u0 æ (P#(u$))); [DET{u, u$}]18

(106) everyu,u$vu,u# , kPet.kP#et. maxu,u#(u,u#(P(u))); maxu$vu(u$,u#(P#(u$))); [EVERY{u, u$}] (107) maxu,u#(u,u#([FARMER{u}]; [sing(u#), DONKEY{u#}, OWN{u, u#}])); maxu$vu(u$,u#([sing(u#), BEAT{u$, u#}])); [EVERY{u, u$}] The sequence of updates in (107) proceeds as follows. The restrictor 0 update maxu;u (u;u0 ( . . . )) stores under u and u# all the pairs of individuals such that, relative to any row i in the output info state, ui is a farmer and u#i is a donkey that ui owns. Importantly, the sing(u#) condition contributed by the singular indefinite au# donkey is in the scope of the distributivity operator u;u0 ( . . . ); which ensures that this singleton condition is vacuously satisfied. The nuclear scope update stores under u$ all the u-farmers that beat each and every one of their corresponding u#-donkeys. This maximal and distributive reading for the singular donkey pronoun itu# is due to the distributivity operator u00 ;u0 ( . . . ); which instructs us to examine each pair consisting of a farmer and a donkey, that is, each row i in the matrix, and check that the farmer u$i in that pair beats the corresponding donkey u#i. Thus, the distributivity operator u00 ;u0 ( . . . ) ensures the vacuous satisfaction of the second occurrence of the condition sing(u#), which is contributed by the singular donkey pronoun. Finally, we check that the set of u-individuals, that is, farmers that own at least one donkey, is included 17

18

Æu1 ;...;un æ ðDÞ :¼ k Ist :k Jst :ðIu1 ¼w ¼ Ju1 ¼w ^ . . . ^ Iun ¼w ¼ Jun ¼w Þ^ ðIu1 6¼w;...;un 6¼w 6¼ ; ! I=JÞ^ ðIu1 6¼w;...;un 6¼w 6¼ ; / distu1 ;...;un ðDÞIu1 6¼w;...;un 6¼w Ju1 6¼w;...;un 6¼w Þ: 0

detu;u vu;u1 ;...;un , 0 kPet :kPet0 : maxu;u1 ;...;un ðÆu;u1 ;...;un æ ðPðuÞÞÞ; maxu vu ðÆu0 ;u1 ;...;un æ ðP0 ðu0 ÞÞÞ; ½DETfu; u0 g:


The strong donkey sentence in (100) above is translated as shown in (107) below. Just as before, we assume that the domain of the universal quantifier is non-empty, so we can use the simpler distributivity operators u;u0 ( . . . ) and u00 ;u0 ð. . .Þ:


in the set of u$-individuals, that is, farmers that own at least one donkey and beat every single donkey they own. This sequence of updates is depicted in (108) below. (108)




In sum, the translation in (107) derives the intuitively correct strong reading for sentence (100) because the multiply selective distributivity operators u;u0 ( . . . ) and u00 ;u0 ( . . . ) neutralize the two occurrences of the sing(u#) condition—which is now vacuously satisfied. Consequently, u;u0 the maximization operator max ( . . . ) in the restrictor stores in u# all


(109) Everyu1 ;u4 v u1 ;u2 person who buys au2 book on amazon.com and has au3 credit card uses itu3 to pay for itu2 : The most salient interpretation of sentence (109) is that, for every book (strong reading) that any credit card owner buys on amazon.com, there is some credit card (weak reading) that s/he uses to pay for the book. In particular, the credit card can vary from book to book, for example, I can use my MasterCard to buy set theory books and my Visa to buy detective novels, which means that even weak indefinites like au3 credit card can introduce non-singleton sets. For each buyer, the two sets of objects, that is, all the books purchased on amazon.com and some of the credit cards that the buyer has, are correlated and the dependency between these sets—left implicit in the restrictor of the quantification— is specified in the nuclear scope: each book is correlated with the credit card that was used to pay for it. This paraphrase of the meaning of sentence (109) is formalized in classical (static) first-order logic as shown in (110) below. (110) 8x8y(person(x) ^ book(y) ^ buy(x; y)^ 9z(cardðzÞ ^ have(x; z)) ! $z#(CARD(z#) ^

HAVE(x,

z#) ^

USE-TO-PAY(x,

z#, y)))

The indefinite au2 book receives a strong reading, which in our account means that it is co-indexed with the determiner everyu1 ;u4 vu1 ;u2 : The resulting translation for this mixed-reading donkey sentence is provided in (112) below.


the donkeys owned by each u-farmer—and not only one such donkey—and the nuclear scope retrieves all these donkeys one at a time. We correctly predict that singular donkey anaphora can only have weak, that is, existential and singular, or strong, that is, maximal and distributive, readings—irrespective of which generalized determiner we co-index the indefinite with. This is because the co-indexation is cashed out in terms of multiply selective maximization and distributivity operators that are common to all determiners and that are completely separate from the static DET condition that is specific to each generalized determiner. The present account of donkey anaphora generalizes to mixed weak and strong relative clause donkey sentences like the one in (109) below, which are problematic for many static and dynamic accounts (see Brasoveanu 2008 for more discussion).


(111) everyu1 ;u4 vu1 ;u2 , kPet :kPet0 : maxu1 ;u2 (u1 ;u2 (Pðu1 ))); maxu4 vu1 (u4 ;u2 (P0 (u4 ))); [EVERYfu1 ; u4 g] (112) maxu1 ;u2 (u1 ;u2 ([personfu1 g]; [sing(u2 ); bookfu2 g; buyfu1 ; u2 g]; [u3 j sing(u3), CARDfu3g, HAVEfu1, u3g])); maxu4 vu1 (u4 ;u2 ([sing(u2 ); sing(u3 ); use-to-payfu4 ; u3 ; u2 g])); [EVERYfu1 ; u4 g]

3 DECOMPOSING MODAL QUANTIFICATION This section extends PCDRT with drefs for possible worlds, which enables us to decompose dynamic modal quantification and provide an analysis of modal subordination that is parallel to the analysis of quantificational subordination.

3.1 Intensional PCDRT We extend Dynamic Ty2 (and PCDRT) with modal drefs by adding a new basic type w for possible worlds. The result is a Dynamic Ty3 logic with four basic types: t (truth values), e (individuals; variables: x; x0 ; . . .), w (possible worlds; variables: w; w0 ; . . .) and s (variable


The update proceeds as follows. First, we store in u1 all the people that buy books and have credit cards and in u2 all the books that they buy. Then, relative to each u1-person and each u2-book, we (nondeterministically) store in u3 one credit card that the person has. This is a consequence of the fact that the sing(u3) condition is in the scope of the multiply selective distributivity operator u1 ;u2 ( . . . ): The nuclear scope update stores in u4 all the u1 people such that, for each of the u2-books they buy, they use the corresponding u3-card to pay for the book. Finally, we test that the set of u1-people is included in the set of u4-people. The entire sequence of updates is true iff there is at least one way to successfully update the initial info state Iw with this sequence of updates, which is the case iff the first-order formula in (110) above can be satisfied.


Possible-world drefs have two uses: (i) they store possible scenarios (in the sense of Stone 1999), for example, the set of worlds introduced by the conditional antecedent in (10a), that is, a possible scenario containing a man that is alive, which is further specified by the consequent of the conditional in (10a), and (ii) they store propositional contents, for example, the content of the entire conditional in (10a), that is, the content of the premise of the Aquinas argument (this is just a specific, restricted version of the previous use and, as such, can be derived from it). In an intensional Fregean/Montagovian framework, the compositional aspect of interpretation is largely determined by the types for the extensions of the saturated expressions, that is, names and sentences, plus the type that enables us to build intensions out of these extensions.


assignments; variables: i; i0 ; . . . ; j; j0 ; . . .); Dt, De, Dw and Ds are nonempty and pairwise disjoint sets. In the spirit of van Rooy (1998) and Stone (1999), we analyse modal anaphora by means of drefs for static modal objects. This enables us to explicitly capture the parallels between anaphora and quantification in the individual and modal domains. The resulting Intensional PCDRT system takes the research program in Muskens (1996), that is, the unification of Montague semantics and DRT, one step further: it unifies in classical type logic the static Lewis (1973, 1981)–Kratzer (1981) analysis of modal quantification and the extensional Dynamic Plural Logic of van den Berg (1996). Just as before, subscripts on terms indicate their types: xe ; ww ; is ; . . . : We also subscript lexical relations with their world variable—for example, SEEw(x, y) is intuitively interpreted as x sees y in world w. These notational conventions, meant to improve readability, are the reason for using boldfaced w for the type of possible worlds (while all the other basic types are italicized)—it distinguishes this type from the subscripted world variable w. Just as a dref for individuals u is a function of type se from assignments is to individuals xe, a dref for possible worlds p is a function of type sw from assignments is to possible worlds ww. Intuitively, the world pswis is the world that i assigns to the dref p. A dref p stores a set of worlds, that is, a proposition, with respect to an info state I, as shown in (113) below: p[I] is the image of the set of assignments I under the function p. (113) p[I] :¼ {pswis : i 2 I}


Let us abbreviate them as e, t and s, respectively. A sentence is still interpreted as a DRS, that is, as a relation between info states, hence t :¼ (st)((st)t). A name is still interpreted as an individual dref, hence e :¼ se. Finally, s :¼ sw, that is, we use the type of possibleworld drefs to build intensions. The basic translations for some lexical items are provided in table (114) below. They are simply the intensional counterparts of their extensional PCDRT translations. We will henceforth use the following notational conventions:

(114)

Lexical item

Translation

Type e :¼ se t :¼ (st)((st)t) s :¼ sw

alive

kve.kqs. [ALIVEq{v}] where ALIVE is of type e(wt)

e(st)

have

kQ(e(st))(st).kve. Q(kv#e.kqs. [HAVEq{v, v#}]) where HAVE is of type e(e(wt))

((e(st))(st))(e(st))

man

kve.kqs. [MANq{v}] where MAN is of type e(wt)

e(st)

heu

kPe(st).kqs. [singq(u)]; P(u)(q)

(e(st))(st)

Harveyu

kPe(st).kqs. [u j u ¼

au

kPe(st).kP#e(st).kqs. [u j singq(u)]; P(u)(q); P#(u)(q)

(e(st))((e(st))(st))

detu,u#vu

kPe(st).kP#e(st).kqs. maxu(Æuæ(P(u)(q))); maxu#vu(Æu#æ(P#(u#)(q))); [DETq{u, u#}]

(e(st))((e(st))(st))

not

kP st :kqs : ½;PðqÞ

(st)(st)

HARVEY];

P(u)(q)

(e(st))(st)


u; u#; . . . are drefs (i.e. constants) of type e and v; v#; . . . are variables of type e; p; p#; . . . are drefs (i.e. constants) of type s and q; q#; . . . are variables of type s; P; P 0 ; . . . are variables over dynamic propositions; their type is st; P; P0 ; . . . are variables over dynamic intensional properties of individuals; their type is e(st); and


Q; Q0 ; . . . are variables over dynamic intensional quantifiers; their type is (e(st))(st).

Ip6¼w :¼ {i 2 I: pi 6¼ w} pI :¼ {pi: i 2 Ip6¼w} Ip¼w :¼ {i 2 I: pi ¼ w} singp(u) :¼ kIst. pI 6¼ ; ^ "w 2 pI(sing(u)Ip¼w) DETp{u, u#} :¼ kIst. pI 6¼ ; ^ "w 2 pI(DET{u, u#}Ip¼w) Ip6¼ w;u1 6¼w;...;un 6¼ w :¼ fis 2 I : pi 6¼ w ^ u1 i 6¼ w ^ . . . ^ un i 6¼ wg (121) Rp fu1 ; . . . ; un g :¼ kIst : Ip6¼w;u1 6¼w;...;un 6¼w 6¼ ; ^ 8is 2 Ip6¼w;u1 6¼w;...;un 6¼w (Rpi (u1 i; . . . ; un i))

(115) (116) (117) (118) (119) (120)

The definition of intensional atomic conditions in (121) above relies on static lexical relations Rw (x1 ; . . . ; xn ) of the expected intensional type en(wt). For any type s, ens is defined as the smallest set of types such that e0s :¼ s and em+1s :¼ e(ems). The notions of new dref introduction, structured inclusion, maximization and distributivity for possible-world drefs are parallel to the corresponding notions for individual-level drefs. [p] :¼ kIst.kJst. "is 2 I($js 2 J(i[p] j)) ^ "js 2 J($is 2 I(i[p] j )) p#6p :¼ kIst. "is 2 I(p#i ¼ pi _ p#i ¼ w) p#v p :¼ kIst : (p0 6p)I ^ 8is 2 I(pi 2 p0 I ! pi ¼ p0 i) maxp(D) :¼ kIst.kJst. ([p]; D)IJ ^ :$Kst(([p]; D)IK ^ Jp6¼w=Kp6¼w) (126) maxp#vp(D) :¼ maxp#([p#vp]; D) (127) distp(D) :¼ kIst.kJst. pI ¼ pJ ^ "ww 2 pI(DIp¼wJp¼w) (128) Updating the info state I with the DRS D distributively over the dref p: (122) (123) (124) (125)


The intensional singleton requirement singp(u), the intensional condition DETp{u, u#} and intensional lexical relations are defined below. Just as we have a dummy individual we, we will assume that there is a dummy world ww relative to which all lexical relations are false, that is, any n-ary relation of the form Rw (x1 ; . . . ; xn ) is false if w is w. We can think of the dummy world ww as the world where no individual exists. Lexical relations are false in ww because a relation between individuals obtains at a world only if the individuals exist in that world.


(131) a. Linusu does notp have au# car. b. Heu wouldp have nowhere to park itu#.

3.2 Indicative sentences We will analyse the discourse in (132) below all over again to see the intensional system in action. The two sentences of this discourse are compositionally translated in Intensional PCDRT as shown in (133) and (134) below. (132) a. b. (133) a. b.

Au wolf came in. Itu ate Harveyu#. wolf , kve.kqs. [WOLFq{v}] au wolf , kP#e(st).kqs. [u j singq(u)]; [WOLFq{u}]; P#(u)(q)


(129) p(D) :¼ kIst.kJst. Ip¼w ¼ Jp¼w ^ pI 6¼ ; ^ distp(D)Ip6¼wJp6¼w (130) Æpæ (D) :¼ kIst :k Jst : Ip¼w ¼ Jp¼w ^ ðpI ¼ ; ! I ¼ JÞ ^ (pI 6¼ ; ! distp (D)Ip6¼w Jp6¼w ) We define sentential negation as a test [see not,kP st :kqs :[;P(q)] in table (114) above] only for simplicity. We could have easily defined it as introducing a maximal possible-world dref p storing all and only the worlds satisfying the ‘sentence radical’ in the scope of negation. This is needed to account for examples of modal subordination like (131) below, which can be easily analysed within the framework developed in this section.


c. au wolf came in , kqs. [u j singq(u)]; [WOLFq{u}]; [COME-INq{u}] (134) a. ate , kQ(e(st))(st).kve. Q(kv#e.kqs. [EATq{v, v#}]) b. ate Harveyu# , kve.kqs. [u# j u# ¼ HARVEY]; [EATq{v, u#}] c. itu ate Harveyu# , kqs. [singq(u)]; [u# j u# ¼ HARVEY]; [EATq{u, u#}]

(135) indp , kP st : [singðp )]; P(p )20 (136) sing(p) :¼ kIst. jpIj ¼ 1 When we apply the two indicative morphemes to the two ‘sentence radicals’ of our discourse, as shown in (137) below, we obtain the final DRS translations for the two sentences. Dynamically conjoining these DRSs gives us the translation for the entire discourse, provided in (138) below. We can rewrite this in the more familiar DRT format as shown in (139). 0

(137) indp (au wolf came in): indp (itu ate Harveyu ): (138) [sing(p )]; [u j singp ðuÞ; [wolfp fug]; [come-inp fug]; [sing(p )]; ½singp (u)]; [u0 j u0 ¼ harvey]; [eatp fu; u0 g] 19 This analysis of indicative mood is simply a proof-of-concept intended to show that verbal moods can be fruitfully analysed in parallel to pronouns. The analysis needs to be further developed to account for (among other things) the contrast between indicative and subjunctive in English—and, in richer mood systems, for the contrast between indicative and various kinds of non-indicative moods. The hope is that the resulting analysis of mood systems can be usefully compared to analyses of pronominal systems that realize various contrasts, for example, proximal v. distal demonstratives, indexical v. anaphoric personal pronouns, overt v. covert pro-forms, past v. present tense and so on. For more discussion, see Stone (1997) and Bittner (2001, 2007) among others. 20 We could take the dref p* to store the current context set (Stalnaker 1978). Since p* stores exactly one world relative to a plural info state [by virtue of sing(p*)], we could think of the context set as the set p I1 [ p I2 [ p I3 [ . . ., whose elements are all the worlds that p* stores relative to the plural info states I1 ; I2 ; I3 ; . . . that are still live options at any given point in discourse.


The translations of the two sentences, more precisely, of the two ‘sentence radicals’, are two dynamic propositions of type st. We assume that each of the two sentences has an indicative mood morpheme (morphologically realized as part of their past tense morphology), the meaning of which is provided in (135) below. The indicative mood takes the dynamic proposition P st denoted by the remainder of the sentence (i.e. by the ‘sentence radical’ in its scope) and applies it to the designated dref for the actual world p*. We capture the deictic nature of indicative morphology by the fact that its translation is parallel to the translation of singular pronouns [see (37) above].19 The single world that p* stores relative the input state I is (for the purposes of the current discourse/conversation) the actual world w*.


(139) [u; u0 jsing(p ); singp (u); wolfp fug; come-inp fug; u0 ¼ harvey; eatp fu; u0 g]

(140) [p* j p* ¼ w*] (141) p* ¼ w* :¼ kIst. I 6¼ ; ^ "is 2 I(p*i ¼ w*) (142)

3.3 Dynamic modal quantifiers Following Kratzer (1981), we analyse modal verbs as quantifiers over possible worlds that are contextually parametrized. The contextuallyprovided parameters are the modal base b and the ordering source x, represented as indices on modal verbs, as shown in (143) and (144) below. (143) A wolf mightb,x come in. (144) If a wolf comes in, it mightb,x eat Harvey. Our dynamic notion of modal quantification is parallel to the notion of dynamic quantification over individuals proposed in the previous section. The translation for modal verbs in (145) below is parallel to the translation for determiners that anaphorically retrieve their restrictor in (91) above. The translation for modalized conditionals in (146) below,


Given that our default discourse-initial state Iw assigns the dummy world w to all world drefs, including p*, we follow Bittner (2007) and assume that a start-up update precedes all discourses. This start-up update is just the ‘commonplace’ update of Stalnaker (1978) and ‘include[s] any information which the speaker assumes his audience can infer from the performance of the speech act’ (Stalnaker 1978). Thus, the start-up update introduces the dref p* (among other things) and constrains it to store the world w* in which the speech act is performed, as shown in (140) below. The two anaphoric indicative moods in (137) above can now be successfully interpreted and the sequence of updates in (138) can now be depicted as shown in (142) below.


that is, for if-clauses that modify a matrix clause containing a modal verb, is parallel to the translation for generalized determiners in (77) above. The if-clause is a way to overtly provide the restrictor for the modal quantifier. Note that the types of the translations in (145) and (146) are exactly the types we would expect in an intensional Montagovian framework, that is, (st)(st) and st((st)(st)), respectively. p0 vp

Just as extensional generalized determiners relate two dynamic properties P and P# of type et, modal verbs relate two dynamic propositions P and P 0 of type st. These dynamic propositions are used to extract a maximal restrictor set of worlds and a maximal nuclear scope set of worlds, which are stored in the drefs p and p#. These drefs are then related by a modal condition MODAL that is relativized to a modal base b and an ordering source x. This condition contributes the static modal force that is specific to each modal quantifier. Thus, the modal condition MODALq,b,x{p, p#} is parallel to the DET{u, u#} condition. The only difference is that the modal condition brings in the extra contextual parameters b and x—and this is where the static analysis of modal quantification in Lewis (1973, 1981)–Kratzer (1981) is incorporated into our dynamic notion of modal quantification. Both b and x are drefs of type s(wt), that is, they are drefs for sets of worlds, and they store a set of sets of worlds, that is, a set of propositions, relative to a plural info state I, as shown in (147) below. The dummy value for drefs like b and x is the singleton set {w} whose sole member is the dummy world, as shown in (148). (147) a. b. (148) a. b.

bI :¼ {bi : i 2 Ib6¼{w}} xI :¼ {xi : i 2 Ix6¼{w}} Ib6¼{w} :¼ {i 2 I : bi 6¼ {w}} Ix6¼{w} :¼ {i 2 I : xi 6¼ {w}}

The sets of propositions bI and xI are none other than Kratzer’s static conversational backgrounds. That is, they are the set of propositions B of type (wt)t which is the contextually provided modal base, and the set of propositions O of type (wt)t which is the contextually provided ordering source—as shown in (149) below. Encoding conversational backgrounds by means of drefs captures their context-sensitive nature


(145) modalb;x , kPst :kqs : maxp0 vp(Æp0 æ (P(p0 ))); [MODALq;b;xfp; p0 g] p0 vp (146) if p +modalb;x , 0 kP st :k P 0st :kqs : maxp ðÆpæ (P(pÞ)); maxp vp (Æp0 æ (P 0 ðp0 ))); [MODALq;b;x fp; p0 g]


directly. Moreover, encoding them by means of drefs for propositions enables us to capture the fact that the propositional contents of sentences in logic puzzles like (1) above can be assembled together to form such conversational-background drefs. (149) a. B ¼ bI ¼ fbi : i 2 Ib6¼fwg g b. O ¼ xI ¼ fxi : i 2 Ix6¼fwg g

(150) w

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