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JOURNAL OF SEMANTICS AN INTERNATIONAL j oURNAL FOR THE INTERDISCIPLINARY STUDY OF THE SEMANTICS OF NATURAL LANGUAGE MA...

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JOURNAL OF SEMANTICS AN INTERNATIONAL j oURNAL FOR THE INTERDISCIPLINARY STUDY OF THE SEMANTICS OF NATURAL LANGUAGE

MANAGING EDITOR: PETER BoscH (IBM Germany and Universiry of Osnabriick} REVIEW E DI TOR: TIBOR Kiss (IBM Germany) E DITORIAL B O AR D: N. AsHER (Universiry of Texas, Austin} R. BARTSCH (Universiry of Amsterdam) J. VAN BENTHEM (Universiry of Amsterdam) B.BocuRAEV (IBM Researc�. Y orktown Heights} D. S. BREE (Universiry of Manchester) H. BREKLE (Universiry ofRegensburg) G.BROWN (Universiry of Cambridge) 0. DAHL (Universiry of Stockholm) S.C.GARROD (Universiry of Glasgow) B. GEURTS (Universiry of Osnabriick) M. HERWEG (Universiry of Hamburg) P.HoPPER (Carnegie Mellon Universiry) L.R. HoRN (Yale Universiry) S. (SARD (Universiry of Edinburgh) P.N. joHNSON-LAIRD ( Princeton Universiry} H. KAMP (Universiry of Stuttgart) E. LANG (Universiry ofWupperral)

S. LEVINSON ( MPI Nijmegen) S. LOBNER (Universiry of Diisseldor0 SIR JOHN LYONS (Universiry of Cambridge) A.MANASTER-RAMER (Wayne State Universiry} W. MARSLEN-WILSON ( MRC, Cambridge) J. McCAWLEY (Universiry of Chicago) L. M.G. NoORDMAN (Universiry ofTilburg) R.A. VAN DER SANDT (Universiry of Nijmegen) T.SANFORD (Universiry of Glasgow) R.SCHA (Universiry of Amsterdam) H. ScHNELLE (Universiry of Bochum) P.A.M. SEUREN (Universiry ofNijmegen) A.VON STECHOW (Universiry ofTiibingen) M. STEEDMAN (Universiry of Pennsylvania) W.W AHLSTER ( DFKI Saarbriicken) B.WEBBER (Universiry of Pennsylvania} H. ZEEVAT (Universiry of Amsterdam)

E DITORIAL A D DRESS: Journal ofSemanrics, c/o Dr P. Bosch, IBM Germany Scientific Centre, Vangerowstr. 18, D 6-900 Heidelberg, Germany. Phone: (4 is (3), uttered in a situation where no noise has come from the direction of the door: (3) The king of france is knocking on the door. Likewise, example (4), uttered in a situation where an obviously untouched sandwich is on the table, seems straightforwardly false: (4) The king of france ate that sandwich.

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When a definite noun phrase fails to refer, the statement containing it is often felt to lack a rruth value, as in The king ofFrance is bald . In other examples, however, the statement seems intuitively false, and not rruth-valueless: consider the case of a speaker who points at an obviously empty chair and says The king ofFrance is sitting in that chair. The difference appears to depend on the pragmatics of verification; we know the sentence is false because the chair is empty-the question of the existence of the king of France need not even come up. A semantics is sketched for assigning rruth values to sentences relative to information states. A sentence containing a definite NP may be evaluated as false relative to a given information state rather than simply truth-valueless if, after removing the information that the NP fails to refer, the resulting information state still cannot be consistently extended to one making the sentence true. On this assumption, existing proposals for the semantics ofnegation in information-state semantics turn our to correspond to internal and external negation, respectively.

1 14

Existence Presuppositions and Background Knowledge

Conversely, in the sa�e situation, sentences true:

(s)

(s)-(7)

are straightforwardly

The king of France is not sitting in that chair. The king of France is not knocking on the door. The king of France has not eaten that sandwich.

(6)

(7)

What makes the difference here? These examples may be reminiscent of the following examples, discussed by Strawson (1964):

(8)

The Exhibition was visited yesterday by the king of France.

Sentence

(8)

may express a false statement even if there is no local swimming

pool, and sentence France.

(9) may express a false statement even if there is no king of

Strawson suggests that truth-valuelessness may depend on articulation of a statement into topic and comment. A topic phrase may, if it fails to refer, result in a truth value gap for the statement in which it appears; but a definite noun phrase which forms part of the comment may fail to refer without causing a

truth value gap. Similar ideas have been suggested more recently by Jay Atlas

(1988) and others.

This idea has some attractiveness for examples like (8) and (9), and may very well be correct. It seems less plausible for examples like (2) through

(7),

however, so I think something more needs to be said. One need only look at the chair or the sandwich, or listen at the door, to determine that (2)-{4) are false and that

(s)-(7) are true; it makes little difference

whether we regard these

statements as 'about' the king of France on the one hand, or the chair, door and sandwich on the other.

A somewhat different hypothesis might trace the distinction between example (r) and examples (2)-(7 to the fact that is bald is an 'individual' level and subsequent work, while is predicate, in the terminology of Carlson 1

)

( 977)

sitting in that chair is a 'stage' level predicate. However, this hypothesis is quickly disconfirmed by examples like (ro).

(ro)

The king of France is on the University ofRochester faculty.

I take this sentence to be clearly false, but is on the University ojRochesterfaculty is an individual level predicate, not a stage level predicate.

A more likely hypothesis attributes the difference not to the semantics of the predicate, but to the pragmatics of verification. Sentence (2) seems false and sentence

(s) seems true because in the situation described we can see that there

is no one in the chair. This is enough to assign truth values to these sentences without the question ofthe existence ofa king ofFrance even coming up. Likewise, we know enough about the Rochester faculty to feel intuitively that (ro) is false,


(9)

Jones spent the morning at the local swimming pool.

Peter Lasersohn

II5

without ever having to consider the question of whether there is a king of France. In contrast, example (I) can only be judged true or false on the basis of information about the king of France himself, it cannot be verified or falsified without addressing the issue of whether there is a king of France. There is a likelihood of misunderstanding here, so let me state very plainly and emphatically that I am NOT claiming that the sentence in general must be objectively verifiable (or falsifiable) in order to have a truth value.1 I do believe that an affirmative statement which might otherwise be judged of indeter minate truth value (because it contains a term which fails to refer) can instead be judged false, provided the context makes it possible to determine that the statement could not possibly be true regardless of whether the term has

(2)-(7)

and and {Io) on the other, and has the result that {I) may be judged of indeterminate truth value if there is no king of France, even while and (ro) are not. It will be useful, in formulating an analysis of these facts, to adopt a semantic

(2)-(7)

framework in which truth is relativized to 'data sets' or 'information states'. This approach is adopted, for example, in the framework of Data Semantics, developed in Veltman (I9 8 1 ) and Landman (I986), which I will adopt in broad

outline here; however, it will matter little for current purposes whether we use precisely the theory advocated by Landman and Veltman, or some other framework which adopts a similar notion of truth-relative-to-a-data-set.2 We write 'D f-

rp' for 'rp

is true on the basis of data set D ', and 'D -1 rp' for

'rp is false

on the basis of data set D'. Data sets themselves will be assumed to be consistent sets of propositions, with the requirement that if rp E D then D 1- rp. The possibility is left open that

D f- rp even if rp � D, corresponding to the intuition that a proposition may be concluded on the basis of a set of data, without being encoded directly in that set

{rp I

D f- rp) corresponds to the closure of D under of data. We assume that some suitable consequence relation.3 The possibility exists that for a given D and rp, neither D 1-

rp

nor D-1 rp. But

of course this should not be taken as meaning that rp lacks a truth value in any

absolute sense; data sets may be limited in the information they encode, and rp may just be undecidable on the basis of D. Ordinarily-though perhaps not in cases of presupposition failure-D may be extended to some more complex data set D' on the basis of which

rp

does evaluate as true or false.

In giving an analysis of the sentences discussed above, we will have to make use of data set revisions -that is, transitions from one information state to another-including revisions which non-monotonically 'remove' information.

rp be the Given a data set D, and assuming rp not to be tautological, let D data set as much like D as possible, compatible with the condition that -


reference or not. Conversely, negative statements can be judged true in analogous circumstances. This is the difference between (I) on the one hand

116


(11) a. D I- (the x:¢) 1/J iff D I- 3y (Vx(¢ - x = y ) & 1/J). b. D -1 (the x:¢ ) 1/J iff for all D' such that (D - -.3y 'Vx [¢- x y]) � D', it holds that D' -1 3y [Vx [¢ - x = y] & 1/J ] . =

In English: The P is Q is true on the basis of data set D just in case i t is true on the basis of D that there is a unique P, which is Q. The P is Q is false on the basis of D iff after removing from D the information that there is no unique P, the resulting data set still only extends to ones on the basis of which it is false that there is a unique P, which is Q. Taking this approach has an interesting consequence. Supposing that we can never know that the king of France would not be bald if there were one ( perhaps a questionable supposition), The king ofFrance is bald will come out truth-valueless relative to any data set encoding the information that there is no king of France-even in data sets which are 'total' in the sense of not allowing any proper extensions. Thus we have a truth value gap that represents something more than simple incompleteness of information. Aside from its persistence into total information states, however, this truth value gap has the same status as more run-of-the-mill gaps of the sort that have nothing to do with presupposition, but only with the general relativization of truth to data sets. In the context of this sort of semantic framework,it is perhaps not best to think of an individual sentence as 'coming with' presuppositions,


D -¢If ¢.4 We understand D- ¢ to be the data set which results from the removal of any commitment to ¢ from D. Besides the removal of information from a data set, we must also consider the addition of information. In particular we will have occasion to quantify over the possible ways of extending a given data set. We write D � D' for 'D' is an extension of D',which we understand to mean simply that D' is a consistent superset of D. We can now return to our original examples. Why is it that someone who points at an empty chair and says The king ofFrance is sitting in that chair seems to be saying something false? I would like to suggest that it is because even ifwe suspend our knowledge that there is no king ofFrance, there is no way ofconsistently extending our information to include the proposition that the king ofFrance is sitting in the chair. Such an extension is impossible because we know the chair to be empty. In contrast,if we suspend our knowledge that there is no king of France,our information may then be extended either to include the proposition that the king of France is bald, or to include the proposition that the king of France is not bald. This suggests a falsehood clause for definite descriptions like that in ( I I b), which we pair with the more ordinary Russellian truth clause in (11a):

Peter Lasersohn

I I7

which must be met if the sentence is not to be sapped of the tiuth value it would otherwise have; rather, the gap represents a kind of residue of undecidability, left even after all possible ways of extending a data set are considered. In this context, it is worth considering the interaction of definites and negation. Veltman ( I 98 I) suggests the following clauses for negation in Data Semantics: (1 2) a. D 1- -.� iff D _, � b. D _, -.� iff Dl- �

(1 3) Dl- -.� ifffor all D' � D, D'lf �Here, as with ( I 2), The king ofFrance is not sitting in that chair is assigned the value true in the relevant context. However, The king ofFrance is not bald comes out not truth-valueless, but true. I take this not to be the correct result in the general case. However, it is possible to view ( I 3) as giving the semantics for so called 'external', presupposition-cancelling negation, and ( 1 2) as giving the semantics of the more usual 'internal' presupposition-preserving negation. This idea is attractive, but I doubt that it really tells the whole story on this kind of negation. More likely, presupposition-cancelling negation is just one instance of the much more general phenomenon of 'metalinguistic' negation, as argued by Horn (I985). It may be worth contrasting the analysis given here with that of Lappin and Reinhart ( I 988), which is similar in certain respects. Like the proposal presented here, Lappin and Reinhart's analysis attempts to account for speaker intuition of a truth value gap by appealing to the pragmatics of verification. Unlike the present proposal, Lappin and Reinhart's analysis makes heavy use ofgeneralized quantifier theory, and is stated without explicit appeal to partial information states. On Lappin and Reinhart's view, the apparent truth value gap which results when a definite noun phrase fails to refer is just one instance of a more general phenomenon which occurs with all strong determiners.5 For example, speakers will regard sentence (I 4) as of indeterminate truth value, given that there have been no American kings:


Combined with the rules given above for definites, these clauses appear to give the desired results: A sentence like The king ofFrance is not sitting in that chair will be assigned the value true in a context where it is known that the chair is empty; but The king if France is not bald will not be assigned a truth value assuming it is known that there is no king of France, and in the absence of information which would settle the baldness issue if this knowledge were suspended. It is interesting to contrast the clauses in ( 1 2) with the one given in (I 3), essentially that used in Kripke-sryle semantics for Intuitionistic Logic:

I I8


{I4) All American kings lived inNew York. In contrast, analogous sentences with weak determiners, e.g. (I5), will normally be judged false in similar circumstances: (I5) Five American kings lived inNew York.

(17) a. Santa Claus weighs exactly 275 pounds. b. Santa Claus is sitting in that chair.


Lappin and Reinhart suggest that sentences containing weak determiners differ from sentences containing strong determiners in how they may be assessed for truth or falsity, and it is this difference in assessment procedures which results in the intuition of a truth value gap for examples like (I4). The truth or falsity of a sentence containing a weak determiner in its subject noun phrase may· be assessed simply by checking the cardinality of the intersection of extension of the determiner's N' argument with the extension of its VP argument. For example, the truth or falsity of example {I5) may be assessed simply by checking the cardinality of the intersection of the set of American kings with the set of things that lived in New York. If this inter section is of cardinality 5 or greater, the sentence is true; if it is of cardinality less than s, it is false.Note that the cardinality of the extension of theN', the set of all American kings, need not be checked. In contrast, according to Lappin and Reinhart, in order to assess the truth or falsity of a sentence with strong determiner, one must check the extension of the determiner'sN' argument. Sentence ( I 4), for example, cannot be assessed for truth or falsity simply by checking the set of American kings that lived in New York; one must check the set of all American kings. According to Lappin and Reinhart, the fact that one must check this empty set is what results in the intuition of a truth value gap. In their words: 'whenever the assessment of a sentence must start with a scan of anN' set of a given NP, assessment is stalled if this set is empty. In this case, the sentence is marked as anomalous, empirically irrelevant, or undefined, regardless of its semantic interpretation.' Since the assessment of the sentence as true or false 'stalls', speakers will not have clear intuitions as to whether the sentence is true or false. Lappin and Reinhart's proposal can be attacked from several angles. First, it is stated entirely in terms of the logical properties of determiners. For that reason it would not appear to extend naturally to determinerless examples-those involving proper names, for instance. However, proper names behave much like definite descriptions with regard to reference failure and the intuition of truth value gaps. Given that the legend of Santa Claus does not specify his exact weight, sentence {I7a) does not seem intuitively true or intuitively false. However {I7b), uttered by someone pointing at an obviously empty chair, is clearly false:

Peter Lasersohn

I I9

·

( 18) No unicorn is sitting in that chair. In fact, it may be that nothing is sitting in the chair, in which case the extension of the N ', the extension of the VP, and their intersection will all be empty. Yet the sentence is trivially easy to assess for truth. Apparently, it is only the N' set of a determiner which causes a stall if it is empty; otherwise the empty set may be scanned with no problems. This is a rather surprising asymmetry, and it is mysterious why it should obtain.


The basic approach suggested above, however, would seem to extend to such examples fairly straightforwardly. Example ( 17b) will be assigned the value false in the context given, because even if we suspend our knowledge that there . is no Santa Claus, we cannot consistently extend our data set to one where he is sitting in the chair-we can see that the chair is empty. But once we suspend our knowledge that there is no Santa Claus, it seems that we could equally well extend our data set to one where he weighs exactly 2 7 5 pounds, or one where he doesn't. Lappin and Reinhart's proposal can also be attacked on more technical grounds. As they themselves point out (following an anonymous reviewer), it is not really the case that the truth value of a sentence containing a universal determiner can only be assessed by checking the extension of the determiner's N' argument. Instead, a sentence of the form 'Every A is a B', for example, can be assessed by scanning the set A-B. Given the standard generalized quantifier semantics for universal determiners, if this set is empty, the sentence is true; one need not check the entire set A at all. Since one need not check the entire N' set of the determiner, there is no point at which the assessment procedure must stall if this set is empty. Lappin and Reinhart attempt to meet this objection by asking us to consider examples such as Every unicorn is intelligent. They claim that if one attempts to assess this sentence by checking A-B (that is, [unicorn]-[ intelligent]), 'the speaker will have to represent and scan the set of things that are not intelligent. From the perspective of computational efficiency, this is the least efficient way to assess the sentence.' Hence, this procedure will not be easily available. However, Lappin and Reinhart's analysis would seem to require precisely this procedure for examples like Five unicorns are unintelligent , so it is not at all clear that this explanation can go through. We may also object to Lappin and Reinhart's proposal on the grounds that it simply is not clear why 'scanning' an empty set should cause the assessment procedure to stall. In fact it is clear that Lappin and Reinhart must allow the empty set to be successfully scanned in certain circumstances. For example, to assess the truth or falsity of a sentence like ( I 8), on their view one scans the set of unicorns sitting in the chair; If it is empty, the sentence is judged to be true; no stall of the assessment procedure takes place.

1 20


Acknowledgements Thanks to three anonymous referees, and to Louise McNally and Peter Svenonius, who practically deserve co-author status, but should not be held responsible for errors. PETER LASERSOHN Department ofForeign Languages, Literatures and Linguistics University ofRochester 390 Dewey Hall Rochester, NY 14627 USA

Received 20.1 2.91 Revised version received 1 5-07-92


Finally, we may note that Lappin and Reinhart's analysis does not allow the kind of sensitivity to context and background knowledge that the analysis suggested here does. Their analysis does not predict that sentences like The king ofFrance is sitting in that chair will be judged as false in the context given, for example. Since there is no king of France, the N ' set of the determiner the is empty. In Lappin and Reinhart's view, this set must be scanned to assess the sentence for truth or falsity, since the is a strong determiner. But if the N ' set is empty, then scanning it should result in an assessment stall, and the sentence should be judged of undefined truth value. But this result is incorrect; the sentence seems clearly false. I think we can conclude that in certain circum stances, the truth or falsity of a sentence containing a strong determiner can be assessed without 'scanning' the determiner's N ' set, and that an analysis which crucially assumes that this set must be scanned is inadequate. To summarize, we find that certain sentences containing non-referring definite descriptions are clearly false, while others do not provoke clear intuitions of either truth or falsity. The crucial difference seems to be that, in cases of clear falsity, the context provides an independent reason to believe that the sentence cannot be true, regardless of the question of whether the definite succeeds in referring or not. To account for this, I sketched a semantics in which truth values are assigned relative to data sets. The truth value ( relative to a given data set) of a sentence containing a definite description was analysed as depending in part on what information was supported even if the knowledge that the definite fails to refer is suspended. This yields a system in which reference failure sometimes results in truth-valuelessness and sometimes results in falsehood (for affirmative sentences). This proposal was contrasted with one suggested by Lappin and Reinhart (1988), which was shown to be problematic in several respects.

Peter Lasersohn

I2I

NOTES I

2

4

5

-

(i) a. *There is the unicorn in the garden. b. *There is every unicorn in the garden. c. *There are all unicorns in the gar den. d. *There are most unicorns 111 the garden. e. *There is neither unicorn 111 the garden. Strong determiners contrast with weak determiners, such as a (n), some, many, no, the cardinal number determiners, and others which can appear in this position: (ii) a. There is a unicorn in the garden. b. There are some umcorns 111 the garden. c. There are many urucorns 111 the garden. d. There are no unicorns in the garden. e. There are five unicorns in the gar den. For relevant discussion see Milsark (I977), Barwise and Cooper (I 98 I).

REFERENCE S Atlas, Jay David (I988), 'What are negative existence statements about?', Linguistics and Philosophy, II, 4, 373-94· Barwise, Jon & Robin Cooper ( I98 I ), 'Gene ralized quantifiers and natural language', Linguistics and Philosophy, 4, I59-2I9. Carlson, Greg ( 1977), 'Reference to kinds in English', University of Massachusetts dis sertation. Gardenfors, Peter (I988), Knowledge in Flux: Modeling the Dynamics of Epistemic States, MIT Press, Cambridge. Horn, Laurence R (1985), 'Metalinguistic

negation and pragmatic ambiguity', Lan guage, 61, I, 121-74. Kripke, Saul ( 1965), 'Semantical analysis of inruitionistic logic 1', in Crossley & Dum mete (eds), Formal Systems and Recursive Functions, North Holland, Amsterdam. Landman, Fred ( 1986), Towards a Theory of Information: The Status of Partial Objects in Semantics, Foris Publications, Dordrecht. Lappin, Shalom & Tanya Reinhart (1988), 'Presuppositional effects of strong deter miners: a processing account', Linguistics , 26, I021-37·


3

Nor am I claiming that sentences must be verifiable in order to be meaningful, or that the rules which assign truth condi tions to sentences must be stated in terms of the procedures by which we verify that a sentence's truth conditions are satisfied, or anything of the sort. Relativization of truth to information states is not unique to Data Semantics, of course, and goes back at least to Kripke's (I965) semantics for Inruitionistic Logic. This is not to claim that we must take the consequence relation as antecedently given and define (¢1 D I- ¢) in terms of it. Rather, one can give a recursive definition of the notions of truth and falsity on the basis of D, and then define the consequence relation in terms of these data-oriented notions of truth and falsity. A rigorous definition of D ¢ is not a trivial enterprise. See, e.g., Gardenfors (I988) for relevant discussion. Strong determiners are those which cannot appear in postcopular position in an existential there construction, and include the, every , all, most, neither , and related determiners:

122 Existence Presuppositions and Background Knowledge Milsark, Gary (1977), 'Toward an explanation of certain peculiarities of the existential construction in English', Linguistic Analy sis, J, 1-30. Sttawson, P. F. (1964), 'Identifying reference and truth values', Theoria, JO. Reprinted in

P. F. Sttawson (1971), Logico-Linguistic Papers, Methuen, London. Veltman, Frank (1981), 'Data semantics', in J. A. G. Groenendijk et al. (eds}, Formal Methods in the Study of Language, Mathe matisch Centrum, Amsterdam.


journal ofSemantics 10: 123-179

©Oxford Universiry Press 1993

Dealing with Ambiguities by Underspecification: Construction, Representation and Deduction UWE REYLE

University ofStuttgart

Abstract

1

INTRODUCT ION

Utterance interpretation is based on a relation between the linguistic form of the utterance and its meaning. Current approaches to narural language understanding assume that the linguistic form of an utterance is given by some syntactic analysis and that the relation between this form and its meaning is characterized by a translation process into some semantic representation strucrure. In almost all cases this relation is not functional. Whenever semantical ambiguities arise there is a set of meanings associated with a single form. To decide whether some other sentence logically follows from this form

it has

to

be shown that it fo1lows from each of these associated meanings. It is,

therefore, the notion of disjunction on which such a theory of meaning relies. In this paper we develop a theory of language meaning that represents scope ambiguities by underspecified strucrures. The translation into semantic form will thus be functional. The way ambiguities will be represented does not correspond to any of the usual concepts of formalizing ambiguities by means of disjunctions (of completely specified strucrures). A proof theory is provided that relates these structures directly, without considering cases. Consider the following argument. (I) Many a problem about the environment preoccupies every politician. Every politician who many a problem about the environment preoccupies proposes a solution. Every politician proposes a solution.


In this paper we develop a theory of language meaning that represents scope ambiguities by underspecified structures. The set of possible meanings ofa sentence, or text is determined by a set of meta-level constraints that restricts the class of semantic representations appropriately. Thus the way ambiguities are represented does not correspond to any of the usual concepts of formalizing ambiguities by means of disjunctions (of completely specified structures). A sound and complete proof theory is provided that relates these structures directly, without consider ing cases.

1 24

Dealing with Ambiguities by Underspecificarion

(2) (Pl 1\ P�) V (Pf A Pl) V (Pf 1\P�) V (Pl 1\ P�)

but by P; 1\ P 2. where P; and P2 are the underspecified representations of the meanings ofP1 andP2, respectively. The truth conditions that our theory assigns to these underspecified representations will, however,guarantee thatP; 1\ P 2 is true just in case (2) is. And the deduction rules will be such that no recursion to the four cases in (2) is necessary. Our approach thus has not only the advantage to provide a solution to the combinatorial explosion that goes off in any proof that uses (2) as premiss. It also provides a solution to what is called mapping problem by Kempson & Cormack ( I 98 I ):P; 1\ P 2 is a representation that comes quite close to the combination of the syntactic structures ofP1 and P2, which clearly isn't the case for (2). We consider an ambiguous sentence to be true in a model if and only if one of its disambiguations is. And we say that P� 1\ P2 I= G if every model of P; 1\ P2 is also a model of G. To see that I= is indeed a proper consequence relation the reader easily convinces himself that it satisfies the basic properties a consequence relation should obey, 1 namely reflexivity, transitivity and mono tonicity. One might consider other possibilities as well. For example, one may abandon the policy to reckon with the worst as regards the premisses and accept the argument one has to provide already if its conclusion follows from some of the readings of its premisses,and not necessarily all of them. Or one may define the consequence relation in such a way that the conclusion follows if each-and


The first sentence,P1, of ( I ) has two readings. The first reading,Pl, is the one where the scope relation of its two NPs corresponds to their linear order; the other reading,Pf, gives every politician wide scope over many a problem about the environment. In the second sentence,P2, many a problem about the environment cannot have wide scope over every politician, because the scope of ( proper) quantifiers is bound to their local domain-in this case to the relative clause. So, its ambiguity depends only on the way the indefinite a solution is interpreted: either as specific indefinite, or as dependent on every politician. Therefore the second sentence has two read ings, call them P� and P�. Also for the same reason the conclusion, G, of ( I ) is two times ambiguous. Thus there are four possible readings of the premiss set 2 1 of ( I ), and two readings of the conclusion, G and G . How are we going to relate these two readings of the conclusion to the set of readings of the premisses? What are the inferential properties of ambiguous representations? And can they be characterized by one and only one notion of logical consequence? We have already emphasized that we will not present a theory that represents the meaning of ambiguous sentences or texts by the disjunction of their meanings. Thus we will not represent the meaning of the premiss set of ( I ) by

Uwe Reyle

125

(3) (Pl

1\

P1) v (P� 1\ P1) v (P� 1\ P�) v (Pl 1\ PDf- G1 v G2

for the purpose of deductive manipulation. As a consequence each of the representations Pl. ..., P� of the different readings of the premiss set over specifies its meaning-and this overspecificarion has then to be compensated for by taking the disjunction (2) of all possible combinations. But there is a further disadvantage of the mentioned representations. Consider the sentence (4) Every professor who recommends a book is admired. which we may represent a la Schubert & Pelletier by

(s) admired (Vx (professor(x ) 1\ recommend(x , 3y book (y ))))

What the papers cited have in common is that they do not have a dynamic representation of the meaning of the indefinite a book which accounts for the fact that it is interpreted as universally quantified if it has narrow scope with respect to every professor and that the other reading assigns it an existentially quantified meaning. This means that the disambiguation algorithm must deal with the problem of choosing the correct quantification type when creating the different meanings.2 Thus in the framework of unscoped representations, sentences such as (4) cause the same problem as donkey sentences do. The problem is that the indefinite article is regarded as expressing existence. In DRT, this problem does


not only one-of its readings is true in the models that satisfY the premisses.We reject both options (i) because they violate reflexivity and (ii) because we think that a possible deviance from the consequence relation as we defined it is the result of interpretative principles which rely on some definition of coherency of discourses or dialogues. We are not in the position to touch the matter in this paper. We think, however, that if such a definition were available then its effect would be simply to eliminate readings that otherwise were available. Thus the task of drawing inferences will not be affected; nor will our consequence relation. How are we going to represent the meaning of sentences without specifYing the scope relations between their quantifiers? There are quite a few proposals in the literature. (See, for example, Schuben & Pelletier (1982), Fenstad et al. (1987), Hobbs & Shieber (r987), Nerbonne (1992).) What all these proposals have in common is the idea of deriving unscoped representations which then may be transformed algorithmically into sets of corresponding disambiguated representations. If the algorithm is simple and effective, there is certainly a benefit to all these approaches. But effective as the algorithm might be, it has the disadvantage of being obligatory. Even though there is an unscoped representation for ( r ), it has to be translated into a representation of the form

126

Dealing with Ambiguities by Underspecification


not occur because the existential import of the indefinite in the cases where it has wide scope in {4) is not a consequence of the meaning of the NP as such, but rather of the way truth is characterized. The base for our unscoped representations is the separation of information about the structure of a semantic form and the content of the information bits the semantic form combines. Consider the language ofDRSs. DRT represents meaning as the result of an interpretation process in a way that also suits the interpretation of subsequent input. It encodes the semantic connections between successive pieces of sentences or texts-such as, for instance, those produced by pronouns whose anaphoric antecedents occur in earlier sentences-which are largely responsible for the cohesion that distinguishes genuine texts from mere successions of unconnected sentences. The task of establishing the set of semantic connections for a given text relies heavily on the structure of DRSs. In the case of two pieces of discourse being anaphorically linked, for example, the set of possible antecedents is restricted by this structure. Note that the structural information is exploited only when the construction of the meaning representation of that piece of text in which the antecedent occurs has already been accomplished. The constraints that restrict the possible semantic connections are meta-level constraints ; i.e. they are not part of the meaning of linguistic entities, but are used to restrict the set of well-formed DRSs. The language of underspecified DRSs will allow us to express such constraints in the object language. We will, therefore, be able to associate structural constraints declaratively with lexical entries. This does not only apply to constraints that govern anaphoric linkage, but also to constraints that restrict scope ambiguities. In order to achieve this we express structural information by a language with one predicate :::;; that relates individual constants l, called labels. The constants are names forDRSs. They are also used to positionDRS-conditions at the right place in the hierarchy. This is done by writing l:y for an occurrence of aDRS condition yin aDRS named 1. Given such a separation of structural information and purely linguistic content we are able to indicate that, for example, proper names always end up in the top-level DRS. Assume that the label of the top-levelDRS is 1r, then we can specify the target position of any proper name 1r in the lexicon by writing 1r:.7l. The scope potential of indefinite descriptions-like a book in (4)-is also dealt with in the lexicon: suppose that the meaning component of the indefinite is given by (a set of conditions of the form) 1 ':y; then we can express the fact that the indefinite may take arbitrarily wide scope by adding a 1:::;; 1', where l represents the minimal position 1' can occupy. The construction of meaning representation for a given sentence will then consist in relating names that show up in conditions associated with the phrases to be combined. To say that, for example, the subject of a sentence has to have

Uwe Reyle

127

2. 2.1

CON STRUCTION

Sources ofscope ambiguity

We now consider in more detail the distinction between indefinite and quantified NPs and we show that different mechanisms are at work to produce the two different types of scope ambiguities. This will provide a natural motivation for the way we represent and construct meaning representations.3 Specific and other wide scope indefinites

It is widely accepted that indefinite descriptions admit of two uses, a specific and a non-specific use. Specifically used indefinites act as referring terms, terms that refer to parricular things, whose identity is fixed independently of the context in which the term occurs. Referring terms always establish their discourse referents in the universe of the main DRS and thus are not properly within the scope of any other NP. Non-specifically used indefinites may introduce their discourse referents within the scope of other NPs, i.e. at some position subordinate to the main DRS. There are several factors that determine the lower limit of this positioiL The first factor simply guarantees that only proper DRSs are constructed. The second condition depends on the syntactic theory of scope restrictions. And the third restriction results from linking the indefinite with a pronoun or a definite NP. (i) The discourse referent for an indefinite NP must be introduced into a DRS that is accessible from the DRS that contains the verb of which the indefinite NP is an argument.


wide scope over its object we enrich the structural information built up so far by the additional formula 1' � L where 1 is the label associated with the meaning of the subject and 1' is the label associated with the object. This process of enrichment is characteristic for the construction of meaning representation: information from different sources (syntactic and semantic knowledge as well as knowledge about the world) may be added in a monotonic manner to narrow down the possible range of readings. The main advantage of this approach is that it comes closer to a representa tion of meaning that has been thought desirable by scholars from different areas especially from the field of cognitive science. From a cognitive perspective it seems plausible that the recipient of an ambiguous sentence often forms a representation of it that is underspecified with respect to its scope relationships.

128


(ii) Its lower limit is determined by the set of scope bearing elements that must have narrow scope with respect to the indefinite. (iii) It must be introduced into a DRS that is accessible from all the pronouns (or definite NPs) for which the indefinite acts as antecedent Let us call this position minimal with respect to the verb (lrnin J. the underlying syntactic theory (lrnin ..J• and the anaphoric potential (lrnin,••). .,.,. respectively. Whenever it is clear what we mean we will simply talk of minimal positions.• The following example shows that there are also maximal positions. ••

·

In (8) the indefinite may have scope over the other arguments of the clause in which it occurs, but it cannot receive a specific interpretation. In (9) the DRS captures the reading in which it occupies its maximal position. The position is maximal with respect to the anaphoric potential of the indefinite. It is the relative clause which the student has already read in (8) which excludes the possibility of interpreting it specifically. To our knowledge there are no other kinds of restrictions on maximality for indefinite NPs. .

'

· .

'

(9)

z

x ·y u· student(x) book(y) u=x u has already read y

professor( z )

.=?

I

z

recommends y to x

=?

_I

l lucky(x) j

This distinguishes indefinite NPs and quantifiers. Quantifiers do have restrictions on maximality that correspond to (i) and (ii) above. We will discuss them shortly. Let us first note that the processing of indefinite noun phrases does allow for the introduction of their discourse referents anywhere between the universe of the main DRS (or its maximal position) and the (highest) minimal position. This is shown by the interpretation ( I I ) of ( 10 ). ( 1 o) If every student to whom every professor recommends a given book passes the book is useful.


(8) Every student to whom every professor recommends a certain book which the student has already read is lucky.

Uwe Reyle

{ II )

I 29

y book(y)

u

X

student (x ) z

z

=}

professor( z )

=}

recommends y to x

I x passes 1

=}

u=y useful(u)

that book is useful. On the other handy cannot be introduced into any universe that is more subordinate, because this would violate the minimality with respect to its anaphoric potential. It could no longer serve as antecedent of the description the

book in the then clause. Summing up we state the following:

Principle for the interpretation of indefl.nite NPs The meaning of indefinite NPs is underspecifled with respect to their position in the hierarchy of the DRS. The range of possibilities for introducing the meaning components of indefinites in a DRS is restricted by their minimal and maximal positions. Graphically we might display the result of having applied this principle to (10) by ( I2) (

I 2)

.

�------

! l

' student(x J I

I

,.

---- ..I:1 y

: book(y)

X

z

�------�

professor( z)

:I : I

u

��----��

�-·rccommelia's y to

x

=}

1 x passes !

=}

u y useful ( u ) =

The area marked by the dotted box in (12) indicates the range between the minimal position with respect to the verb and the maximal position of a book, which in this case is the main

DRS.

The small dashed box containing the

indefinite's meaning components y and

book(y) covers the possible locations


According to this interpretation there is no particular book such that if every student who has that book recommended to him by every professor passes then

1 30


according to the minimal position with respect to its anaphoric potential and its maximal position. (I 2) is a graphical device to represent the contribution of the meaning of the indefinite a book according to the above principle. To implement this in the DRS language itself we have to add meta-level features that enable us to talk about the hierarchical organization of DRSs. To do this we introduce labels and assume that each discourse referent x and each DRS-condition y comes with such a label, e.g. l:x and k:y. By way of example, ( I I ) is represented this way by ( 13).

( r 3) lo: ��· lz) =>

The conditions of the form 1: => � l") in ( I 3) are sufficient to determine the structure of the DRS ( r r ). To get an underspecified representation correspond ing to ( 1 2) we need more freedom in describing the hierarchy. We achieve this by extending the language by a relation between labels, namely the one that corresponds to the notion of subordination (� of DRSs. This subordination relation � enables us to represent the meaning of indefinite NPs in the following straightforward way. Suppose x and N(x) are the discourse referent and condition introduced by an indefinite NP (according to a standard DRS construction algorithm). Then ',

l:x l:N(x) 1IDl.n�,b � 1 1 nun•aapb � 1 · � ·max•upb .

is the labelled meaning component, which is underspecified with respect to scope. Here lmin•za.8pb , lmax-•ph are labels corresponding to the minimal and maximal


ll:y 11:book(y) l2:u l2:u- y 12:useful(u) II: => �3• 14) l3:x 13:srudent(x) 14:x passes l3 => �s• �) l5:z l5:professor(z) �:z recommends y to x

Uwe Reyle

I3I

positions with respect to the anaphoric potential, and Imin..,., is the minimal position with respect to the verb. These labels must be identified during the

actual construction of the sentence meaning. We will show how this is done in

detail in the next section. For the purpose of this section let us assume that the labelling for the construction of the labelled representation corresponding to

( 1 2) turns out to be exactly like the one in ( 1 3) except for the contribution of the indefinite a book ( 1 4)

Il:y I1:book(y).

(1 s)

l,:y l7:book(y) Imin "' � I7 . IntJn•-pb � I7 ••

I, �

Imax·-pb

Iminft,. will be instantiated during the construction by

� ; and

once the ana

phone relationships have been established, we will end up with an instantia tion of lmin,"'•• by I1 and 1 max,"••• by Jo. This way we get the representation (r6) of ( 1 2).

( r 6)

17:y 17:book(y)

12:u

12:u

=y

12:useful(u) 13:x 13:student(x) 14:x passes 15:z

11: � (13, 14) lcs � 17

I I � 17 I7 � lo

l3: � (Is, lcs)

I5:professor(z) lcs:z recommends y to x

Proper quantifiers and their scope Scope relations between proper quantifiers obey further restrictions. We have already noticed that in contrast to indefinite descriptions quantified phrases cannot cake arbitrarily wide scope. ( 1 7) Some people believe that a problem about the environment preoccupies every serious politician.


To construct the representation corresponding to ( 1 2) we use the following lexical entry for a book.

132


(I 8)

s -------

--

NP

�

D ET

I

a

�

I

�N P I �

V

N

N

VP

PP preoccupies DET

�

problem Prep

I

NP

I

every Adj

�

about DET

I

N

�

N

I

sen

I

N

I

o us politician

the environment

To obtain an underspecified representation we might use the graphical device of the last section to represent the two readings for the embedded sentence in (17) by (1 9). (1 9)

r � - - - - - - - - - - - - - - �

'

X

serious politician(x)

=>

y problem about the �e_n_v)!
But this does not help us very much. If we replace a problem about the environment by a proper quantifier such as, for example, many a problem about the environment, then the two readings of


On one reading the embedded sentence means that there is some particular environmental problem that has the attention of every serious politician. On the other reading every serious politician is concerned with some environmen tal problem, while not all politicians need be concerned with the same problem. For any reading of the embedded sentence (17) as a whole states that there is a small group of people (the very optimistic ones) who believe in what one of these readings says. But (17) does not have a reading according to which there is for each serious politician a separate group, the members of which share such a belief with respect to this particular politician. Hence we may assume that scope assignment of proper quantifiers is restricted syntactically by its local domain . Let us call the upper limit that this local domain imposes on the scope assignments of quantifiers maximal with respect to the local domain. For the purpose of this section we will assume that the local domain of a quantifier is given by the clause in which it occurs. For every serious politician this is the subtree dominated by S.

Uwe Reyle 1 3 3

(2o) Many a problem about the envuonment preoccupies every serious politician. are (21) and (22).5 Here no natural possibility seems to exist to represent both readings in one underspecified structure. This is true as long as we ignore the way (2 1 ) and (22) are constructed. To get an ambiguous representation of (2 1 ) and (22) we must somehow encode the ways in which the meaning components contributed by the verb and NPs are combined.

X

;

'*

proble about the environment(y)

�

pwblo """ " the en vironmen t(y)

� W

�

X SCfJ O U S

politician ( x )

Y

=:-

[

y P""""Pi� x

y preoccupies x

I I

�-----

(23)

I.

13: '* �3)> 132) 131:x 13 1 : serious politician(x) 2. 11 : many a y (1u, 11 2) 1u: y 1u: problem about the environment(y) 3· 12: y preoccupies x

What are the minimal restrictions on the possible ways of combination? The least we know is that the possible combinations are restricted by the semantic requirement that all discourse referents are properly bound. This is true iff the meaning of the verb is subordinate to each of the meanings of its arguments. More precisely the verb must be subordinate to the scope of its argument meanings. This is captured by the following conditions. (24)

1 . 12 � 132 2. 12 � 11 2

Furthermore we know that all argument meanings must be subordinate to the DRS into which the meaning of the whole sentence (or clause) will be incorporated. The label of this DRS is given by the label of the local domain, 1max••m. This gives US


serious politician(x)

1 34


(2 5 ) }3 � }maxdom }1 � }lDSXJom

These additional conditions together with (2 3) specify all of what is common to (2o) and (2 1 ). What they do not specify is the scope of t}le two NPs relative to each other. Nothing is said about 11 being strictly subordinate to 12, or vice versa. And this is as we want it to be, except that there are syntactic restrictions that limit the range of scope ambiguities. It should be clear how to deal with these. Suppose the syntactic theory states that subject must always have scope over object. Then we account for this by adding (26). (26) 13 � 112

(27)

h

� )\ )\

2

(27) represents the structural information given in (23), (24) and (2 5 ). The result of adding (26) is represented in (28). The example already shows that we are going to develop a more radical departure from traditional approaches to constructing meanings out of syntactic structures. The set of possible meanings of a sentence (that arise from scope ambiguities) is determined by a set of conditions of the form 1 � 1 ' that restricts the class of semantic representations appropriately. This set of conditions together with the meaning componentS of the NPs and the verb-as they are given in (23) above-will then be the underspeci.fledsemantic representation· of the sentence.6 By keeping disjunction out of our representations of scope ambiguities we do more justice to the claim that language users represent meanings of complex


In the case of our example an additional condition like (26) removes all ambiguities and completely specifies a structure which is isomorphic to the DRS (21 ). It is convenient to represent the 'structural' information given by the subordination relation and by conditions of the form 1: => (11, 12), 1: ....., (11), 1: quantifier x (11, 12) graphically.

Uwe Reyle

I

3s

of conditions.

I. 2.

1:x, where 1 is a label and x a discourse referent. l:P(x1,

.

•

•

, xn), where 1 is a label, x1, •

n-place predicate. 1: ...., 11, where 1 and 11 are labels. 1:

=>

• •

, xn are discourse referents and P is an

(11, 12), where l, 11 and 12 are labels. ·

1 ::E; 1 '. ::E;

is a partial order, more precisely an upper semilattice with

r -element. UDRSs are defined as pairs

X = �,

D), where

:t' = (L, ::E;)

is an upper

semilattice of labels and D a set of labelled conditions of type I above.

Furthermore$ and D are such that if l: ....,I , in D, then I1 ::E; I in :t", and if l: => (11, 12) in D, then I, ::E; 1 and I2 ::E; 1 in $'. Some remarks are in order. First, we only include standard quantifiers in the fragment, because we restrict ourselves to first-order logic when we deal with deduction. Second, in Section 4 we will give the precise definition of UDRSs.

This definition is more complicated than the examples of this section suggest. The reason is that in the present section we only considered UDRSs that resulted from an application of the construction algorithm to syntactic structures. Because the construction procedure guarantees that the UDRSs it produces are 'well formed' there was no need to discuss the additional

constraints that occur in the definition of Section 4·

The labelled DRS language we use to describe underspecified structures differs essentially from any kind of data structure in that it is a language of some logic:

the logic ofreasoning with ambiguities .


sentences in some underspecified . manner. Thus the language of underspecified DRSs (UDRSs) that is able to deal with scope ambiguities consists of two types

1 36

Dealing wirh Ambiguities by Underspecificarion 2.2

Meaning

We will assume that an ambiguous expression is true in a given situation just in case one of its disambiguations is. (2o), or its underspecified DRS given in (23) and (27) is true with respect to some model M iff one of (2 r ) and (22) is true in M. The definition of truth will, therefore, rely on a disambiguation algorithm. A precise formulation of this algorithm will be given in Section 4· For a better understanding of what will be discussed until then we give an informal description here. We have already mentioned that for the translation of (27) into (28) it is sufficient to augment the structural information given in (27) with 13 :::;; I1 2 Analogously we get the reading in (2 1 ) if we add 11 :::;; I32 to (27). In more complex examples this operation has to be applied recursively. The structure in (29), for example, allows for four different readings, which can be characterized by the following orderings of its scope-bearing elements: (14, I2 , I1), (I2 , 14, I1), and (12, I1, I4). All these readings will be produced by a disambiguation procedure that starts at the top node and decides if l4 shall have scope over 12 or 12 over I4• The former choice gives us the reading (I4, I2, I1). The latter choice yields a structure that is underspecified with respect to the relative scope of l1 and 14 Applying the disambiguation procedure to 122 in (3o) gives the two other readings. •

lo

�

)\

b ==> l·n

I

)\ 2 .3

)\

Construction

In the examples in Section 2. 1 we passed over almost all of the details of the construction algorithm. We will now look at the construction process more


•

Uwe Reyle

1 37

lo

I

)\

I . the instantiation of the parameters l ma x and l min.... 2. the instantiation of the argument slots of the verb with the discourse ••m

•

referents representing the corresponding NP's.

3· the instantiation of the parameters lmax..,p• and lmin..,p• ' and 4· the integration of the meaning components of the processed sentence into the (ambiguous) DRS (representation) constructed so far.

The answers to the first three questions will in the end depend on the underlying syntactic theory. We will devote Section 2.4 to applying the present approach to the theory of scope developed by Frey ( 1 990). It is outside the scope of this paper to deal with question 3 from a sophisticated syntactic point of view. In this section we will nevertheless discuss some problems concerning binding that are independent of the particular syntactic theory the reader prefers. 2. 3 . 1 Integration

The first problem is related to question 4· Let us assume that the syntactic input is given by a c-structure tree together with a mapping that correlates the argument NPs with the argument slots of the verb. Consider the sentences in

( 3 I ).


closely and we will make some final decisions concerning the language of underspecified structures and we will also be able to state some of its logical properties. There are four kinds of questions we have to address. They concern

1 38


(3 I ) (i) A problem preoccupies a politician.

(ii) A problem preoccupies every politician. (iii) Every problem preoccupies every politician.

The lexical entries we will use for the construction of their meanings are

(32)

a:

problem: preoccupies: every:

1;,� problem( )

lm: preoccupy( , ) (/;P, , 1;.,)

l;p: every X;p l;,. : xi,

[ill � /maxdom IlDln,.nb . � /.IPz /p: politician(

)

We assume that all the labels and discourse referents occurring in the lexicon are not proper labels and referents but only slots which get instantiated by newly created labels and referents when the words of the sentence to be processed are mapped to the lexical entries. The construction algorithm starts with building up the meaning components of the NPs. It combines the meaning of the determiner and the meaning of the noun by, first, identifying the argument of the noun with the discourse referent introduced by the determiner, and, second, by identifying the label of the noun with the label of the (restrictor of the) determiner. Then the discourse referents introduced by the determiners are mapped to the argument slots of the verb. For the second sentence of (3 I ) this gives us ( 33).

( 33) }1 : 11: problem(x) 13: preoccupy(x, y) 14: every y (141, 142) 141 : y 141 : politician(y) X

1 .

nun...,,

�

11

Fixing lminw,., is no problem. We always take the label of the (main) verb of the same clause. And the value of lmaxd.m gets instantiated with the label of the value of the DRS into which (3 3) will be incorporated. For a sentence like ( 3 1 .ii) this is (in general)' the label of the main DRS; call it IT. It is convenient to represent the 'structural' information given in the second column of ( 3 3 ) graphically in ( 3 4). The lines between the labels indicate the subordination relation. The meaning of � is obvious. By IT being the 1-element of the semi-lattice it follows that 11 � IT. Proceeding along the same lines gives us the structures in (3 s) for (3 I.i) and ( 3 I.iii).


politician:

1;: X; . � /.t IDlUI.,m

Uwe Reyle

1 39

(34)

h

� )\ )\ l u ===>

12

The graph for (3 I .i) is not connected, although we know that I1 and 1.� must be subordinate to IT. But adding this information does not help in cases where (3 I .i) occurs as subordinate clause. (36) Everybody believes that a problem preoccupies a politician. Here Inuu:dom of the subordinate clause will be identified with the label I,.1 introduced by the matrix verb. We therefore adopt a general principle which states that 1.

2.

Imin...o is always subordinate to Inuu:._m • and every label is subordinate to IT.

Then the structure for (36) has the following shape.


(3 5)

1 40


(37)

X

y

problem(x) politician(y) preoccupies(x,y)


For (31.i) we then get (37), in which 13 � 1T is not represented explicitly because this information is subsumed by, for example, 13 � 14 and 14 � 1T. Also lot � lT and lo2 � IT is implicitly contained in this structure. Note that (37) is not isomorphic to the DRS (3 8). To get the isomorphism and with it the existential force of the two indefinite NPs we must identify 1 1, 1.� and 13 with 1T. This identification will be an instance of a corresponding inferential principle. We therefore need not carry out this identification during the construction.

Uwe Reyle

141

2. 3 .2 Accessibility and semantic binding

The second problem is more syntax-dependent than the first one. It is best explained by considering restrictions on anaphoric linking. In Section 2.1 we used the notions of minimal, lmin•n•pb , and maximal positions, lmax•aaph , of NP meanings with respect to their anaphoric potential. (8) and ( 1 0) showed how we may use these positions to restrict the set of possible readings of a sentence. We expressed these restrictions on semantic bindino by means of conditions lmin•n•pb � 6 l and l � lmax•••p•• But we did not say how the parameters will be instantiated. This is what we will discuss in more detail now. First, we add the accessibility relation (Ace ) to our UDRS-language.

(i) l ' � l, or if (ii) there is a condition 1 "':

�

(1, 1 ") in D, and l '

�

l ".

By means of Ace we may automatically ensure semantic binding if we replace the conditions Imin•n•pb � 1 and l � lmax,,..,. by the single condition l ' Ace I, where l ' is the label of the discourse referent representing the antecedent of the pronoun. We assume the following lexical entry for pronominal anaphors like he, or definite NPs like the book. l:x l:x - r , where r is the discourse referent representing the antecedent by the condition l ' : r l' Ace l Inu.n..�,b � I

It is easy to check that this gives us the correct result for examples like ( 1 o): if we construct the UDRS for ( 1 0) according to the new lexical entry of the book, then the new structure differs from the one in ( 1 6) in that the conditions 11 � 17, 17 � Jo, 12:u and l2:u = y in ( 1 6) are replaced by the following condition set. (39) ls:u ls:U y I7 Ace Is 12 � Is =

(16) follows from the thus modified structure: 11 � 17 follows from 17 Ace Is and 12 � Is, and because 1o is the !-element of (L, �). 17 � I.,. A more interesting case is presented by example (8). Let us assume the following entries had already been constructed.


Definition Let% � �, D) be a UDRS, I and I ' elements ofL. We say that I is accessible from l ' (shorr: l Acc l '), if

142


(40) 1 . : � (111 , 11 2) 1 u :x 111:srudent(x) 12: � (12 1 • 122) 12 1:z 12 1:professor(z) �:lucky(x) 13:z recommends y to x 15:u has already read y 17:y 17:book(y)

(41 ) 14:u 14:u - x 1 11 Ace 14 15 � 14 To see the problem more clearly, we represent the structure underlying (4o) and (41 ) graphically. The problem is that (42) permits the addition of the condition 1 1 � 17, which assigns wide scope to a book, while keeping accessibility between 14 and 111• Although consistent and well formed, this addi tion does not represent any of the readings of (8): it is impossible to give wide scope to the head of the indefinite in (8) without at the same time assigning wide scope to the relative clause too. Thus the addition of 11 � 17 must be accompanied by a veto to add 14 � 111 or 15 � 111 to the structure.


Then the contribution of the definite NP the student will be the following.

Uwe Reyle 1 43

To solve the problem we must have some way of indicating the syntactic dependency of the student on a book. We will do this by admitting complex labels. We define complex labels as follows. Every label is a complex label. Ifl ' is a complex label and 1 a label, then 1(1 ) is a complex label. '

(43 )

ls(�(lu))

The effect of using complex labels is the following. Suppose we want to give 17 a specific interpretation by adding 11 1 � 17• Then we may do this only under the following proviso: when 111 � 17 is added, then the dependency of 17 on 11 1

8


Complex labels will be created whenever there are embedded sentences. Take the case of the complex NP every student to whom every professor recommends a book which the student has already read. Suppose the construction proceeds top down, dealing with every student first. As before, it introduces the condition set {11: � (11 1, 112), 111:x, 111:srudent(x) }. Also as before, 11 1 is taken to be the upper bound of the local domain of the relatj.ve clause, i.e. it instantiates its 1max•• m. But now every label 1 that is introduced within this local domain is marked dependent on lmax••m . We use complex labels and write l(lmax••J to indicate this dependency. Thus for a book we get the condition set {17(111):y, 13(111) � 17(111), 17(11 1):book(y) }. The whole procedure is applied recursively, as we go further down the tree, and we get (43). As we defined Ace , the only label accessible from 14 and 17 is lr. Only if we interpret the indefinite with narrow scope with respect to 11 does the set of accessible labels get enlarged. (43 ) makes this option explicit. l7(111) says that we are allowed to give 17 narrow scope with respect to 111, thereby establishing the corresponding accessibility. And 14(17(11 1)) says that 14 may have .narrow scope with respect to 17 and (by transitivity) also with respect to 111.

1 44


2.4

Application to a particular theo ry

We now apply our approach to Frey's scope theory. We make use of the syntactic structure postulated by the version of Government and Binding theory proposed for German by Frey ( 1990). The backbone of these structures is a right-branching tree as, for instance, the one in (4S) for the sentence

(44) Mindestens einen Bewerber habe ich fast jedem Mitarbeiter vorgestellt.

(4S)

CPIIP

� 1 ) 1) ,

M in

�]' ) �

e i n e n Bew rber

� J D�' I �

C/1

ymar

h be

ich

V'

DP

�� f.jed .Mitarb. D P

I

V

I

t1 vorgestellt

Work by Frey and Tappe (see Frey 1990 and Frey & Tappe 1 992) has shown that in German the relation between the actual positions occupied by the quantificational argument phrases8 of the verb and their traces are instrumental in determining the possible scope relations between the arguments. In (44), for example, mindestens einen Bewerber may have wide scope over fast jedem Mitarbeiter because the former NP c-commands the latter; and fast


must be stripped off, i.e. 17(111) is replaced by 17 and 14(17(11 1)) by 14(17). If, in addition, we require that a complex label l(l ') may be subordinate only to those labels it depends on, more precisely 1(1 ') ::;;; 1 " only if 1 ' ::;;; 1" or if 1' depends on 1 ", then the possibility to assign 14 narrow scope with respect to 1 1 is removed. The example shows that we need some means to indicate that labels such as 17, or 14, build a unit with 111 on syntactic grounds. In the remainder of this paper we will only consider syntactic units that are given by entire sentences. This will be important in connection with sequences of sentences. They pose the problem that a quantifier in sentence n cannot take scope over elements of earlier sentences. Although this can be achieved by using complex labels we decided to deal with it by conditions like a(11, 17, 14), saying that all that is dominated by the three arguments results from one syntactic unit, in this case from sentence (8). This is a natural move if we want to formulate the language ofUDRSs and their deductive component independent of any natural language syntax.

Uwe Reyle

145

jedem Mitarbeiter may have wide scope over mindestens einen Bewerber because it c-commands the trace of mindestens einen Bewerber. If on the other hand mindestens einen Bewerber is not moved into the 'Vorfeld', then it cannot take wide scope over any of the other NPs. This is shown by the non-ambiguous sentence (46) Ich habe fast jedem Mitarbeiter mindestens einen Bewerber vorgestellt.

(ich, fast jedem Mitarbeiter, mindestens einen Bewerber) and the order of appearance of the NPs is

(mindestens einen Bewerber, ich, fast, jedem Mitarbeiter).


Frey and Tappe assume that all the argument phrases of German verbs (including their subjects) are dominated by the verb's maximal projection, vmax. If the arguments have been moved from their so-called base position they leave traces that are co-indexed with the moved arguments (compare t1 in (45)). The movements that are relevant for the determination of scope ambiguities are, however, restricted to those occurring within-what is called-the local domain of the moved NP. This is indicated by the non-ambiguity of examples like Fast jeden Besucher meinte mindestens einer babe Maria gekannt, in which the local domain of the NP fast jeden Besucher is-roughly speaking the complement structure of the matrix verb. In GB-terms the precise defini tion is as follows. The local domain of an expression a is defined as the minimal complete functional complex, containing the licensing element of a as well as the lexically realized governor of a , where a complete functional complex is defined as the minimal maximal projection in which all 9-roles are realized. Given the notion oflocal domain we are ready to state Frey's scope principle. Suppose La is the local domain of an expression a . Then a may have scope over an expression f3 if either a c-commands f3 or one of f3's traces. Consider the subtree which results from (44) by eliminating all traces. Then we can apply the construction algorithm as we have developed it without any substantial changes. This gives us a representation that does not yet contain any restriction on scope relations. At this stage all readings are still possible. Only if we add more information about scope restrictions will the set of possible readings be reduced. The restrictions are encoded in the traces, which keep score over the NPs movements. There are several ways to implement an algorithmic procedure that calculates these restrictions. The easiest way is to base the procedure on a comparison of the list that represents the arguments of the verb according to its basic order with the order of their actual appearance.9 . In the case of our example (44) the basic order, BASIC, is represented by

1 46


{ldat :::; lnom}·10

3

S AMPLE D E D U C T I O N S

The general architecture of the proof system for UDRSs is borrowed from the DRS-Calculus presented in Kamp & Reyle ( 1991). In both systems the most basic type of proof consists of a series of applications of inference rules , which permit us to extend the representation of the premisses, but which do not involve any sub-goals. These proofs are called directproofs . They involve one rule ofproof, according to which a goal is proved if its representation is embeddable into the (extended) premiss set. We first develop an idea of how direct proofs are to be performed and then consider other rules of proof, which will allow us to prove goals by establishing intermediate goals.


The task of the construction is to add conditions of the form 1 :::; 1 ' if 1 must have narrow scope with respect to 1 '. Consider (44). There the order of actual occurrence differs from BASIC. We proceed from left to right and consider that the NP marked accusative, mindestens einen Bewerber. If it also figured as the leftmost element on the list of basic order, we could infer that it has wide scope with respect to all other arguments that (are quantifiers and that) it precedes (i.e. c-commands) on this list. Since it does not, we know that it has been moved from its basic position. With regard to scope relations, this tells us that it will, from its landing position, c-command all of them, so that there will be-besides the narrow-scope reading-a wide-scope . reading of the moved argument. This means that neither lace :::; ldat nor I." � l nom will be added to the UDRS under construction. Here I." is the label of the accusative NP mindestens einen Bewerber, ldat the label of the dative fast jedem Mitarbeiter, and lnom the label for ich. The next step is to delete the argument that has been processed, i.e. mindestens einen Bewerber, from BASIC, and to proceed with the next element appearing in the sentence, namely ich. We find that it is the first element of BASIC. Therefore it must have wide scope over the other quantifiers on the list, namely over fast jedem Mitarbeiter. So the condition ldat � l nom will be added. Of course in the case ofich this addition might be redundant, but if we replace ich in (44) by niemand it will be needed. Finally, the other unmoved element (fast jedem Mitarbeiter) is analysed. After the deletion ofich it turns out to be the first element ofBASIC, and would, therefore, trigger the introduction of a further scope-restricting condition; but because it is also the last element of BASIC, nothing is to be added in this case. What we end up with is the set of scoping conditions:

Uwe Reyle 3.1

147

Inforence rules

In this section we consider the fragment without disjunction and identity. The two inference rules needed are non-empty universe (NeU) and detachment (DET). NeU allows to add any finite collection of discourse referents to a DRS universe. It reflects the assumption that there is of necessity one thing, i.e. that we consider only models with non-empty universe. DET is a generalization of modus ponens. We give the 'DRS-formulation' ofDET.

It is useful to have in mind the picture depicted in the detachment diagram.

Detachment

According to this formulation DET is restricted to operate only at the level of the 'main' DRS K. It is, however, correct to apply DET also to subordinate DRSs K ', as for instance in the proof of the argument shown in the diagram. This proof is carried out very easily ifDET is applied a first time inside the sub-DRS X

P(x)

I "�") I I P�y) I I q;,) I =>

=>

K'

r

I "�') I [;J [;J Q( r)

=>

=?

Q ( t)

=?

B


DET Suppose a DRS K contains a condition of the form K1 � K2 such that K1 may be embedded into K by a function £ Then we may add K 2 to K, where K2 results from K2 by replacing all occurrences of discourse referents of UK, by new ones and the discourse referents x declared in UK, by f{x).

1 48


......

(i) ifl: � (11, 12) occurs in K', then f(1): � (f(11), f(12)), (ii) ifl: V (11, 12) occurs in K', then f(1): V (f(l1), f(l2)), (iii) ifl: ....., 11 occurs in K', then f(1): ....., f(l1). Consider the structure in (47) together with the following conditions.

(47)

(48)

11:u 11:applicant(u) l u :x 111:applicant(x) 14:z introduce x to y

lr:v 11:employee(v) 12l :y 121:employee(y)

lr:w 1r:director(w) 131:z 131:director(z)


K ', and a second time within the main DRS. Without such an extended application of DET, the proof is much more involved. Note that extended applications of DET may be applied in cases where not all premisses required for the applications in a subordinate DRS K ' belong to this DRS. In fact, in our example none of them does. DET can also make use of conditions and discourse referents that occur in a DRS superordinate to K '. In Kamp & Reyle (1991 ) it is shown that extended inference rules are correct. To generalize DET to 11 underspecified structures we define an embedding f of a UDRS into a UDRS to be a function that maps labels to labels and discourse referents to discourse referents while preserving all conditions in which they occur. We assume that f is one-to-one when f is restricted to the set of discourse referents occurring in proper sub-universes. Discourse referents occurring in the universe associated with 11 may be identified by £ We do not assume that the restrictions off to the set of labels is one-to-one also. But f must preserve , � and V, i.e. respect the following restrictions.

Uwe Reyle

I

49

In this configuration both antecedents, I11 and I31, are embeddable into Ir. And this property will be preserved under any disambiguation. We give the three readings of(47) in the form of DRSs. (49)

applicant( u ) X

applicant(x)

applicant(x)

l

:

=?

=?

d;cec oc(')

appli can t( u )

X

w employee(v) director(w)

y employee(y) z introduce x to y

�

v

u

w employce(v) director{ w ) y

=?

crnploycc(y) �

z dircctor{z)

ilppl i cil n t ( u )

c

11

l

v

mp o

y

\\'

ce

=?

z introduce x to y

( v ) d i rector(w)

z

\'

d i r

director( z' )

y' cmployce(y')

' z

�

d i recto r (z ) '

( 5 4) �

( s s)

=>

' z

introduce u to y'

y' employee(y') ' z in t rod u ce u to y'

h

� !\ ' [ 7 l'

l'

.

� I;,

�'

4

I; I :y' I ; I : employe:(y')

1 ; 1 : z' l'3 1 ·d - ( z') l'4 ·. z' ,· ntroduce u to y' . 1" rector


( s 3)

-

y' cmp\oyce(y') z' i nt rod uce u to y'

.Uwe Reyle

1s1

Let us add (55) to (47) (plus (48)). Then (56) is equivalent to (47) (plus (48)). That this is indeed the case is seen as follows. Obviously (47) follows from (56). Conversely, suppose (47) is true and (56) false. Consider any disambiguation (s6)

=


that makes (47) true. In case it is (49) or (so) we choose the same disambiguation steps in order to check the truth of (56). Suppose it turned out to be false under that reading. Then the applicant u would be a counterexample to the truth of (47) (under that reading). A contradiction. In case the disambiguation is (5 I ) it is sufficient to convince ourselves that the extension of (5 I) by (54) is equivalent to (57), in which �52) V �53) abbreviates the disjunction between (52) and (5 3). Note that this equivalence only holds because conditions .of the form K1 � K2 are monotonically increasing in their second argument, i.e. they allow for inferences like K1 � K2 1- K1 � K;, where K; K�\({ ), ConK-,) for some . ConK-, � Conx, . This is an important restriction to the applications ofDET in the framework ofUDRSs: DET may only be applied 'in the context of' implicative conditions, or monotone increasing quantifiers. But what does 'in the context of' mean? Suppose we applied DET to (s s), yielding (5 8). Then we see that this application should be forbidden, because (58) is not equivalent to (s s). Thus (ss) provides such a context. Another structure that provides a context in which not all applications of DET are allowed is (47). We have seen that no complications arise if DET is applied with respect to applicant(x). But if we applied it to director(z) we would get the same problems as we had with (5 8). We thus say that an application of DET to some condition I: � (11, 12) is admissible if no

1

52

Dealing wirh Ambiguities by Underspecification

( s 7)

u v w applicant(u) employee( v) director(w) K(s2)

V

-

z

:=} X

applicant(x)

( ss)

y' employee(y') introduce u to y'

:=}

�

y employee(y) z introduce x to y

Ir

I I

I�

�

I

1;1

I'4

disambiguation (with respect to the a-condition to which 1 is subordinate) has the effect of embedding 1 into the scope of a non-monotonic operator. If 1: => (11, 12) allows for an admissible application of DET y;e also say that 1: => (11, 12) is not in the context of a non-monotonic operator. There is a further difficulty we have to discuss before we come to the rules of proo£ Consider the following argument. ( 59) There is a problem. John is a politician whom every problem preoccupies. . Every politician whom a problem preoccupies proposes a solution for it. John proposes a solution. The difficulty arises because the meaning of the NP a problem in the third sentence of the premiss set can be introduced as being subordinate to the


director( z )

z

K(s3)

Uwe Reyle

I 53

rescrictor of the quantifier every politician, or it can be introduced at top level. For the sake of simplicity assume that j is the referent for John and the discourse referent for the pronoun is the one for its antecedent. Then we . have the following readings of the premisses of ( 59). Let us consider the DRS proofs for the two cases and see what happens. First, consider (6o). In order to proof the conclusion, we infer the condition preoccupy(u, j) by means of the first implication, and then apply DET to add (62) to the main DRS of (6o). From this it follows thatJohn proposes a solution. (6o)

J u

X

=:;.

proble m ( x )

prcoccu p y ( x j )

y

X

z

politician ( x ) problem(y) prcoccupy(y,x)

solution ( z ) p ro p o sc( x , z ) for( z , y )

=:;.

J

ll

\'

problc1ll ( 11 ) po l i t i c i a n ( j ) problem ( \' )

X

problc m ( x )

=:;.

prcuccu py( x ,j ) z

X

politician ( x ) p reocc u p y ( v , x )

=:;.

sol u tion ( z ) p roposc( x , z ) for(z,v)

z' solution(z') propose(j ,z') for(z',u)


problem( u ) pol itician(j )

1 54

Dealing with Ambiguities by Underspecificarion z' solution(z') propose(j ,z') for(z',v)

3 .2

Rules ofproof

Rules of proof are used to prove goals by establishing sub-proofs. The system of Kamp and Reyle (Kamp & Reyle 1 99 1 ) contains two rules of proof One is the rule of conditional proof (COND) which allows us to prove a DRS-condition of the form K1 � K2 by adding K 1 to the premisses and deriving K2• The other rule is Reductio ad Absurdum (RAA) according to which a DRS K is shown if a contradiction can be derived from adding -.K to the premiss set. We will see that-although we might adapt these two rules without any substantial changes to UDRS proofs-we need a further principle that allows us to detect inconsistencies of UDRSs. But before we come to this we have to decide how to deal with ambiguities that occur in embedded positions as, for example, in antecedents of conditional sentences, or in relative clauses that are attached to restrictors of universally quantified, or negative NPs. There is the question of intuition: do we understand a sentence like (64) Every nurse, who showed no doughnut to every boy is brave. as saying that (
(69)

�•'\, ,. 7'

1-

I '2

y' doughnut( y ' ) ate(x',y')

not entailed by that reading of the antecedent in which --. has wide scope over

=>.

So, let us try to apply weak RAA first. We formulate weak RAA in analogy to weak COND, i.e. we apply standard RAA after having given wide scope to the subordinate level in which the negation occurs. It thus transforms (66) into (7o). The premiss set of(7o) is, however, not inconsistent because we may choose che reading (7 1) for its first condition, and then consider a model with no boys. Let us reconsider what we did: we started our computation with an ambiguous representation Q. We were confronted with the choice to apply


(68)

Uwe Reyle

1 S7

I FI � I ; ,

I )\

t;l ==:::} 1 ;2

fal se

J'2

bo ( x )

y ..., doughnut(y) touched( x,y)

weak COND before weak RAA, or vice versa. We made our choice and then failed (in each case). The problem is that when we try the other possibility we start from scratch again, i.e. from the premiss set of (66). All we have learned while pursuing one possibility is thrown away before the second try. This is not reasonable. The reasonable course of action is to have a backup task which can make use of the work already done. Thus we can start with goal Q, try to achieve it some way or other, and if one way proves to be impossible, switch back to goal Q, using the results already obtained. The rule we just described is called RESTART rule (Gabbay 1 98 5). To illustrate the rule consider once more (68), which we obtained after applying COND to (66). Suppose we continue this subproof by RAA, yielding (72), and then apply RESTART, replacing false by the original goal, i.e. the one in (66), followed by another application ofRAA. Then we get (7 3), the premisses of which are clearly inconsistent. Given RESTART we may adopt the formulations of weak COND and weak RAA that correspond to the moves from (66) to (7o) and from (66) to (68). You might think that we can do it without RESTART if we take the weak version of COND together with the standard version of RAA. Then we could transform (66) to (74), which can be shown to succeed if we add the information that eating implies touching. We will prove later that the standard version of


I; I

=>

-

7

{ 2)

I

.

.. : . e�.snby Under eci= �_:_ sp-fic_:: a n·� o n�-------

1 s s oeartng with-� Amb·�gm

__

'::.:.

i

A

h =l' 2

I I'

I

/\

� In

_

3

l'fr

"\7'

false

f-

1;

(73 )

I T -I'3 2

h =l"

( '

w

T

I'

I'

l r

1\

(\l

1, .

-c;

f- false

I"2

7 (4 )

f- fa lse


2

Uwe Reyle

1

S9

RAA is in fact derivable from weak COND, weak RAA and RESTART; and we will show completeness with respect to weak COND and standard RAA. To decide between the two options consider the argument (7s).

(75) If a man kisses a woman then he touches her. No man is touching no woman.

No man is kissing no woman.

-.

c

-.


We assume for the sake of the argument that the two indefinite NPs of the first sentence are interpreted non-specifically. Let%; be the representation of the sentence i ( 1 � i � 3); and let -.X) be the reading ofX; (2 � i � 3) in which the first negation has been assigned wide scope and -.X; for the second. The proof that uses the standard version ofRAA assumes that -.Jf"3 is true. By means of two other RAA sub-proofs it is shown that under this assumption the negations of both the readings of the conclusion, i.e. ( Jf"l) and -.(--x-n, are also true. From this the truth of %� and X� will be derived by RAA. By means of the first prerniss, %1, it can be inferred that.%1 and .Jt1 are true. But this is-as we will discuss below-a contradiction to.%2• The proof with the weak version ofRAA goes as follows. Its first application chooses a reading of the conclusion, in which one of the two negations has maximal scope and then adds the UDRS expressing that reading without -. to the data. Suppose the reading chosen is -.Jtj, then %� will be added. (Note that two RAA sub-proofs were necessary in order to come to this point, when we used strong RAA.) At this stage we RESTART and add.%� to the data. The rest of the proof proceeds as above. We leave it to the reader to decide which proof he prefers, and end this section with a discussion of what we need to discover inconsistencies.

1 60


(77)

(7R) l 2 � lo 14 � lo

11 � 122 1 3 � 1 12 1 3 � 142

(79) 1 2 � lo

14 � 122 1 1 � 122 13 � 112 13 � 142


Consider the structures (76) and (77) of Section 2 (repeated here for convenience). Recall that (76) represents the set of readings (14, 12, 1 1 ), (12, 14, 1 1 ), and (12, 11, 14), whereas (77) stands for the disambiguations (12, 14, 1 1), and (12, 1 1, 14). Suppose now that some data contains (76) and the negation (of some alphabetic variant) of (77), i.e. we add the structure that results from (77) by replacing lo by 10: -. Io to (76). Then this set of data is equivalent to the reading given by (14, 12, 11 ). Let us sketch the proof that this reading follows from the data. It is by RAA: we first add the negation of the goal to the data. Then we have to show a contradiction. In this case the contradiction is manifest in the fact that there is no possible order of the quantifiers left. To establish the contradiction we have to make some calculations on the structures. This will be done along the following lines. Assume that the structures (76) and (77) are described by (78) and (79), respectively.

Uwe Reyle 1 6 1

Let u s call .'T�) - { I :s;; 1': .2" F= I :s;; I') the theory of$. Then we calculate the structural difference between (7S) and (79) by I.

taking the set theoretical difference between the theories of the two structures, and 2. adding the negation of each formula in this set to the information about the structure. The theory of(7S) is (So). (So) 12 1 :s;; 12

111 :s;; 12

13 :s;; 11 2 13 :s;; 142

13 :s;; II 13 :s;; 14

13 :s;; 122 13 :s;; lo

13 :s;; 12

and the difference to the theory of (79) is ( S I ). (S I ) 14 t :s;; l22 142 :s;; 122 14 :s;; 122

14 t :s;; l2 142 :s;; 12 14 :s;; 12

In the same way we calculate the structural difference between (79) and the goal. This gives us (R2). (S2) 12 1 :s;; 142

122 :s;; 142 12 :s;; 142 l 1 1 :s;; 142 112 :s;; 142 II :s;; 142

12 1 :s;; 14 122 :s;; 14 12 :s;; 14 l 1 1 :s;; 14 11 2 :s;; 14 II :s;; 14

Now negate each of the formulas in (S 1 ) and (S2) and add it to (7S). A consistency check will show that we have obtained an inconsistent set. There is no structure .2" satisfying all the formulas in the thus extended (7S). This completes the proof The notion of structural difference will play an important role as we go on. It generalizes the traditional notion of inconsistency, according to which a UDRS would be inconsistent if it contained conditions of the form lr:y, lr:-.1, and l :y', where y ' is some alphabetic variant of y. When we build up the structural difference between two structures%1 and %1. we have to distinguish two cases. In case the structural difference is empty, the constant false will be added to the data, making the inconsistency overt.


1 22 :s;; 12 141 :s;; 14 142 :s;; 14 1 1 1 :s;; 1 1

12 1 :s;; lo 122 :s;; lo l.u :s;; lo 142 :s;; lo 1 1 1 :s;; 122

162

D�aling with Ambiguities by Underspecification

And in case the structural difference is given by a non-empty set we need a consistency check in order to find out if the resulting structure is an inconsistent UDRS. To do this we need deduction rules which reason about the partial order of.$ and the conditions of the form a(l1, . . ., 1n ). We will call them structural rules. We will not state them explicitly. But it is easy to see how they might be implemented. For example, we might interpret conditions of the form a(l2, 14) as abbreviations of the following clause. 14 � 12 v 12 � 14 We have to show that this set together with is inconsistent, which is straightforward. 1 4

2

REPRE SE N T AT I O N , ME A N I N G A N D D E D U C T I O N

The aim of this section is to give a precise definition of the language LvnRs of UDRSs as well as of their truth conditions. The definition ofLvnRs will tum out to be more complex than the structures we considered in the previous sections suggested. There it seemed sufficient to define a UDRS to be an ordered pair (Z, @ ), with .$ (L, �) an upper semi-lattice with 1 -element, and @ a set of ' conditions of the following forms. =

(a) l:x, where 1 is a label and x a discourse referent. (b) l:P(x1, , xn), where 1 is a label, x1, . . ., xn are discourse referents and P is an n-place predicate. (c) 1: ...., 11, where 1 and 11, are labels. (d) 1: � (11, 12), where 1, 11 and 12 are labels. (e) 1: V (11, , 1n), where 1, 11, , 1n are labels. (D 1:a(11, , 1n), where 1, 11, , 1n are labels. •

.

.

•

•

•

•

•

•

.

•

•

•

•

•

This simple characterization was sufficient up to now, because the construction procedure produced only UDRSs obeying further well-formedness conditions. Now that we are going to give an abstract definition of UDRSs we must make these further restrictions explicit. The first requirement we want our UDRSs to meet is that the expressive power of LunRS should not exceed that of first order predicate calculus. We, therefore, do not allow structures containing conditions 1: � (11, 12) and 1: � (13, 14) together with some label 1 ' such that 1 ' � 12 and 1 ' � 14. Such structures would correspond to a language that allows for finite partially ordered quantifier prefixes (c£ Barwise 1 979; Westerstahl 1987). To formulate further restrictions let us introduce some terminology. If .X


--.12 � 14 and --.14 � 12

Uwe Reyle

163

contains a condition o f the form 1: --. 1 1 , 1: � (11, 12), o r 1 : V (11, , 1.), then 11, , 1. are called parts ofl. The subset oflabelled conditions of the form 1: � is •

•

•

• • •

called a

of the UDRS, denoted by D1•

node

scope

is a function from the set of

labels L to L. It associates with each node a scope of this node. Linguistic evidence suggests that in the case of disjunctive nodes (see below) the value

(iii)

which the function scope should associate with this ncide is not determined by the node alone, but scope depends in this case on additional contextual factors such as, for example, the linear order of the surface structure. Our definition of

scope

(iv)

scope(l) = 11, if D1 = {1: ....., (11)} scope(l) = 12, ifD1 - {1: � (11, 12)} scope(l) = 1; for some (contextually determined) 1; (i � {1: v (ll, . . . , 1.)} otherwise scope(l) - 1

I,

. . . , n), if D 1 =

Recall that we restricted the operation ofl1 taking scope over some sisters to those sisters which are part of the sentence meaning to which 11 contributes.

a ,

, 1.) and said We accommodated for this by conditions of the form 1: (l 1 that these conditions identify the set of daughters 11, , 1. of some node 1 • • •

• • •

which 'belongs to' one single sentence meaning. We now require this identification to be unique in the sense that any label may be subordinate to

a

two different -conditions only if these two conditions are themselves subordinate to each other (see clause (v.a ) of Definition I . Further uniqueness

)

requirements are that complex conditions, i.e. conditions of the form (c) to (f) above, never share any arguments (see (v.y )), and that each daughter of 1 is connected to 1 by some complex condition (see (v./3)). We say that a node D1 is scope-bearing if it has one of the fonns (i) to (iii), i.e. if scope(l) f= 1.U IfD1 is a scope-bearing node we call 1 a scope-bearing label. For convenience, if scope(l) =1- 1, we define res(1) to be the set of daughters ofl that are distinct from scope(l); otherwise res (l) is empty.

Definition 1 : An underspecifled scope , res ), where

DRS (UDRS) is a structure

X - (..Z'x,

Dx,

(a) F ·is a pre-partial ordering of labels (Lx, �. 1T) with 1 � 1T for all 1 e..Z'X. Moreover, the structure ({�] : 1 e..Z'x}, �. [1T]), where �] = {1 ': 1 ' � 1 /\

1 � 1'}. is an upper semi-lattice. (b) Dx is a finite set of labelled conditions of the following types

-

h, where 1 is a label and x a discourse referent - l:P(x1, , x.), where 1 is a label, x1, . . . , x. are discourse referents and P is •

•

•

an n-place predicate

- l:false - l: --. 11, where 1 and 11 are labels. D


(i) (ii) (iii)

ignores these subtleties.

1 64


- 1: � (11, 12), where 1, 11 and 12 are labels. - 1: V (11, , 1n), where 1, 11, , 1n are labels. - l:o(l1, , 1n), where l, 11, , In are labels. •

•

•

•

•

•

•

•

•

•

•

•

The last four types of conditions are called complex, the first two atomic conditions. (c) scope and res are determined as above. $x and ox are subject to the following restrictions.

•

.

•

•

•

.

•

•

•

• • •

•

•

•

•

•

•

.

.

•

•

•

•

• • •

The goodness condition guarantees interpretability. Suppose, for example, 1 is a scope-bearing node such that there is some l ' with l ' � scope(l) and l ' � res(l). Suppose further that 01. contains free variables x and y which are declared in res(l) and scope(l), respectively. Then we have a structure which does not correspond to a DRS in any natural way. (Recall that with respect to DRSs � means nestedness!) We therefore rule out such structures by goodness. In view of the obvious translation from DRSs to UDRSs we will feel free to talk of DRSs as if they were represented in the language of UDRSs. The translation induces a number ofsyntactic notions connected with UDRSs. First, each label I of a UDRS has its set of locally declared discourse referents , which we


(i) ifl: ...., 1 ' E D , then l � l ', and l ' is a daughter ofl in.2"X; x (ii) ifl: � (11, 12) E ox, then 11 � 12 and 11 and 12 are daughters ofl in.2"x; (iii) ifl: V (11, , 1;) E ox, then l; � lj for all i,j - I , , n with i � j, and 11 to 1" are daughters ofl in.2"x; (iv) ifl:a(l1, , 1n) E ox, then 1; � lj for all i,j - I , . . ., n with i � j, and 11 to In are daughters ofl in .2"x; (v) Uniqueness: ( a ) Suppose 1:a(11, , In) E ox, k:a(k1, , km) E D.X: Then either k � l , l � k, or each path that connects k and l goes through a label k ' such that k � k ' and l � k '. ({3) Ifl has a daughter 1 ', then l ' is not part ofl iff l ' occurs as argument of some a-condition. (y) Suppose {11, , 1n) and {k1, , km) are the argument sets of some complex conditions. If for some k;( I � i � m) and lj( I � j � n) k; � lj, then (11, , 1n) n {k1, , km) is empty. (vi) First order property: suppose 1:¢ and l ':¢ ' are negative, implicative, disju?ctive conditions, or a -conditions, and suppose there are daughters l; and lj of arguments ofl:¢ and l ':¢ ', respectively, such that {l;, lj ) has an infimum. Then l ' � l. (vii) Goodness: No l is subordinate, i.e. �. to two different labels of the same complex condition.

Uwe Reyle

165

also call its local universe, and its set of (DRS-)conditions . Second, we generalize these notions to sets of discourse referents and DRS-conditions of some 1 which do not only include the universe and conditions local to 1 but also universes and conditions local to any 1 ' which is subordinate (or superordinate) to l. Finally, we will define the sub-UDRS of a UDRS dominated by some label to be the UDRS containing all labelled universes and labelled conditions subordinate to l.

Definition 2.:

=

(b)

Xf IJ

U

.!f·Y>- J • ..;; J A I ..;; l '

Xf.

where X e {U, C, D, U, �. D).

Whenever there is risk of confusion we will omit the superscript .%.

Definition 3: (a) The set of free variables FR(D1) of some node is defined by (i) FR(l:P(x1, . : ., x n )) - {xi , . . ., xn} (ii) FR(l: --, (11)) - FR(ll) (iii) FR(l: '* (11 , 12)) - FR(l 1) v (FR(l2)\(Ut .) (iv) FR{l: V {11, . , ., 1n)) = FR{l 1) V V FR{ln) (v) FR(l:a (l1 , . . ., 1n)) = { } (vi) FR(Dt) = uy � 1 , 12)}, such that either k - I.;., or D1., = { a (k1, • . •, kn)} and k k; for some i, l � i � n. Let XR; be defined as in DET. Then the CP-proof triggered by this goal is for some possibly empty R l s R1 XvX'1, vX�· 1-- XI,. where XI, results from Jfi, by capturing all runaways from 1; w.r.t. a (k t , . . ., kn)· =


Rules of proof are used to prove goals by establishing sub-proofs. The system of Kamp & Reyle (I 99I) contains two rules ofproo£ One is the rule of conditional proof (COND) which allows us to prove a DRS-condition of the form K 1 � K2 by adding K1 to the premisses and deriving K2• The other rule is Reductio ad Absurdum (RAA) according to which a DRS K is shown if a contradiction can be derived from adding ...., K to the premiss set. We have already formulated the principle DIFF that allows us to detect inconsistencies ofUDRSs. What is left is to give precise formulations of the weak versions ofCOND and RAA as well as the strong version of RAA. Recall that the difference between the strong (or standard) and weak version ofRAA is that the strong version can be applied to any goal, whereas we allow the weak version only to be applied to negative conditions occurring either at top level or in subordinate positions.

1 76 Dealing wirh Ambiguities by Underspecificarion

RAA

We formulate weak in analogy t� weak COND, i.e. we apply standard RAA after having given wide scope to some subordinate label.

weak RAA:

...., I t ), such 1 � i � tL

Suppose :K ' is a goal containing a negative label k, i.e. Dk {k: l.J., or D1-1 { a(k1, , k, } and k k1 for some i, that either k

-

-

. . •

)

=

-

The RAA-proof triggered by this goal is :K u :K " fresults from% ' by capturing all runaways from 11.

false,

where X "

1985).

(sub)computation by replacing the current goal with the original one.

RESTART:

l

Suppose we have :K f-X '. Then X ' may be replaced by :K ", where x · is the original (or some previously introduced) goaL It is convenient to introduce the following conventions: let �X - ({11), {11: -.1)), where 1 is the top node of:K ; and let FALSE be the UDRS containing only the condition 11:false.

Reductio ad Absurdum:

Suppose :K' is a goal. The RAA-proof triggered by this goal is :K u �

:K'

f-

FALSE.

Theorem

1 : The rules are sound.

We sketch the proof of the theorem for DET: Let 11:a(k1,

11) be the conditions of .%

.

.

.

, k, ) and k1: � (11,

relative to which DET is applied. The proof is by induction on the number ofreadings of:K . We distinguish the following cases. The a -condition is of the form 11:a(k1). Here no ambiguities are involved

and the correctness follows from the correctness of the DRS-version of DET. Suppose

a

has more than one argument. We have to show that for each

model M and each disambiguation a ifM I= �a(.%0) there is some disambigua tion a ' such that M I= �a'(g(X j,)). We distinguish the following two cases. (i) a assigns wide scope to

k1: => (11, 12) over all elements of Ri· By condition

•

(ii) ofDET Jf"R; 1- .%�; must hold for every Ri � R1 Because :KR; has less


To compensate for the failure in both cases we need a further rule. It is called RESTART rule (introduced in Gabbay RESTART allows to continue any

Uwe Reyle

I 77

readings chan X M is also a model ofX f. The embedding f chat verifies �0(X0) in M may now be extended to an embedding f' that verifies �a·{g(Xj)) in M: this is shown as in the proof of DRS-DET. Because by assumption g(X i,) does not contain any free variables declared in R1 the existence of f' is independent on the particular choice of R ;. Therefore

M I= �a'{g{Xi)) for all R;.

A similar consideration gives us the soundness of ONE and

MTP. To prove COND and RAA one has to show that the structure X,+s+t has a model if X, has {see Definition q). Again we have to leave the details to the reader. The soundness of weak RAA and Restart follows from the following theorem. Let &1 be the deduction system with the rules DET, COLL, NeU, COND, DIFF, EFQL, weak RAA and Restart, &2 the system with the rules DET, COLL, NeU, COND, DIFF, EFQL and RAA.

Theorem 2: X 1-St % ' iff X 1-Stl % ' I

It is easy to see how applications of strong RAA can be eliminated. The effect of applying strong RAA to % 1-jj', % ' is X u �X' 1-St, FALSE. Assume that this can be shown without further applications of strong RAA i.e. X u 2-, X ' 1-St, FALSE. Consider % 1-51', %'. We first add a show line show: 2..., X '. To prove this we may apply weak RAA, yielding % vX' 1-51', FALSE. We now apply RESTART and immediately succeed. This allows us to cancel the show line and get % v 2-, .Y{" ' 1-.91', %', which also succeeds because X v 2-, .Y{"' 1-St, FALSE succeeds by assumption. We end this section with a theorem that allows us to conclude that our rules are complete. ,

Theorem 3: X --1 1- V � "(Erl(x) n(l:T)

The proof mainly uses RAA and DIFF and is left as an exercise for the reader.

Theorem 4: The Rule systems &I and &2 are complete.

Because our rule system is a generalization of the system in Kamp & Reyle ( 199 r ), this follows from the completeness ofKamp & Reyle's proof system and the preceding theorem.

•


(ii) Suppose any ocher argument kj of a is assigned wide scope by a . Ifkj E R1 we argue as above. Assume kj E R2• Then we consider the disambiguation a ' of g(X i,) that also assigns wide scope to kj. By induction hypothesis we may correctly add the result of a DET application to scope (kj)· On the other hand, kj must be a monotonic operator by assumption, which allows us to show �a'(g(Xj,)) as exemplified by (57).

1 78 Dealing with Ambiguities by Underspecification

Acknowledgements Special thanks go to Hans Kamp. His suggestions and comments, after struggling through an earlier version of this paper, have greatly improved it. Research partially supported by DFG through a grant to visit Imperial College during the academic year 1990/91 . UWE REYLE

Received 0 1.00.92 Revised version received 16. 1 1 .92

Institutfiir Maschinelle Sprachverarbeitung Universitiit Stuttgart Azenbergstr. 1 2 D-7000 Stuttgart 1 Germany

1 See Gabbay (1991). 2 In Fenstad et a/. (1987) the problem is approached from a somewhat different perspective: In order to get the non specific reading of a book they analyse the NP Every professor who recom mends a book as binary quantifier. 3 In this paper we do not consider scope ambiguities with respect to tenses, nega tion, sentential connectives or adjuncts. 4 From a formal semantical point of view there is no difference between (lminwJ and (lmin...,.)-positions. Both restrictions aim at the same thing: to construct proper DRSs only, i.e. DRSs that do not contain free discourse referents. Exam ple (6) shows that there are also non trivial cases for (i). (6) Every professor who works with an industrial parmer has a beautiful secretary. The (lmin_,)-position of an industrial partner with respect to the verb works

guarantees that the content of the indefinite is not introduced in the consequent box of the complex condi tion triggered by every professor. The same principle guarantees that the related example

(7) A manager of every company has a beautiful secretary. is translated into a proper DRS. For the dr-theoretical treatment of general quantifiers, see Kamp & Reyle ( 1993)· 6 It is important to note that we do not use disjunction to represent ambiguities. Using disjunction we can represent the meaning of (2o) by combining (23) with

(*) (12 - 112 1\ 11 - 132) V (12 - 132 1\ 13 - 112) This use of disjunction would collapse our approach to a description of the DR theoretical construction algorithm which is suitable for efficient imple mentation. The labelled DRS language would serve no purpose beyond point ing at some similarities between labelled DRSs and familiar data structures in computer science. 7 We are not considering cases of modal subordination, a discussion ofwhich can be found, for example, in Roberts (1987)8 By 'quantificational' argument phrase we understand a real generalized quan tifier. This means that indefinites are


NOTES

Uwe Reyle nor quantificational and rhus nor sub jeer co rhe restrictions discussed. 9 We shall nor consider rhe role of the !-Subject in this paper. 10 In Frank & Reyle {I992) an HPSG

and chen reason by cases. Ifwe did it this way the data would have rhe following form.

(1,, I2, I1) v (I2, I,, I1 ) V (12, I1 , I,) {(12, I,, I1) V (12, I 1 , I,))

grammar is presented for a fragment of German that deals with quantifier scope ambiguities triggered by scrambl ing and/or movement. The syntax

I2

�

To proof the goal we must prove it

I3

separately from each disjunct (plus the negated formula). We would therefore have to consider three sub-proofs. When we deal with plural a node of rhe (1:¢ {X)), where ¢ (X) is some form 01 condition with a plural discourse refer ent X occurring free in it, will also be considered as a scope-bearing node. See Section 3 . 1 . W e defined rhe theory .7(-Z') o f .z' a t rhe end o f the previous section. -

I4 I5

RE FERENCES Barwise, Jon ( 1979), 'On branching quanti fiers in English',]. Phil. Logic , 8, 47-80. Fenstad, ]. E., P.-K. Halvorsen & ]. van Benthem (1 987), Situations, Longuage and Logic, Reidel, Dordrechr. Frank, A. and U. Reyle

( 1 992), 'How to cope

with scrambling and scope', in G. Gertz (ed.), CONVENS 92, Springer, Berlin. Frey, W. (I 990), Syntaktische Bedingungen fur die Interpretation , AIMS No. OI-90, Stutt gart. Frey, Werner & Thilo Tappe, Grundlagen eines GB-Fragmentsfur das Deutsche, appears as Arbeitspapier des Sonderforschungsbereichs 340 , Stuttgart. Gabbay, D. (I98 5), 'N-prolog: an extension of prolog with hypothetical implications. Part II', journal ofLogic Programming, 4·

Gabbay, D.

( I 99I),

'Theoretical foundations

for non-monotonic reasoning. Part 3: a general theory of structured consequence

relations', MS, London. Hobbs, ]. R & S. M. Shieber ( I987) 'An algorithm for generating quantifier scop ings', Computational Linguistics, 13. Kamp, H. (198 5), 'Context, thought and

communication',

Proceedings of the Aristot elian Society, 85, 239-6 1 . Kamp, H. & U . Reyle ( 1 993), From Discourse to Logic , Vol. I, Kluwer, Dordrecht . Kamp, H. & U. Reyle (I99I), 'A calculus for first order discourse representation struc tures', Arbeitspapier des Sonderforschungs bereichs 340 , Stuttgart.

Kempson, R. M. & A. Cormack (198 I), 'Ambiguity and quantification', Linguistics

and Philosophy , 4, 259-309.

Nerbonne, J. ( 1992), 'A feature based syntax/ semantics interface', MS, Saarbriicken. Roberts, C. (1987), 'Modal subordination, anaphora and distribution', Ph.D. diss., University of Massachusetts, Amherst. Schubert, L. K. & F.]. Pelletier (1982), 'From English to logic: context free computation of conventional logic translations', journal

of the Association for Computational Linguis tics . Westerstahl, Dag (I987), 'Branching general ized quantifiers and natural language' in Peter Gardenfors (ed.), Generalized Quanti fiers , Reidel, Dordrecht, 269-98.


I1

semantics interface designed there gives a precise statement of the syntactic conditions on quantifier scoping according to the theory developed here. The final definition will be given in the next section. It is interesting to compare this proof by reasoning about structural differences with the traditional way to proceed, namely to consider all disambiguations

I 79

Journal oJ&mantics

10: 1 81-191

© Oxford University Press 1993

Book Review

Wendy Wilkins (ed.). Syntax and Semantics 20: Thematic Relations . Academic Press, San Diego/London,

1 988. xii + 308 pages.

Co VET

henceforth TRs). The phenomena analysed are: the locative alternation (load hay on to the wagon vs. load the wagon with hay) (Maika Rappaport & Beth Levin);

control and non-thematic predication (Peter W. Culicover); control in

A

infinitival relatives and in purpose clauses and obligatory control (William Ladusaw & David R Dowty; Charles Jones); the relation between simple and complex predicates

(hate

vs.

feel hatred toward) (K. A

Jayaseelan); verbal

morphology in Choctaw (George Aron Broadwell); inheritance of TRs in morphological derivation Ganet H. Randall); derived nominals in English and Polish (Bozena Rozwadowska); the lexical and morphological reflexives in

Russian (Linda Schwartz); reflexivization in English and Norwegian (Wendy

Wilkins); the alternation between ergative-absolutive and ergative-dative case marking in Warlpiri verbs in combination with AUX. clitics (Mary Laughren); the acquisition of the 'actional' passives (was hit) and 'non-actional' passives (was

liked);

the role of TRs in the analysis of sense ambiguities and thematic

K.

ambiguities (Greg N. Carlson & Michael Tanenhaus). Most of the authors regard TRs as pertaining to the verb's lexical meaning,

but there is no consensus as to where in the grammar they should lay a role.

Rappaport & Levin, for example, distinguish two levels of lexical representa

tion: the Lexical-Conceptual Structure (LCS) and the Predicate-Argument Structure (PAS). The LCSs represent the meaning of the predicate in the form

of its lexical decomposition. The PASs are derived from LCSs by linking rules

and serve as input for the syntactic component. Laughren presents here analysis of the Warlpiri verbs in the same framework.

Culicover, who adheres to the autonomy hypothesis, places TR-assignment outside the syntactic component of the grammar, in what he calls r-structure.

This structure is derived from s-structure and seems to form a step towards semantic interpretation since TR assignment replaces co-indexation. Wilkins adopts a similar r-structure, in which the notion of external argument and domain of TR assignment play a role as well as a revised form ofJackendofrs

TR hierarchy.


This volume contains thirteen papers which, from different theoretic view points, deal with thematic relations (deep case, 0 -roles, semantic functions;

1 82 Book Reviews

Ladusaw & Dowty argue that TRs are superfluous in the grammar since they can be entailed from the meaning of the verb together with a theory of human action. In the same vein Jones conceives of TRs as clusters of verb entailments

and presuppositions, but argues that a theory which makes explicit use of TRs

provides a better treatment of purpose clauses than a theory that does not. Jayaseelan enriches Chomsky's 0 -theory with a mechanism which promotes arguments from the deverbal nominal (e.g.

hatred) to

the domain of the host

verb (e.g.fee/). This leads to structures in which different TRs are assigned to the same argument. Broadwell is also forced to adopt underlying structures in which more than one TR is assigned to the same element with the same consequences for Chomsky's 0 -criterion.

and uses these to explain why some arguments cannot show up in the specifier position of derived nominals or, in Polish, as a genitive. Schwartz argues that both lexical and morphological reflexivization in Russian can be dealt with in a monostratal approach in which TRs play a role together with a level of case.

Morphological reflexives are formed by means of lexical predicate formation

rules (cf Vet 1 98 5 for a similar treatment of reflexives in French). Lebeaux adopts the view that a child makes use of surface structure and of

d-structure to establish s-structure. TRs are conceived of as clusters of features.

The feature [+ Affected], for example, enables the child to recognize the Theme of a sentence and to build syntactic structure with the help of that TR. Since in non-actional passives there is no [+ Affected] argument the child

acquires this construction only after it has acquired the case-absorbing property

of passive morphology. Carlson & Tanenhaus assume that the parser takes a specific verb meaning together with all its TR-'grids from the lexicon. The TR-grids remain available

during the parsing process. Consequently it costs more to select a new meaning than an alternative TR-grid. They provide some experimental evidence for this

hypothesis as well as for the idea that TR-positions, even when they are not

'filled', create addresses in the discourse representation and contribute to the cohesion of a discourse. As in Culicover's paper, TRs are regarded here as devices for indexing and re-indexing NPs.

The majority of the papers deal with TRs in a rather 'syntactic spirit'. For

example, assignment of more than one TR to an argument seems only

motivated on formal (syntactic or morphological) and not on semantic grounds Qayaseelan, Wilkins, Broadwell). Rappapon & Levin do not provide any

semantic or conceptual evidence as to why the Lexical Conceptual Structure of

load something with something something on to something (26).

is considerably more complex than that of

load


In Randall's paper a TR hierarchy is adopted which, together with an

inheritance principle, accounts for changes in argument structure of derived nominals. Rozwadowska decomposes TRs into clusters of thematic features

Book Reviews

183

The separation between syntax and lexical information seems also prob lematic. This appears, for example, in the treatment of the double object con struction (I) Mary gave a book to Peter

(2) Mary gave Peter a book

Department ofRomance Languages University .ifGroninxen The Netherlands

RE FERENCES Dik, S. C . ( 197B), Functional Grammar, Norrh Holland, Amsterdam. Vee, C. (19B s). 'Passive, reflexive and causat ive predicate formation in French', in

A. M. Bolkescein, C. de Groot & J. L. Mackenzie (eds), Predicates and Terms in Functional Grammar, Foris, Dordrecht, 4969.


in three of the papers.Jayaseelan proposes an analysis in which the two 'objects', here (Peter, a book), constitute a small clause and where neither Peter nor a book receives its TR from give ( 1 07). In this way (2) needs to be dealt with by means of more complicated syntactic processes than (I). Carlson & Tanenbaum assume that in John bought a bookfor Sally Sally is not assigned a TR by the verb, whereas in John bought Sally a book it is. Wilkins accounts for the alternation by assigning different TRs to the arguments: book is (Theme, Patient) in (I) and (Theme) in (2); Peter is (Goal) in ( I ) and (Goal, Patient) in (2). In all these proposals it seems to be taken for granted that there are at least two different verbs buy and give with different TR-grids. Again this difference seems only motivated by the syntactic form of( I) and (2), and not by the mean ing of the verbs. A more elegant and general proposal for the treatment of these cases is given in Dik ( I 978: 69 f.). At the lexical level Dik adopts only one predicate from (TR-grid) for these verbs. The alternation between ( I ) and (2) is accounted for by the assignment of the syntactic role Object to either the book or to Peter (Sally). Object assignment is determined by a universal 'Semantic Function Hierarchy' which tells us that for English the Object role can be assigned to Patient (as in ( I ) ). Recipient (as in (2)), and (animate) Beneficiary. In French it can only be assigned to Patient, and in a very restricted way to Recipient. The cur-off point in the hierarchy is language-dependent and turns out to be a syntactic and not a lexical phenomenon. In spite of the great variety of (pre-)theoretical approaches this volume offers some interesting papers, especially on reflexivization and nominal derivation, as well as some challenging hypotheses about control and parsing.


j j j j j j j j j j j j

llook Reviews

1

Ks

Book Review

M.

Bierwisch & E. Lang (eds). Grammatische und konzeptuelle Aspekte von Dimensionsadjektiven . Studia grammatica XXVI-XXVII. Akademie-Verlag,

MECHTHILD RICKHEIT

Meaning representations of dimensional adjectives obviously are a challenge for linguistic, logical, and psychological theories. The research project 'Cognitive Linguistics', carried out at the GDR Academy of Sciences under the guidance of Manfred Bierwisch and Ewald Lang, presents a semantic interpretation system supposed to be basic for human cognition. Following the assumption of modular organization of cognitive processes, specifications of different mental representation levels and a theory of a mediating level between language structures and conceptual structures are central points of interest. In accord with a predominantly linguistic approach to cognition, each of the contributions reveals a considerable amount of sensibly ascertained and systematically ordered language data to admit conclusions of associated mental processes. This survey refers to the German edition which requires some effort on the reader's part because it offers condensed information in spite of its 700 pages, presupposing expert knowledge in the fields of generative grammar, cognitive psychology, and standard logic. Each paper reveals the necessiry of enlarging the traditional scope of phenomena to be explained within the relevant discipline and of developing new techniques in scientific description. In a more technical sense as well, the book is condensed because it introduces abbreviations; a subject index not being available, the reader risks getting lost if he does not do any bookkeeping of his own. The English edition is considerably more attractive to read; it is reduced in size and clearly laid out. It does not include, however, three chapters contained in the German publication: 'Dimensional Adjectives and the Structure of Language Behavior' by Manfred Bierwisch, Wolfgang Ullrich Wurzel's article 'On the Morphology of Dimensional Adjectives', and Johannes Dolling's contribution 'Logical Properties of Dimensional Adjectives'. ··


Berlin, 1 987, ISBN J-os-ooo i 6 I -s. 707 pages. English edition: Dimensional Adjectives: Grammatical Structure and Conceptual Interpretation . Springer-Verlag, Berlin/Heidelberg, 1 9X9. ISBN 3-S40-'S063J-O Springer-Verlag, Berlin, Heidelberg, New York. ISBN o-3 X7-506 3 3-0 Springer Verlag, New York, Berlin, Heidelberg, 523 pages.

1 86 Book Reviews

Manfred Bierwisch's chapter 'The Semantics of Gradation'

(9 1 -286) exposes

the theoretical framework of the project. Systematic semantic characteristics of gradable adjectives-which are adjectives allowing for all sorts of comparative constructions-give rise to the assumption of conceptual parameters deter

mining the mental operation of comparison. Degrees are understood as complex mental structures generated by processes which compare values on the

relevant scale. The 'semantics of gradation' defines types of scales, operations on scales, conditions for standard values, and, last but not least, rules which translate the various relevant natural language expressions into a conceptual

representation. The theory offers a propositional-algebraic method for conceptual interpretations of possible morpho-syntactic constructions con

quite correct but understandable. It allows the formal reconstruction of a series of phenomena like antonym relations, nominative versus normative use of

adjectives, duality of comparative and equarive forms, restrictions in the use of factor phrases and degree phrases, and differences between dimensional adjectives and evaluative adjectives.

To establish a correspondence between elements and structures on the

conceptual level and meaning representations on the level of grammatical

description, Bierwisch introduces the mediating level of 'semantic form'. A

'semantic form' is a tree structure composed of functor-argument-structures of categorial grammar specifying relationships over certain semantic constants and variables. The five constants of 'semantic form' constitute the relevant

dimensional aspect of an object, the quantification of the object-specific extent of this dimension, the operation of comparison, and the processes of 'addirion/ subtraction' of difference values. These constants are interpreted by functions

connecting them to their conceptual counterparts. The three variables of 'semantic form' represent the adjective's referent, the value of comparison, and

the value of difference. Theta roles are understood as lambda operators binding these variables according to the rules of syntax. Thus, the semantic form of a lexical item contains structural information about inherent semantic factors and their syntactic realization. Two important aspects in the 'semantics of gradation' should be mentioned.

Firstly, it indicates the necessity of specifying the conditions that determine the

value of comparison. These conditions relate conceptual principles (scale projection principles in particular) to the structure of an adjectival phrase and

restrict the interpretation of semantic configurations. They constitute one

central component of the 'theory of gradarion'....:. the 'theory of semantic form'

being the other one. Secondly, Bierwisch elaborates the composirionality of semannc forms. Each lexical item-affixes included-encloses semantic and

syntactic conditions concerning its en�ronment. Semantic forms being part of


taining grade adjectives. It explains the impossibility of certain configurations, and it opens ways of reinterpretation if the natural language expression is not

Book Reviews

187


the grammatical component, the composition ofseveral basic semantic forms is subjected to specific binding conventions such as the absorption of theta roles. The constants and variables in the semantic representation of a context dependent conceptual interpretation. The assumption that the level of semantic form is part of the logical form gives rise co questions concerning its interaction with the theory of syntactic structures. Some syntactic effects of semantic form are treated in Ilse Zimmermann's contribution 'On the Syntax of Comparative Constructions' (29-90), which mainly deals with deep structures of adjectival phrases. The development of an appropriate generation mechanism within an X-bar framework caBs for decisions on how to adjust syntactic transformation co lexical information or on replacing them by rules of another type. As far as the internal structure of syncactica11y incomplete comparative sentences is concerned, Zimmermann agrees with the proposal of Bierwisch co use semantic form information and adopt semantic interpretation rules instead of transformations. The relevant interpretation rules fill empty categories by conceptually motivated pro-elements. Conceptual complexity, as it appears in semantic forms of degree adjectives and their comparative affixes, in comparative, equative, and superlative constructions, goes back co comparison features such as 'dimension', 'extent', 'polarity', and 'norm'. Wolfgang Ullrich Wurzel's contribution 'On the Morphology of Dimensional Adjectives' (459-516) presents a view of how morphology contributes co express such features. An increase in semantic com plexity is often accompanied by an increase in formal means which constitutes the principle of 'constructive iconism'. Wurzel observes significant iconic dif ferences between positive and comparative forms, whereas comparative and superlative/excessive forms do not show comparable differences in morpho logical effort. Referring co facts ascertained by investigations of more chan twenty languages of different types, he confirms the special morphological sta tus of dimensional adjectives chat makes them a part of the elementary vocabu lary. The difficult job of bringing conceptual structures associated with the use of dimensional adjectives to light is done by Ewald Lang in 'The Semantics of Dimensional Designation of Spatial Objects' (287-48 5). Detailed studies in che distribution and combination of the relevant adjectives and empirically proved evaluations of dimensional aspects of objects lay the ground for his conceptual interpretation system. He investigates compatibility restrictions, antonym relationships and entailments as well as context-dependent variations and transitions in adjectival meanings, relates these linguistic data co what is known about spatial perception and conception, and incorporates the results into a theory of dimensional designation. In accordance with the theory of semantic form, Lang discriminates lexical

1 8 8 Book Reviews


meanings and conceptual structures. On the level of semantic form, the lexical entry of a dimensional adjective contains a parameter who designates a spatial property of the adjective's referent. Obviously, the use of a dimensional adjective does not only mark a specific extent of an object, but it may also convey information pertaining to the position of an object in its environment as well as to an observer's perspective. Dimensional extents and their pro portions, object delimitation, symmetry characteristics, canonical and in herent orientation, canonical and intrinsic perspectivation are factors that enter as defining properties of objects into conceptual configurations called 'object schemata'. Lang ascertains seven types of object schemata and their subtypes representing all possibilities of object categorization under the aspect of dimensional extent. Word meanings develop during the process of mapping semantic form parameters on to object schemata. The adjective may be used to identifY an axis of the object, or it may function as contextual specification of an object's extent and thus turn a gestalt-property into a position-property. 'Parameter fixation rules' establish a connection between its semantic form and its conceptual interpretation by matching designation parameters with object schemata informatioiL This interaction, as well as the object schemata themselves, are based on a small number of compatibility conditions for parameters of gestalt and position-properties. The explanation of context-dependent differences in word meanings necessitates the access to conceptual structures invisible at the linguistic surface. The same holds for the inverse aspect, which focuses the influence of a word's meaning on the semantics of the surrounding sentence. The hypothesis that conclusions drawn from a statement may be influenced by an internal 'logic of words' is held by Johannes Dolling in his article 'Logical Properties of Dimensional Adjectives' (s I 7-74). He presents two possible extensions of standard logic which allow inferences on natural language sentences contain ing dimensional adjectives. First, he outlines a system of meaning postulates within the framework of model theory, taking lexical units of a natural language as atoms. A dimensional adjective appears as a two-place predicate constant whose first argument position is ftlled by terms for singular objects and whose second argument position is either instantiated by the individual extent or by the class of com parison, depending on the nominative or contrastive use of the adjective. Second, he proposes a system of lexical decomposition interpreting words as structures consisting of universal semantic constants. As a system of lexical decomposition allows for conditioned definitions and introduces semantic constants independent of lexical realization, it reveals logical means of contextual meaning differentiations. On the one hand, conceptual structures are not necessarily bound to

Book Reviews 1 89

language, on the other hand, linguistic structures have to be acquired in order to express conceptual knowledge. Under certain circumstances, for example

during the process of language acquisition, discrepancies may occur beween both levels. This leads to psychologically interesting questions concerning the interaction of cognitive and linguistic abilities. In her study 'Language Acquisition and Quantity Judgements-an Analysis of "bigger-" and "more-"

Responses Produced by Children' (57 5-6oo), Karin Goede discusses a phenom enon of regression in the use of the adjective 'groB' [big, large, tall].

Children at the age of four apply the word 'groBer' to refer to some dominant length of an object and thus leave the aspect of three-dimensionality out of consideration, although at an earlier stage they correctly use this

word which, in an initial phase, is related to the meaning of 'viel' [much], thereafter appears to express length or height, and finally refers to all three

dimensions of an object. Goede demands detailed studies in the acquisition

of word meanings under the basic assumption of incomplete lexical knowledge and its interrelation with language-independent cognitive devel

opment.

Reinhard Blumer focuses on principles in the process of language comprehension and their experimental verification. His paper 'Understanding

Verification Comparatives: the Process of Conceptual Interpretation' (6o 1 -47) outlines an approach which takes into account inferencing and problem

solving processes (especially 'term problems'), the relevance of analogue

representations (e.g. comparison of scale values), and lexically determined

cognitive asymmetries (e.g. polarity). Blumer investigates the processing of simple comparative sentences and negated equative sentences. To represent

their grammatical and conceptual structure, he adopts a simplified modifica tion ofBierwisch's proposals. By a series of verification and question-response

experiments Blumer gives evidence for the influence of preferences. If contextual influences such as postponed questions do not intervene, pref erences determine an automatic primary interpretation and have to be taken into account when relating structural asymmetries and asymmetries in language processing.

The papers of Karin Goede and Reinhard Blumer give an impression of how

difficult it is to verify the cognitive reality of semantic representations and to clarify basic principles of mental operations by means of experimental research. Linguistic structures are not the only factors that determine language

processing, and differences in linguistic complexity do not necessarily result in comparable differences on the cognitive level. Goede and Blumer confirm

general assumptions of gradation theory, giving examples for the application of central parameters within psycholinguistic research. However, psychological verifications of semantic form representations and clarifications of principles


adjective to express volume. Goede supposes changes in the semantics of this

1 90 Book Reviews


underlying mental operations such as comparison and dimensional designa tions are still pending. In their concluding remarks 'Somewhat Longer-Much Deeper-Further and Further: Epilogue to the Dimensional Adjective.Project' {649-99), Manfred Bierwisch and Ewald Lang summarize the essentials of the theory of semantic form. They emphasize the status of semantic form as an autonomous level of semantic representation, discuss similarities and differences with regard to the levels oflogical form and conceptual structure, and give arguments in favour of their 'two level approach', as opposed to theories which treat elements oflexical decomposition either as elements of conceptual structure or as lexical elements. Subsequently, they outline possible contributions of dimensional adjective analyses to a theory of markedness, and, finally, they open horizons for applications in other research domains such as the analysis of the 'spatial lexi con', the investigation of conceptual universals, and the comparison of 'spatial orientation schema' with other conceptual modules. Within the framework of AI, structure and processing of spatial knowledge has already been modelled along the guidelines ofEwald Lang's theory at the Institute of Information Science at the University of Hamburg (cf Lang & Carstensen 1 990; Lang, Carstensen & Simmons 1 990). 'OSKAR' is an implementation in Prolog originally supposed to check consistency and exhaustiveness of the formal apparatus. Meanwhile, it supports the theoretical approach and in addition uses object schemata to compute positional features of objects and certain effects of object manipulations on the basis of verbal input. Bierwisch and Lang offer a clear-cut distinction between 'lexical semantics' and 'conceptual interpretation', the first one taking into account the vagueness of lexical units, the latter introducing disambiguating contexts. The lexical units treated so far are adjectives, prepositions, and comparative morphemes, all having in common the fact that they bear meaning slots to be instantiated by conceptually obligatory complements-e.g. variables for the adjective's referent, the value of comparison, and the value of difference. Analogous meaning reconstructions of verbs and nouns, however, require additional theoretical assumptions because these words often have different readings which do not necessarily share meaning slots. The 'one semantic form hypothesis' either presupposes a general semantic structure abstracted from all readings or a primary reading from which the others can be generated by 'conceptual shift' or 'conceptual differentiation' (Bierwisch 1 983). The elaboration of suitable semantic forms requires further investigations. Such an approach should not be determined by predominantly linguistic points of view. A cognitive model of word comprehension should not only refer to psycholinguistic argumentation in order to verify a linguistically motivated theory, but should be developed on linguistic as well as on psycholinguistic

Book Reviews 191

grounds. Only then can clarifications concerning the modularity of cognitive processes be achieved. The book presents central hypotheses in this respect, but it leaves some integration work to be done.

University ofOsnabrock Germany

REFERE N C E S

ing Dimensional Designation and Posi tional Variation of Objects in Space',

IWBS Report 109, IBM Germany, Stutt gart. Lang, E., Carstensen, K.-U. & Simmons, G. ( I 990), Modelling Spatial Knowledge on a Lin

guistic Basis: Theory-Prototype-Integration , · Springer-Verlag, Berlin/Heidelberg/New York (Forthcoming in Lecture Notes on

Artificial Intelligence).


Bierwisch, M. (I98 3). 'Semanrische und kon zepruelle Reprasentation lexikalischer Einheiten', in R Ruzicka & W. Motsch (eds), Untersuchunxen zur Semantik , Studia grammatica XXII, Berlin, S. 6 I -99· Lang, E. & Carstensen, K.-U. ( I 990), 'OSKAR-A Prolog Program for Modell

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