JOURNAL OF SEMANTICS AN INTERNATIONAL j OURNAL FOR THE INTERDISCIPLINARY STUDY OF THE SEMANTICS OF NATURAL LANGUAGE
MANAGING EDIT 0R: PETER BoscH (IBM Germany and University of Osnabriick) REVIEW EDITOR: TIBOR K1ss (IBM Germany} EDITORIAL BOARD: N. AsHER (University of Texas, Austin} R.BARTSCH (University of Amsterdam) J. VAN BENT HEM (University of Amsterdam) B.BoGURAEV (IBM Research, Yorktown Heights} D. S. BREE (University of Manchester) H. BREKLE (University of Regensburg) G. BROWN (University of Cambridge) 0. DAHL (University of Stockholm) S. C. GARROD (University of Glasgow) B. GEuRTS (University of Osnabriick) M.HERWEG (University of Hamburg) P. HOPPER (Carnegie Mellon University} L. R. HORN (Yale University} S.lsARD (University of Edinburgh) P. N. joHNSON-LAIRD ( Princeton University} H. K AMP (University ofSruttgan) E.LANG (University ofWuppenal)
S.LEVINSON ( MPI Nijmegen) S.L6BNER (University ofDiisseldor� SIR JOHN LvoNS (University of Cambridge) A.MANASTER-RAMER (Wayne Scare University} W. MARSLEN-WILSON ( MRC, Cambridge) J. McCAWLEY (University of Chicago) L.M.G.NooRDMAN (University of Tilburg} R.A.VAN DER SANDT (University of Nijmegen) T. SANFORD (University of Glasgow) R. ScHA (University of Amsterdam) H. ScHNELLE (University of Bochum) P.A.M.SEUREN (University of Nijrnegen) A.VON STECHOW (University of Tiibingen) M. STEEDMAN (University of Pennsylvania) W.WAHLSTER (DFKI Saarbriicken) B.WEBBER (University of Pennsylvania) H.ZEEVAT (University of Amsterdam)
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JOURNAL OF SEMANTICS Volume
10
Number 3
CONTENTS LAURA A MICHAELIS 'Continuity' with Three Scalar Models: the Polysemy of Adverbial Still
193
JAN VAN EIJCK The Dynamics of Description
239
) [R/t ] Ti > [R/ti+IJ T.I+ I > [R/ti+2J Ti+2 > ... C
i
c
c
Figure 2
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In the context of this analysis, 'situation' is to be construed as the particular time line invoked in the interpretation of the still -bearing sentence. A time line is a two-dimensional scalar model (Fillmore, Kay & O'Connor I 988; Kay I 990), in which some situation (a component state of a process} is coupled with a point at which it obtains. Sentence (24) presupposes a time-line model for a presidential campaign. Its 'primitive' is a week. The minimal unit of the time line evoked in (2 I } may be a year. Given this framework, we use the term 'moment' to code any minimal unit of a time scale. A moment is, as usual, opposed to an interval-a grouping of moments. Under this view, still 'selects' that portion of a state which obtains at a moment, rather than that which obtains at an interval. While time lines often code a course of development, the time line at issue here codes persistence of a given state of affairs. The sequence of component states arrayed across the time line are identical to one another. An overall perception of stasis is expressed by the evocation of two component moments of an imperfective process. It should be noted that this analysis explicates the semantics of temporal still at two levels. At one level, still is viewed as a scopal operator, which mediates between presupposed and asserted propositions. The two propositions code the same state of affairs. At another level, still is said to express persistence of a state of affairs across time; it highlights an 'advanced' instance of that state, which obtains at reference time. It is at this second level that the scalar nature of temporal still emerges most clearly; still operates upon a scalar model of persistence. The origin of this scale is equated with the inception of the state in question. A diagrammatic representation of the second type of explanation is provided by the scalar model given in Figure 2. At first glance, this representation does not seem to qualify as a scalar model in terms of Fillmore, Kay & O'Connor (I 988} and Kay ( I 990). In models presented by these authors, an 'argument space' is represented as a set of coordinates, such that the resulting structure is a lattice: an argument space is a set of diads, each member of which is culled from a distinct ordered set or scale. The two distinct scales are the two dimensions of the model: values along one
Laura A Michaelis
21s
__
Harry upset n z . The statement 1'/V : .7l p erforms a non-deterministic action, for it sanctions any assignment to v of an individual satisfying n . Th e statement acts as a test at the same time: in case there are no individuals satisfying .7l the set of output states for any given input state will be empty. In fact, the meaning of YJV : .7l is equivalent to YJV : skip; .7l, or in more standard notation, v := ?; .7l . It follows imm ediately from this explanation plus the dynamic meaning of sequential composition that YJV : (n 1 ); n 2 is equivalent with YJV : (n 1 ; n 2 ). The interpretati on conditions for L assignment make clear how the unique ness condition is h andled dynamically. The statement tV : .7l consists of a test fol lowed by a deterministic action in case the test succeeds: first it is checked whether there is a unique n; if so, this individual is assigned to v and .7l is perfor med; oth erwise the program fails (in other words, the set of output states is empty). It is not difficult to see that this results in the Russell treatment for defi nite descripti ons. Also, we see that th e two programs LV : (n1 ); n 2 and LV : (n1 ; n 2 ) are not equivalent. The program w : (n 1 ; n 2 ) succeeds if th ere is a unique object d sati sfying n 1 ; n 2 , while the requirement for tV : (n1 ); n 2 is stronger: there has to be a unique indivi dual d satisfying n 1 , and d must also satisfy n 2• Th e clause for dynamic implication should take care of th e proper treatment of th e definite description his wife in example (I s ).
(I s ) Ifjohn is married, his wife will be cross with him .
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Note that it follows from th e abbreviation conventions and the definition of [ · l u that [skip] .��(A ) = {A ) and that [fail] .�� (A ) = 0. Truth is defined in terms of input- output behaviour: .7l is true relative to model vft if th ere are proper states A , B for vft such that B E [ .7l ] .u (A ). Two programs n 1 , n 2 are equivalent if for every model vft and every state A for vft , [ n1 ] .�� (A ) = [n2] .« (A ). Dynamic entailment is defined as follows: n1 dynamically entails n 2 if for every model vft and for all proper states A , B for vft : if B E [ n 1 ] Jf (A ) th en there is a proper state C with C E [n2] .�� (B ).
250
The Dynamics of Description
( 1 6) Ijjohni is married then [hisi wife} will be cross with himi . A suitable DPL translation for the example now runs as follows: ( 1 7) (marriedj ) � ( IX : wife-of (x ,j ); cross-with (x ,j )). Now either the program for john is married will not complete successfully, and then the program for the consequent his wife will be cross with him will not be executed at all, or it will indeed give precisely one output (this is because the antecedent program is a test). But then the fact that there is an output guarantees that there will be a unique referent for t assignment in the con sequent, so the program for his wife will be cross with him will only fail if the per son who is in fact John's wife is not cross with John. 6 M A K I N G A S S E RT I O N S A B O U T D P L P R O G R A M S Because our intuitions about static meaning seem to be much better developed than our intuitions about dynamic meaning, we can, for a large class of natural language sentences, check whether the · intuitive meaning of a sentence S corresponds to the meaning of its DPL translation :rc in the following precise sense. Does the intuitive meaning of S precisely describe the set of states for which :rc succeeds? In terms of so-called assertion logic for imperative programs we can describe the set of states for which :rc succeeds by means of the so-called weakest (existential) precondition of :rc with respect to some statement which is always true. One way of expressing weakest preconditions of DPL programs is by supplementing the proper state semantics of DPL with an axiom system in the style of Hoare (see Apt ( 1 98 1 ) for an overview of this approach, and Hoare
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To get this translated into DPL, under the intended reading that the possessive pronoun his is anaphorically linked to john , we have to decide what to do with proper names. The trouble is that proper names do not observe the same anaphoric constraints as definite or indefinite descriptions. It seems to me that the anaphoric behaviour of proper names can be accounted for by assuming that they are assimilated to descriptions, but this will only work if descriptions are treated as carrying uniqueness presupposi tions. Since we are now exploring a Russellian treatment of definites, this road is not yet open to us, however. Therefore I will sidestep the issue for now, and just treat anaphoric links to names by translating the anaphor as the constant which also translates its name antecedent. An indexing for example ( 1 s ) using constants as indices for antecedent and anaphors, as in (1 6), paves the way for this.
Jan van Eijck 25 1
I. 2.
3· 4· 5·
If R is an n -place relation, and t1, tn are terms, then Rt1 If t1, t2 are terms, then t1 = t2 E QDL . If cp , tjJ E QDL , then ( cp 1\ tjJ ), -.cp E QDL . If v e V and cp e QDL , then 3vcp E QDL . If n e DPL and cp e QDL , then ( rr )cp e QDL . •
•
•
•
•
•
tn E QDL .
We need to distinguish the programs of QDL from the static QDL relations. We use boldface for the test program R t 1 tn and italics for the formula Rt 1 •
•
•
. . . ln .
We will continue to use the abbreviation conventions with respect to DPL programs in the QDL format. As is customary, we abbreviate -. (-.cp 1\ -. tjJ ) as ( cp V tjJ), -. ( cp 1\ -. tjJ) as ( cp - tjJ ), ( cp - tjJ ) 1\ ( tjJ - cp ) as cp - tjJ , -.(rr)-.cp as [rr] cp and -.3v-. cp as 'rJvcp . Also, we omit the outermost parentheses for readability. Finally, we add the conventions for QDL formulae that T is an abbreviation of'rJv0(v0 - v0) and .L an abbreviation of -. T. Note that there is a distinction between skip, the DPL command to do nothing, and T , the QDL formula which, as we will see, is always true. Similarly, there is a distinction between fail, the DPL command to fail, and .L , the QDL formula which, as we will see, i s always false. We can now define the notion of satiifaction of a QDL formula by a state A for a model ..,{( - (M, I). I.
..,{( I=A R t . . . ln if (V .A (t l), . . ., V ,u .A { tn)) E l(R ) l
,g
(this is the standard Tarski satisfaction definition). 2 . ..,{( I=A t 1 = t2 ifV.ff .A ( t 1 ) = V,u .A ( t2) (again the standard Tarski satisfaction definition). 3· ..,{( I=A -.cp if it is not the case that A I=A cp . 4· ..,{( I=A cp 1\ t/J i f ..,{( I=A cp and ..,{( I=A t/J · S · ..,{( I=A 3vcp iffor some d e M, A I=A iv:-dJ cp . 6. ..,{( I=A ( rr )cp if there is some B E [ n ] ,u {A ) with ..,{(
1=8
cp .
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(1 969) for the original proposal). Such a calculus is presented and proved sound and complete with respect to the proper state semantics in DPL in van Eijck & de Vries (1 992). Here, I want to present a slightly different kind of assertion language, in the style of Pratt's system of dynamic logic (Pratt 1 976). If we want to be able to use the full range of logical connections between static assertions from predicate logic and programs from DPL we need a powerful assertion language. I will define a version of quantified dynamic logic, inspired by Pratt's dynamic logic (Pratt 1976; Goldblatt 1 987; Kozen & Tiuryn 1 990), that gives us the expressive power we need. The assertion language QDL will have the same relation symbols, the same individual constants and the same variables as the DPL language we want to make assertions about. In fact, the DPL programs will occur as dynamic operators in the QDL statements. Here is the definition of the assertion language.
2 5 2 The Dynamics of Description
7 A C A L C U L U S F O R P R O PE R STATE SEMAN T I C S This section gives a proof system for dynamic interpretation with proper state semantics. We build this proof system on top of an axiomatization for predicate logic, so assume AP to be a set of axioms for predicate logic. See e.g. Enderton (1 972) for one possible choice, plus discussion and motivation. . The atomic predicates ofDPL act as tests. The following test axiom schemata account for their behaviour. Atomic Test Schemata A I (Rt l . . . tn ) cp - (Rtl, . . . tn 1\ cp ). A 2 ( t 1 = t 2)
