Context and the Composition of Meaning

Transcription

1 Context and the Composition of Meaning Jan van Eijck CWI and ILLC, Amsterdam, Uil-OTS, Utrecht LOLA7 Invited Talk, Pecs August 2002

2 Abstract Key ingredients in discourse meaning are reference markers: objects in the formal representation that the discourse is about. It is well-known that reference markers are not like first order variables. It is the received view that reference markers are like the variables in imperative programming languages. However, in a computational semantics of discourse that treats reference markers as dynamically bound variables, every noun phrase will get linked to a dynamic variable, so it will give rise to a marker index. Where do these indices come from? How do we handle them when combining pieces of discourse? The merge problem of discourse representation has arisen. We will argue that reference markers are better treated as indices into context, and we will present a theory of context and context extension based on this view. In context semantics, noun phrases do not come with fixed indices, so the merge problem does not arise. This solves a vexing issue with coordination that causes trouble for all current versions of compositional discourse representation theory.

3 Summary The Composition of Discourse Meaning Merging DRSs An Unsolved Puzzle with Coordination Context and Context Extension Doing Away with the Need for Merge Handling Coordination Salience and Salience Update Reference Resolution Conclusions and Further Work

4 Dynamic Account of Linking Pronouns to Their Antecedents Basic ingredients: contexts, constraints on contexts. A DRT-style representation for a piece of text: context constraints on context

5 Information Growth through Representation Update Information conveyed by a piece of text grows... Representation structures get updated... context constraints on context update new context new constraints on context This picture can only be made to work if contexts are represented smartly.

6 Example DRT Style Initial representation for a man entered : x Mx Ex Successive update of representation: x Mx Ex A woman entered x y Mx Ex Wy Ey He smiled at her x y Mx Ex Wy Ey Sxy

7 Rational Reconstruction Assume sentences to be added to existing representation have a representation of their own: x Mx Ex + y Wy Ey = x y Mx Ex Wy Ey a man entered a woman entered

8 The Variable Clash Problem What happens if one gets a variable clash? x Mx Ex + x Wx Ex =? Note: in [Kam81] and in the DRT textbook [KR93], the merge problem does not occur.

9 Merging DRSs Compositional versions of DRT presuppose a definition of merge. Lexical entry for determiner a : λp Q. x P x Qx. Lexical entry for determiner every : λp Q. ( x P x) Qx How to pick a reference marker x? How to define?

10 Classical DRT View Compositional DRS Definition ( Zeevat-style ): Basic DRSs: (, ), (, {P r 0 r n 1 }), (, { }), ({x}, ). Merger of DRSs: δ δ := (V δ V δ, C δ C δ ). Implication of DRSs: δ δ := (, {δ δ }).

11 Semantics of DRT With respect to First Order Model M = (M, I): [(, )] = (, M U ), [(, {P r 0 r n 1 })] = (, {f M U M = f P r 0 r n 1 }), [(, { })] = (, ), [({x}, )] = ({x}, M U ), [δ δ ] := [δ] [δ ], where (X, F ) (Y, G) := (X Y, F G), [δ δ ] := [δ] [δ ], where (X, F ) (Y, G) := (, {h M U f F (if h[x]f then g G with f[y ]g)}).

12 This suggests: x Mx Ex x Wx Ex = x Mx Wx Ex Certainly not the outcome one would like. Can such variable clashes be avoided? Can such variable clashes get repaired (e.g., by means of an alternative merge operation)?

13 An Unsolved Puzzle with Coordination A man entered and a man left. a man : λq. x Mx Qx. entered : λy. left : λy. Ey and : λpq.p q. Ly This gives: a man entered and a man left : x Mx Ex Lx

14 Referent Systems [Ver95] Basic idea: distinguish two aspects of a variable: variable name variable address or memory slot Referent systems are like pointer structures in imperative programming. x [ ] [ ] x y [ ] y z [ ] [ ] u

15 Merging Reference Systems x [ ] [ ] x y [ ] y z [ ] [ ] u [ ] x [ ] x y [ ] y [ ] [ ] = x [ ] [ ] x y [ ] y z [ ] [ ]

16 Merging referent system DRSs [m] x Mx Ex [n] x Wx Ex = [m] [n] x Mx Ex Wx Ex Note that the referent m becomes unaccessible: there is no variable name attached to it anymore.

17 Sequence Semantics [Ver93] Interpret x as a stack [d 0,..., d n 1 ]. Each new introduction for x extends the stack by means of an operation [d 0,..., d n 1 ] [d 0,..., d n 1, d n ] Equivalently: assume that each variable x comes with a sequence x, x, x... of extensions. x x x x x d 0 d 1 d 2 d 3 d 4

18 New introductions are never destructive, for they refer to an extension: x Mx Ex x Wx Ex = x,x Mx Ex Wx Ex Note that both x and x remain accessible.

19 Abstraction over Context Essence of what is needed: a simplification of referent systems and sequence semantics. λ context context + context extension constraints To know how to do this, one should identify what is the essence of context.

20 The Nature of Context Contexts are (essentially) lists of reference markers. Reference markers serve to encode discourse information: keeping track of topics of discourse. Order of discourse topics is relevant: topics mentioned most recently are (other things being equal) more readily accessible for reference resolution. Additional information: Gender and number information. actor focus: agent of the sentence. discourse focus: what is talked about in the sentence.

21 How to Abstract over Context? Start out from Incremental Dynamics [Eij01]: represent a context as a stack of items. c 0 c 1 c 2 c 3 c 4 Existential quantification is context extension: c 0 c 1 c 2 c 3 +d = c 0 c 1 c 2 c 3 d Use indices to refer to context elements: n 1 n c 0 c 1 c 2 c 3 c 4 c n 1 d

22 Replacing Merge by Context Composition Types of contexts: [e]. Types of context transitions: [e] [e] t. This is the type of a characteristic function on contexts. Assume c, c :: [e] and x :: e, and define context extension: := λcc. x(cˆx = c ) Assume ϕ, ψ :: [e] [e] t and c, c composition: :: [e] and define context ϕ ; ψ := λcc. c (ϕcc ψc c )

23 New Entries for Determiners Assume P, Q :: ι [e] [e] t. Lexical entry for determiner a : λp Qc.( ; P i ; Qi)c where i = c. Universal quantification gets defined in terms of context negation: ϕ := λcc.(c = c c ϕcc ) Lexical entry for determiner every : λp Qc.( ( ; P i ; Qi))c where i = c.

24 Handling Coordination This gives: Similarly: a man : λqcc. x(mx Qi(cˆx)c )c where i = c. entered : λjcc.(c = c Ec[j]) where j c. left : λjcc.(c = c Lc[j]) where j c. and : λpq.p ; q. a man entered : λcc. x(mx E(cˆx)[i] cˆx = c ) λcc. x(mx Ex cˆx = c ). a man left : λcc. x(mx Lx cˆx = c )

25 Solution of the Coordination Problem a man entered and a man left : λcc. x(mx Ex cˆx = c ) ; λcc. x(mx Lx cˆx = c ) λcc 1. x(mx Ex cˆx = c 1 ) ; λc 2 c. y(my Ly c 2ˆy = c ) λcc. x(mx Ex y(my Ly cˆxˆy = c )).

26 Salience Anaphoric reference resolution is incremental. Information needed to determine the reference of a pronoun in a text is determined on the go, on the basis of: Syntactic properties of the sentence that contains the pronoun. Information conveyed in the previous discourse. Background information shared by speaker and hearer (the common ground).

27 Syntactic Form and Salience Surface syntactic form is an important determinant for salience. It is usually assumed that subject is more salient than object. John hit Bill. He was upset. First choice for resolving He is John. Bill got kicked by John. He was upset. First choice for resolving He is Bill. In both cases, John and Bill are the two obvious candidates for resolving the reference of the pronoun He, because both John and Bill have been made salient by the preceding text.

28 Contexts and Salience Update Consider the following context: W-Alex Maxima Nelson M Salience update in context is a reshuffle of the order of importance of the items in a context list. This may make princess Maxima the most salient item: Maxima Nelson M W-Alex

29 To allow reshuffling of a context with princess Maxima in it, in such a way that we do not loose track of her, we represent contexts as lists of indexed objects, with the indices running from 0 to the length of the context minus 1: 0 Maxima 1 Nelson M 2 W-Alex Reshuffle this to make Willem Alexander most salient: 2 W-Alex 0 Maxima 1 Nelson M Note that the indices 0,..., n 1 determine a permutation of the context list. Call these lists of indexed objects contexts under permutation.

30 Context Manipulation In a context c, the entity with index i is given by c[ i]. ( 2 W-Alex 0 Maxima 1 Nelson M ) [ 0] = Maxima

31 If c is a context under permutation, let (i)c be the result of placing the item (i, c[ i]) upfront. (1) ( 2 W-Alex 0 Maxima 1 Nelson M ) = 1 Nelson M 2 W-Alex 0 Maxima (i)c is the result of moving the item with index i to the head position of the context list. Successive applications of this operation can generate all permutations of a context.

32 If d is an object and c a context, then d : c is the result of putting item ( c, d) at the head position of the context list. Beatrix : ( 2 W-Alex 0 Maxima 1 Nelson M ) = 3 Beatrix 1 Nelson M 2 W-Alex 0 Maxima The operation (:) is used for adding a new element to the context, in most salient position.

33 Further Refinement of Entries for Determiners Let p[e] be the type of contexts under permutation. Assume c, c :: p[e], P, Q :: ι p[e] p[e] t. New definition of context extension := λcc. x((x : c) = c ) Lexical entries for determiners now use this new definition instead of the old one.

34 The new translation of a man effects a salience reshuffle: λqcc x(man(x) Qi(x : c)c ) where i = c. The referent for the indefinite that gets introduced appears in most salient position in the new context. Note that (x : c)[ i] points to the newly introduced referent x. In any c that is an extension or permutation of (x : c), c [ i] will continue to point to x.

35 Discussion It may seem that the integration of salience reshuffling in dynamic semantics precludes an account of the role of surface syntax in establishing salience. The context semantics is flexible enough to take syntactic effects on salience ordering into account. Lambda abstraction allows us to make flexible use of the salience updating mechanism. In systems of typed logic, predicate argument structure is a feature of the surface syntax of the logic.

36 Consider the difference between the following formulas: (λxy.kxy)(b)(j) (λxy.kyx)(j)(b) (λx.kbx)(j) All of these reduce to Kbj, but the predicate argument structure is different. Surface predicate argument structure of lambda expressions can be used to encode the relevant salience features of surface syntax.

37 We can get the right salience effects from the surface word order of examples like the following: Bill kicked John. John got kicked by Bill. John, Bill kicked. To get the desired salience effect, make make sure that the sentence gets translated into a lambda expression with the appropriate predicate argument structure. Next, use this expression for the salience update of the appropriate contexts.

38 Reference Resolution Reference resolution picks the indices of the entities satifying the appropriate gender constraint from the current state, in order of salience. The result of reference resolution is a list of indices, in an order of preference determined by the salience ordering of the state. The meaning of a pronoun, given a state, is an invitation to pick indices from the state, and use those indices to link pronouns to entities. This can be further refined in a set-up that also stores syntactic information (about gender, case, and so on) as part of the contexts.

39 Conclusions The proposed reference resolution mechanism provides an ordering of resolution options determined by syntactic structure, semantic structure, and discourse structure. Pronoun reference resolution can be brought within the compass of dynamic semantics in a relatively straightforward way. The mechanism can be viewed as an extension of pronoun reference resolution mechanisms proposed for DRT [WA86, BB99]. With minimal modification, the proposal also takes the so-called actor focus from the centering theory of local coherence in discourse [GS86, GJW95] into account. Contexts ordered by salience are a suitable datastructure for further refinement of the reference resolution mechanism by means of modules for discourse focus and world knowledge [WJP98].

40 Further Work Plurals and Collective Entities: (Nouwen, this conference) Dialogue Functional approach to parsing. Link up with work on linear grammars. Integration with Visser Style Context Updates The Proper Treatment of Modality and Information Update.

41 References [BB99] P. Blackburn and J. Bos. Representation and Inference for Natural Language; A First Course in Computational Semantics Two Volumes. Internet, Electronically available from [Eij01] J. van Eijck. Incremental dynamics. Journal of Logic, Language and Information, 10: , [GJW95] B. Grosz, A. Joshi, and S. Weinstein. Centering: A framework for modeling the local coherence of discourse. Computational Linguistics, 21: , [GS86] B.J. Grosz and C.L. Sidner. Attention, intentions, and the structure of discourse. Computational Linguistics, 12: , 1986.

42 [Kam81] H. Kamp. A theory of truth and semantic representation. In J. Groenendijk et al., editors, Formal Methods in the Study of Language. Mathematisch Centrum, Amsterdam, [KR93] H. Kamp and U. Reyle. From Discourse to Logic. Kluwer, Dordrecht, [Ver93] C.F.M. Vermeulen. Sequence semantics for dynamic predicate logic. Journal of Logic, Language, and Information, 2: , [Ver95] C.F.M. Vermeulen. Merging without mystery. Journal of Philosophical Logic, 24: , [WA86] H. Wada and N. Asher. BUILDRS: An implementation of DR theory and LFG. In 11th International Conference on Computational Linguistics. Proceedings of Coling 86, University of Bonn, 1986.

43 [WJP98] M. Walker, A. Joshi, and E. Prince, editors. Centering Theory in Discourse. Clarendon Press, 1998.