LTAG Semantics With Semantic Unification

1. LTAG SemanticsWithSemantic Unification Presented by Teodora Toncheva

2. Presented Papers • Scope and Situation Binding in LTAG using Semantic Unification, Kallmeyer and Romero (2005) • Semantic Construction in Feature-Based TAG, Gardent and Kallmeyer(2003) • Sentence Planning as Description Using TAG,Stone and Doran(1997)

3. A Framework for LTAG Semantics Early Approaches

4. Early Approaches • CETM • Derivation steps in TAG correspond to predicate-argument applications  base LTAG semantics on the derivation tree

5. First Approach • Synchronous TAG for the syntax-semantics interface • Pair two TAGs: • for syntax • for L(ogical) F(orm) • do derivation in parallel

6. First Approach Scope problem Not enough information in the derivation tree to construct the desired semantic dependencies correctly

7. Second Approach Semantic representation of each elementary tree ‘is about’ a variable

8. Second Approach

9. Second Approach The missing link problem: not enough information in the derivation tree to construct the desired semantic dependencies. There is no link between trees attaching to different nodes in the same tree. Problems

10. Derivation tree for (1): Derivation tree for (2): like wh s who say s think love s vp claim seem Desired semantics (simplified): claim(p, (seem (love (m, j)))) Desired semantics (simplified): who(x, think (p, say(j, like(b, x)))) (1) Mary Paul claims John seems to love. (2) Who does Paul think John said Bill liked?

11. Proposals to Avoid the Problem The derived tree can be used to compute semantics. Not only information from the derived tree is used, but also from the derivation tree  how elementary trees were put together. First Proposal

12. Second Proposal Computing semantics is based only on the derivation tree which is enriched with additional links. Problem: additional rules are needed for ordering the links for semantics.

13. Third Proposal Use a feature modification mechanism in the derived tree in order to determine the values of semantic arguments. Each elementary tree is associated with a FO logical formula representing its meaning and to some of the tree nodes unification variables and constants are added (to specify which node provides the value for which variable in the final semantic representation). Semantic Construction in FTAG

14. As trees combine during derivation: • variables are unified • semantic of the derived tree  conjunction of the semantics of the combined trees

15. “John loves Mary” The resulting semantic: l0: love(j, m), name(j, john), name(m, mary)

16. Special Cases Quantification l0:(x, h1, h2), h1 l1, h2  l2, l1: dog(x), l2: bark(x)

17. Quantification Quantifier's scope and restriction are expressed by the formula: l0:(x, h1, h2), h1 s1, h2  s2, where the two label variables s1 and s2 indicate the missing arguments. During semantic construction they are unified with the labels l1 and l2 respectively.

18. Intersective Adjectives

19. VP and S Modifiers Pat allegedly usually drives a Cadillac. Three readings are possible depending on the respective scope of “allegedly”, “usually” and “a Cadillac”. In all three cases “allegedly” scopes over “usually”  One VP modifier can be adjoined to the other rather than both being applied to the verb.

21. MLP cases are not problematic for the derived tree based approach. In both cases, FTAG features are shared between the two elementary trees one needs to link but there is not a direct edge in the derivation tree.

22. Who does Paul think John said Bill liked? l3:T(p, h3), h3 s3 l1: S(j, h2), h2 s2 l0: W(x, h0), h0  l3, l1: L(b, x), l2: S(j, h2), h2  l1, l3: T(p, h3), h3  l2

23. Mary Paul claims John seems to love. l0: C(p, h1), h1 s0 l1: S(j, h2), h2 s1 l0: C(p, h1), h1 l1, l1: S(j, h2), h2  l2, l2: L0(j, m)

24. LTAG Semantics With Semantic Unification • Semantic feature structure incorporation in the • derivation tree: • the semantic features are extracted from the • derived tree and are put in a semantic feature • structure linked to the derivation tree. • Each elementary tree in the TAG is linked to a pair • consisting of a semantic representation and a • semantic feature structure description.

25. LTAG Semantics With Semantic Unification • the set of feature structures needed for syntax is finite, the one needed for semantics is countably infinitebecause of the variables allowedas feature values • global features are possible if assigning a semantic feature structure to an elementary tree as a whole Motivation

26. LTAG Semantics With Semantic Unification Motivation • the syntactic features are part of the syntactic objects one is interested in, i.e., they are part of the syntactic structure. Semantic featuresare not part of the semantic representations that get interpreted in the underlying semantic models.

27. Semantic Representation And Semantic Feature Structures • Flat semantic representations: • set of typed labeled formulas • set of scope constraints  expressions x  y, where x and y are propositional labels or propositional variables • Variables are of type e (individuals), s (situations) and <s, t> (propositions)

28. Semantic representation and semantic feature structure of laughs

29. Global Features • Global features are: • not linked to a single node of the elementary tree, but to a tree as a whole • whose values are unique for the whole semantic feature structure (unique for the whole elementary tree)

30. Semantic Unification • Semantic composition consist only of feature conjunction (of descriptions) plus additional feature equations: in the derivation tree elementary trees are replaced by their semantic representations plus corresponding semantic feature structures. Then for each edge in the derivation tree from 1to 2 with position p: • the feature structures 1.p.T and 2.0.T are unified • if 2 is an auxiliary tree, then 1.p.B and 2.f.B are unified (f is the position of the foot node in 2)

31. Semantic representation for John sometimes laughs

32. (3) Semantic representation for John sometimes laughs

33. Disambiguation The semantic representation is underspecified and cannot be interpreted yet. Appropriate disambiguation must be found: Functions that assign propositional labels to the remaining propositional variables, and that assign situations to the situation variables. The disambiguated representation is interpreted conjunctively.

34. Disambiguation • (3) has only one disambiguation: • (s0 is by default the actual situation) • This leads to: • john(x)  some(s, s is part of s0, laugh(x, s)) cannot possibly equal l2 (it must be in the scope of l2) l1. s0

35. Sentence Planning asDescription Using TAG,Stone and Doran(1997) Describes an algorithm for simultaneously constructing the syntax and the semantics of a sentence using LTAG

36. LTAG syntax is combined with declarative specifications of semantics and pragmatics of words and constructions so that syntax and semantics are build simultaneously. • operators used by the algorithm are represented as LTAG elementary trees • TAG operations are used to combine operators • the meaning of each tree is given by a logical formula • pragmatics of operators is modeled by associating with each tree a set of discourse constraints describing when that operator should be used

37. Semantics • The semantics of trees is specified by applying two principles to the LTAG formalism: • the meaning of a tree is conjunction of the meanings of the elementary trees used to derive it • labeling each syntactic node as supplying information about a particular entity or collection of entities  node X:x (about x) can only substitute/adjoin into node with the same label.

38. Pragmatics • Implementation uses four pragmatic distinctions: • NEWNESS  at each point, an entity is new/old to the HEARER/DISCOURSE • SALIENCE  assigns each entity a position in a partial order to indicate how accessible it is in the current context • PARTIALLYORDERED SET RELATIONS  orders the entities in the context • OPEN POSSITIONS  positions containing free variables

39. The Algorithm • System goals: • distinguish x as cat  a description ofthe entity x have to be constructed using the syntactic category cat • communicate p  proposition p have to be included

40. Pseudocode until goals are satisfied: determine which uninflected forms apply; determine which associated trees apply; evaluate progress towards goals; incorporate most specific, best <form, tree>: perform adjunction or substitution; conjoin new semantics; add any additional goals;