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LTAG SemanticsWith

Semantic Unification

Presented byTeodora Toncheva

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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)

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A Framework for LTAG Semantics

Early Approaches

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Early Approaches

• CETM• Derivation steps in TAG correspond

to predicate-argument applications base LTAG semantics on the

derivation tree

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First Approach

Synchronous TAG for the syntax-semantics interface

Pair two TAGs:• for syntax• for L(ogical) F(orm)do derivation in parallel

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First Approach

Scope problem Not enough information in the

derivation tree to construct the desired semantic dependencies correctly

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Second Approach

Semantic representation of each elementary tree ‘is about’ a variable

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Second Approach

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Second ApproachProblems

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.

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Derivation tree for (1):

love s vpclaim seem

Desired semantics (simplified):claim(p, (seem (love (m, j))))

Derivation tree for (2):

like wh swho say s think

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?

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Proposals to Avoid the Problem

First Proposal

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.

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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.

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Third ProposalSemantic Construction in

FTAGUse 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).

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As trees combine during derivation:

1. variables are unified

2. semantic of the derived tree conjunction of the semantics of the combined trees

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“John loves Mary”

The resulting semantic:l0: love(j, m), name(j, john), name(m, mary)

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Special Cases

Quantification

l0:(x, h1, h2), h1 l1, h2 l2, l1: dog(x), l2: bark(x)

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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.

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Intersective Adjectives

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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.

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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.

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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

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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)

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LTAG Semantics With Semantic Unification

Semantic feature structure incorporation in the

derivation tree:the semantic features are extracted from thederived tree and are put in a semantic featurestructure linked to the derivation tree.

Each elementary tree in the TAG is linked to a pair

consisting of a semantic representation and asemantic feature structure description.

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LTAG Semantics With Semantic Unification

Motivation

•the set of feature structures needed for syntax is finite, the one needed for semantics is countably infinite because of the variables allowed as feature values

•global features are possible if assigning a semantic feature structure to an elementary tree as a whole

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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 features are not part of the semantic representations that get interpreted in the underlying semantic models.

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Semantic Representation And Semantic Feature

StructuresFlat 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)

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Semantic representation and semantic feature structure of laughs

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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)

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Semantic UnificationSemantic 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 1 to 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)

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Semantic representation for John sometimes laughs

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Semantic representation for John sometimes laughs

(3)

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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.

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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

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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

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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

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SemanticsThe 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.

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PragmaticsImplementation 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

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The AlgorithmSystem goals:

•distinguish x as cat a description of the entity x have to be constructed using the syntactic category cat•communicate p proposition p have to be included

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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;