LFG Semantics via Constraints

LFG Semantics via Constraints Mary Dalrymple John Lamping Vijay Saraswat {dalrymple, lamping, saraswat}@parc.xerox.com Xerox PARC 3333 Coyote Hill Road Palo Alto, CA 94304 USA Abstract Semantic theories of natural language as- sociate meanings with utterances by pro- viding meanings for lexical items and rules for determining the meaning of larger units given the meanings of their parts. Traditionally, meanings are com- bined via function composition, which works well when constituent structure trees are used to guide semantic com- position. More recently, the functional structure of LFG has been used to pro- vide the syntactic information necessary for constraining derivations of meaning in a cross-linguistically uniform format. It has been difficult, however, to recon- cile this approach with the combination of meanings by function composition. In contrast to compositional approaches, we present a deductive approach to assem- bling meanings, based on reasoning with constraints, which meshes well with the unordered nature of information in the functional structure. Our use of linear logic as a 'glue' for assembling meanings also allows for a coherent treatment of modification as well as of the LFG re- quirements of completeness and coher- ence. 1 Introduction In languages like English, the substantial scaffold- ing provided by surface constituent structure trees is often a useful guide for semantic composition, and the h-calculus is a convenient formalism for assem- bling the semantics along that scaffolding [Montague, 1974]. This is because the derivation of the mean- ing of a phrase can often be viewed as mirroring the surface constituent structure of the English phrase. The sentence Bill kissed Hillary has the surface con- stituent structure indicated by the bracketing in 1: (1) [s [NF Bill] [ve kissed [NP Hillary]]] The verb is viewed as bearing a close syntactic rela- tion to the object and forming a constituent with it; this constituent then combines with the subject of the sentence. Similarly, the meaning of the verb can be viewed as a two-place function which is applied first to the object, then to the subject, producing the meaning of the sentence. However, this approach is not as natural for lan- guages whose surface structure does not resemble that of English. For instance, a problem is presented by VSO languages such as Irish [McCloskey, 1979]. To preserve the hypothesis that surface constituent structure provides the proper scaffolding for seman- tic interpretation in VSO languages, one of two as- sumptions must be made. One must assume either that semantic composition is nonuniform across lan- guages (leading to loss of explanatory power), or that semantic composition proceeds not with reference to surface syntactic structure, but instead with refer- ence to a more abstract (English-like) constituent structure representation. This second hypothesis seems to us to render vacuous the claim that surface constituent structure is useful in semantic composi- tion. Further problems are encountered in the seman- tic analysis of a free word order language such as Warlpiri [Simpson, 1983; Simpson, 1991], where sur- face constituent structure does not always give rise to units that are …

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