Linear Logic for Meaning Assembly

Semantic theories of natural language associate meanings with utterances by providing meanings for lexical items and rules for determining the meaning of larger units given the meanings of their parts. Meanings are often assumed to combine via function application, which works well when constituent structure trees are used to guide semantic composition. However, we believe that the functional structure of Lexical-Functional Grammar is best used to provide the syntactic information necessary for constraining derivations of meaning in a cross-linguistically uniform format. It has been difficult, however, to reconcile this approach with the combination of meanings by function application. In contrast to compositional approaches, we present a deductive approach to assembling 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 allows for a coherent treatment of the LFG requirements of completeness and coherence as well as of modification and quantification.