Author: Dalrymple, Mary, John Lamping, Fernando C. N. Pereira, and Vijay Saraswat

Year: 1995

Title: Linear Logic for Meaning Assembly

Remarks: Proceedings of CLNLP, Edinburgh.

Abstract: Semantic theories of natural language associate meanings
with utterances by providing meanings for lexical items, together with
composition rules for computing the meanings of larger units from the
meanings of their parts.  Traditionally, this semantic
compositionality has been expressed in terms of functional
abstraction, functional application and derived operators such as
function composition. This form of semantic composition relies on
tree-structured syntactic analyses to identify function-argument
relations and specify the order of function application. However, a
variety of linguistic arguments, including cross-linguistic evidence,
supports the view that unordered attribute-value structures, in
particular the functional structures of Lexical-Functional Grammar,
are more suitable for representing the main meaning-determining
structural relationships in sentences. But such analyses do not
provide the tree-structured scaffolding demanded by traditional
compositionality. To solve this problem, we propose a deductive
approach to meaning assembly in which the meanings associated with
attribute-value structures are specified by constraints stated in
linear logic. Linear logic is the right language to specify the
semantic contributions of lexical entries and attribute-value
relationships, and their use in building the meanings of sentences. We
are thus able to give a unified treatment of the LFG requirements of
completeness and coherence as well as of modification and
quantification.