A Resource Sensitive Interpretation of Lexical Functional Grammar

Abstract

This paper investigates whether the fundamental linguistic insights and intuitions of Lexical Functional Grammar (LFG), which is usually presented as a ’’constraint-based‘‘ linguistic theory, can be reformulated in a ’’resource sensitive‘‘ framework using a substructural modal logic. In the approach investigated here, LFG‘s f-descriptions are replaced with expressions from a multi-modal propositional logic (with permutation and possibly limited contraction). In effect, the feature structure ’’unification‘‘ basis of LFG‘s f-structures is replaced with a very different resource based mechanism. It turns out that some linguistic analyses that required non-monotonic devices in LFG (such as the ’’constraint equations‘‘ in the Andrews (1982) analysis of Icelandic) can be straightforwardly expressed in the framework presented here. Moreover, a Curry–Howard correspondence between proofs in this logic and λ-terms provides a semantic interpretation as a by-product of the process of showing syntactic well-formedness.