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The semantics of resource sharing in lexical-functional grammar
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This paper investigates whether the fundamental linguisticinsights and intuitions of Lexical Functional Grammar (LFG),which is usually presented as a ’’constraint-based‘‘ linguistictheory, can be reformulated in a ’’resource sensitive‘‘ frameworkusing a substructural modal logic.In the approach investigated here, LFG‘s f-descriptions arereplaced with expressions from a multi-modal propositional logic(with permutation and possibly limited contraction). In effect, the feature structure ’’unification‘‘ basis ofLFG‘s f-structures is replaced with a very different resourcebased mechanism. It turns out that somelinguistic analyses that required non-monotonic devices in LFG(such as the ’’constraint equations‘‘ in theAndrews (1982) analysis of Icelandic) can be straightforwardlyexpressed in the framework presented here.Moreover, a Curry–Howard correspondence between proofs inthis logic and λ-terms provides a semantic interpretationas a by-product of the process of showing syntactic well-formedness.