This paper investigates whether the fundamental linguistic insights and intuitions of Lexical Functional Grammar, 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. 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 analysis of Icelandic) can be straightforwardly expressed in the framework presented here. Moreover, a Curry– Howard correspondence between proofs in this logic and -terms provides a semantic interpretation as a by-product of the process of showing syntactic well-formedness. (shrink)

Geach’s rich paper ‘A Program for Syntax’ introduced many ideas into the arena of categorial grammar, not all of which have been given the attention they warrant in the thirty years since its first publication. Rather surprisingly, one of our findings (Section 3 below) is that the paper not only does not contain a statement of what has widely come to be known as “Geach’s Rule”, but in fact presents considerations which are inimical to the adoption of the rule in (...) question. With regard to at least some amongst the numerous other points extracted here from Geach’s discussion, we shall not be able to reach so definitive a conclusion, and content ourselves with giving the issues an airing. (shrink)

This article surveys the state of the art in the field of semantic universals. We examine potential semantic universals in three areas: (i) the lexicon, (ii) semantic “glue” (functional morphemes and composition principles), and (iii) pragmatics. At the level of the lexicon, we find remarkably few convincing semantic universals. At the level of functional morphemes and composition principles, we discuss a number of promising constraints, most of which require further empirical testing and/or refinement. In the realm of pragmatics, we predict (...) that Gricean mechanisms are universal, but suggest that the precise nature of presuppositions may be subject to cross-linguistic variation. Finally, we follow E.L. Keenan in concluding that the overarching universal of effability or translatability between languages cannot be upheld in its strongest form. A recurring theme throughout this survey is how much work still remains to be done in the relatively young field of cross-linguistic formal semantics. (shrink)