Abstract

Many variants of categorial grammar assume an underlying logic which is associative and linear. In relation to left extraction, the former property is challenged by island domains, which involve nonassociativity, and the latter property is challenged by parasitic gaps, which involve nonlinearity. We present a version of type logical grammar including ‘structural inhibition’ for nonassociativity and ‘structural facilitation’ for nonlinearity and we give an account of relativisation including islands and parasitic gaps and their interaction.

Highlights

  • Today mainstream linguistics is largely informal and computational linguistics is largely statistical

  • There is a tradition of logical categorial grammar dating back to Ajdukiewicz (1935) which aims to practice linguistics as a branch of mathematical logic

  • A semantically labelled sequent is a sequent in which the antecedent type occurrences A1, . . . , An are labelled by distinct variables x1, . . . , xn of types T ( A1), . . . , T ( An) respectively, and the succedent type A is labelled by a term of type T (A) with free variables drawn from x1, . . . , xn

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Summary

Introduction

Today mainstream linguistics is largely informal and computational linguistics is largely statistical. The task of spelling out completely explicit fragments seems either forgotten or taken too lightly. There is a tradition of logical categorial grammar dating back to Ajdukiewicz (1935) which aims to practice linguistics as a branch of mathematical logic. For a while (especially around 1985–2000) this aspiration blended promisingly with the method of fragments, a methodology promoting the articulation of formal grammar fragments, such as the Montague fragment, and their combination and integration. Before major results were achieved in such comprehensive explicit integrated analysis, the field was overtaken by the aforementioned informal and statistical trends. A small and committed community has remained

Morrill
Framework
Syntactic types
Gentzen sequent calculus
Rules and linguistic applications
Initial examples
Routes we do not take
Relativisation
Possible exceptions
Conclusion
Full Text
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