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Categorial Grammar and Lambda Calculus

In: Mathematical Logic and Its Applications

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  • Johan van Benthem

    (University of Amsterdam, Mathematical Institute)

Abstract

Categorial Grammar and logical Type Theory stem from the same historical source, viz. the Fregean and Russellian idea of a pervasive function/ argument structure in Language. Nevertheless, the two fields have developed in quite different ways, one becoming a more linguistic enterprise, the other a more mathematical one. (For the former, see Bach et al., 1986, Buszkowski et al., 1986 — for the latter, Gallin 1975, Barendregt, 1981.) Even so, there is also a more theoretical logical component to Categorial Grammar, which has been studied recently by various authors (cf. Buszkowski, 1982, Došen, 1986, van Benthem, 1986a,e). And in that direction, various connections have emerged with research in Type Theory and Lambda Calculus — exploiting analogies between categorial grammars, Gentzen calculi for implication and fragments of typed lambda-languages. In this paper, we shall survey this development, adding various new results on definability and preservation.

Suggested Citation

  • Johan van Benthem, 1987. "Categorial Grammar and Lambda Calculus," Springer Books, in: Dimiter G. Skordev (ed.), Mathematical Logic and Its Applications, pages 39-60, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-0897-3_4
    DOI: 10.1007/978-1-4613-0897-3_4
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