Lambek calculus and its relational semantics: completeness and incompleteness

Andreka, H. and Mikulas, Szabolcs (1994) Lambek calculus and its relational semantics: completeness and incompleteness. Journal of Logic, Language and Information 3 (1), pp. 1-37. ISSN 0925-8531.

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Official URL: https://doi.org/10.1007/BF01066355

Abstract

The problem of whether Lambek Calculus is complete with respect to (w.r.t.) relational semantics, has been raised several times, cf. van Benthem (1989a) and van Benthem (1991). In this paper, we show that the answer is in the affirmative. More precisely, we will prove that that version of the Lambek Calculus which does not use the empty sequence is strongly complete w.r.t. those relational Kripke-models where the set of possible worlds,W, is a transitive binary relation, while that version of the Lambek Calculus where we admit the empty sequence as the antecedent of a sequent is strongly complete w.r.t. those relational models whereW=U×U for some setU. We will also look into extendability of this completeness result to various fragments of Girard's Linear Logic as suggested in van Benthem (1991), p. 235, and investigate the connection between the Lambek Calculus and language models.

Metadata

Item Type:	Article
School:	Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences
Depositing User:	Sarah Hall
Date Deposited:	13 Jul 2021 14:51
Last Modified:	09 Aug 2023 12:51
URI:	https://eprints.bbk.ac.uk/id/eprint/45091

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