All finitely axiomatizable normal extensions of K4.3 are decidable

Zakharyaschev, Michael and Alekseev, A. (1995) All finitely axiomatizable normal extensions of K4.3 are decidable. Mathematical Logic Quarterly 41 (1), pp. 15-23. ISSN 0942-5616.

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Official URL: https://doi.org/10.1002/malq.19950410103

Abstract

We use the apparatus of the canonical formulas introduced by Zakharyaschev [10] to prove that all finitely axiomatizable normal modal logics containing K4.3 are decidable, though possibly not characterized by classes of finite frames. Our method is purely frame-theoretic. Roughly, given a normal logic L above K4.3, we enumerate effectively a class of (possibly infinite) frames with respect to which L is complete, show how to check effectively whether a frame in the class validates a given formula, and then apply a Harropstyle argument to establish the decidability of L, provided of course that it has finitely many axioms.

Metadata

Item Type:	Article
School:	Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences
Depositing User:	Sarah Hall
Date Deposited:	08 Nov 2021 19:41
Last Modified:	09 Aug 2023 12:52
URI:	https://eprints.bbk.ac.uk/id/eprint/46656

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