On the products of linear modal logics

Reynolds, M. and Zakharyaschev, Michael (2001) On the products of linear modal logics. Journal of Logic and Computation 11 (6), pp. 909-931. ISSN 0955-792X.

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Official URL: https://doi.org/10.1093/logcom/11.6.909

Abstract

We study two‐dimensional Cartesian products of modal logics determined by infinite or arbitrarily long finite linear orders and prove a general theorem showing that in many cases these products are undecidable, in particular, such are the squares of standard linear logics like K4.3, S4.3, GL.3, Grz.3, or the logic determined by the Cartesian square of any infinite linear order. This theorem solves a number of open problems posed by Gabbay and Shehtman. We also prove a sufficient condition for such products to be not recursively enumerable and give a simple axiomatization for the square K4.3 × K4.3 of the minimal liner logic using non‐structural Gabbay‐type inference rules.

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 14:59
Last Modified:	09 Aug 2023 12:52
URI:	https://eprints.bbk.ac.uk/id/eprint/46630

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