On the products of linear modal logics

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 of Gabbay and Shehtman(1998). We also prove a sufficient condition for such products to be not recursively enumerable and give a simple axiomatization for the square K4.3xK4.3 of the minimal liner logic using non-structural Gabbay-type inference rules.

Full Paper

Postscript version August 1999

Status

Full version submitted August 1999.

Bibtex

@misc{RZ:prodl,
author="M. Reynolds and M. Zakharyaschev",
title="On the products of linear modal logics",
year="1999",
note="submitted"
}