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On the products of Linear Modal Logics

Reynolds, M. (2001) On the products of Linear Modal Logics. Journal of Logic and Computation, 11 (6). pp. 909-931.

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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.

Publication Type: Journal Article
Murdoch Affiliation: School of Education
Publisher: Oxford University Press
Copyright: 2001 Oxford University Press
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