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Non-finitely axiomatisable two-dimensional modal logics

Marcelino, S. ; Kurucz, A.

Journal of Symbolic Logic Vol. 77, Nº 3, pp. 970 - 986, March, 2014.

ISSN (print): 0022-4812
ISSN (online):

Journal Impact Factor: 0,439 (in 2008)

Digital Object Identifier: 10.2178/jsl/1344862170

Abstract
We show the first examples of recursively enumerable (even decidable) two- dimensional products of finitely axiomatisable modal logics that are not finitely axiomatisable. In particular, we show that any axiomatisation of some bimodal logics that are determined by classes of product frames with linearly ordered first components must be in- finite in two senses: It should contain infinitely many propositional variables, and formulas of arbitrarily large modal nesting-depth.