Non-finitely axiomatisable two-dimensional modal logics

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Journal of Symbolic Logic 77 (3):970-986 (2012)
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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 infinite in two senses: It should contain infinitely many propositional variables, and formulas of arbitrarily large modal nesting-depth

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10.2178/jsl/1344862170

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Citations of this work

Combining logics.Walter Carnielli & Marcelo E. Coniglio - 2008 - Stanford Encyclopedia of Philosophy.
Finite Frames for K4.3 x S5 Are Decidable.Agi Kurucz & Sérgio Marcelino - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 411-436.

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References found in this work

Two-dimensional modal logic.Krister Segerberg - 1973 - Journal of Philosophical Logic 2 (1):77 - 96.
Products of modal logics, part 1.D. Gabbay & V. Shehtman - 1998 - Logic Journal of the IGPL 6 (1):73-146.

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