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Non-finitely axiomatisable two-dimensional modal logics

Published online by Cambridge University Press:  12 March 2014

Agi Kurucz and
Sérgio Marcelino
Agi Kurucz
Affiliation:
Department of Informatics, King's College London, Strand, London WC2R 2LS, UK, E-mail: agi.kurucz@kcl.ac.uk
Sérgio Marcelino
Affiliation:
Department of Informatics, King's College London, Strand, London WC2R 2LS, UKSQIG, IT-LISBOA, Instituto Superior Técnico - Torre Norte - Piso 10, AV. Rovisco Pais, 1, 1049 - 001 Lisboa, Portugal, E-mail: sergiortm@gmail.com
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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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Type
Research Article
Information
The Journal of Symbolic Logic , Volume 77 , Issue 3 , September 2012, pp. 970 - 986
Copyright
Copyright © Association for Symbolic Logic 2012

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