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All Finitely Axiomatizable Tense Logics of Linear Time Flows Are CoNP-complete

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Abstract

We prove that all finitely axiomatizable tense logics with temporal operators for ‘always in the future’ and ‘always in the past’ and determined by linear fows time are coNP-complete. It follows, for example, that all tense logics containing a density axiom of the form ■n+1F p → nF p, for some n ≥ 0, are coNP-complete. Additionally, we prove coNP-completeness of all ∩-irreducible tense logics. As these classes of tense logics contain many Kripke incomplete bimodal logics, we obtain many natural examples of Kripke incomplete normal bimodal logics which are nevertheless coNP-complete.

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Authors and Affiliations

  1. School of Information Science, JAIST, Tatsunokuchi, Ishikawa, 923-1292, Japan

    Tadeusz Litak

  2. Department of Computer Science, University of Liverpool, Liverpool, L69 7ZF, U.K.

    Frank Wolter

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  1. Tadeusz Litak
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  2. Frank Wolter
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Correspondence to Tadeusz Litak.

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Litak, T., Wolter, F. All Finitely Axiomatizable Tense Logics of Linear Time Flows Are CoNP-complete. Stud Logica 81, 153–165 (2005). https://doi.org/10.1007/s11225-005-3702-8

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  • DOI: https://doi.org/10.1007/s11225-005-3702-8

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