All finitely axiomatizable tense logics of linear time flows are CoNP-complete

Studia Logica 81 (2):153 - 165 (2005)
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.
Keywords Philosophy   Logic   Mathematical Logic and Foundations   Computational Linguistics
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DOI 10.2307/20016740
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Frank Wolter (1996). Tense Logic Without Tense Operators. Mathematical Logic Quarterly 42 (1):145-171.

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