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

Tadeusz Litak and Frank Wolter
Studia Logica: An International Journal for Symbolic Logic
Vol. 81, No. 2 (Nov., 2005), pp. 153-165
Published by: Springer
Stable URL: http://www.jstor.org/stable/20016740
Page Count: 13
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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 flows time are coNP-complete. It follows, for example, that all tense logics containing a density axiom of the form $\square _{F}^{n+1}p\rightarrow \square _{F}^{n}p$, for some n ≥ 0, are coNP-complete. Additionally, we prove coNP-completeness of all $\bigcap $-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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