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All finitely axiomatizable tense logics of linear time flows are coNP-complete. (English) Zbl 1096.03014
Summary: 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 time flows are coNP-complete. It follows, for example, that all tense logics containing a density axiom of the form $$\square ^{n+1}_{F} p \rightarrow \square^{n}_{F} p$$, for some $$n \geq 0$$, are coNP-complete. Additionally, we prove coNP-completeness of all $$\cap$$-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.

##### MSC:
 03B44 Temporal logic 03D15 Complexity of computation (including implicit computational complexity) 68Q17 Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) 03B45 Modal logic (including the logic of norms)
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