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

Tadeusz Litak; Frank Wolter

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

机译：线性时间流的所有有限可公理化时态逻辑都是CoNP完全的

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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+1 F p → n F 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.

机译：我们证明，所有由线性运算时间确定的，“总是在将来”和“总是在过去”的，带有时间运算符的可有限公理化的时态逻辑都是coNP完全的。例如，对于所有n≥0，例如，所有包含* n + 1 F p→n F p形式的密度公理的时态逻辑，是完整的coNP。此外，我们证明了所有∩不可约时态逻辑的coNP完全性。由于这些时态逻辑类包含许多Kripke不完整双峰逻辑，因此我们获得了许多自然的Kripke不完整普通双峰逻辑实例，但它们都是coNP-完全的。

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《Studia Logica》 |2005年第2期|153-165|共13页
作者
Tadeusz Litak; Frank Wolter;
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作者单位

School of Information Science JAIST;

Department of Computer Science University of Liverpool;

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原文格式 PDF
正文语种 eng
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关键词
NP-completeness; tense logic; temporal logic; computational complexity; frame incompleteness;

机译：NP完整性;时态逻辑;时间逻辑;计算复杂度;帧不完整性;

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

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