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Conference Papers Year : 2016

Axiomatizing the lexicographic products of modal logics with linear temporal logic

Abstract

Given modal logics L1 and L2, their lexicographic product L1 x L2 is a new logic whose frames are the Cartesian products of an L1-frame and an L2-frame, but with the new accessibility relations reminiscent of a lexicographic ordering. This article considers the lexicographic products of several modal logics with linear temporal logic (LTL) based on ``next'' and ``always in the future''. We provide axiomatizations for logics of the form L x LTL and define cover-simple classes of frames; we then prove that, under fairly general conditions, our axiomatizations are sound and complete whenever the class of L-frames is cover-simple. Finally, we prove completeness for several concrete logics of the form L x LTL.
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Dates and versions

hal-03658877 , version 1 (04-05-2022)

Identifiers

  • HAL Id : hal-03658877 , version 1
  • OATAO : 19191

Cite

Philippe Balbiani, David Fernández-Duque. Axiomatizing the lexicographic products of modal logics with linear temporal logic. 11th conference on Advances in Modal logic (AiML 2016), Aug 2016, Budapest, Hungary. pp.78-96. ⟨hal-03658877⟩
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