Axiomatizing the lexicographic products of modal logics with linear temporal logic
نویسندگان
چکیده
Given modal logics 1, 2, their lexicographic product 1 ⇤ 2 is a new logic whose frames are the Cartesian products of a 1-frame and a 2-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 ⇤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 -frames is cover-simple. Finally, we prove completeness for several concrete logics of the form ⇤ LTL.
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