Properties of Tense Logics

Mathematical Logic Quarterly 42 (1):481-500 (1996)

Based on the results of [11] this paper delivers uniform algorithms for deciding whether a finitely axiomatizable tense logic has the finite model property, is complete with respect to Kripke semantics, is strongly complete with respect to Kripke semantics, is d-persistent, is r-persistent.It is also proved that a tense logic is strongly complete iff the corresponding variety of bimodal algebras is complex, and that a tense logic is d-persistent iff it is complete and its Kripke frames form a first order definable class. From this we obtain many natural non-d-persistent tense logics whose corresponding varieties of bimodal algebras are complex
Keywords Complex variety  Tense logic  Kripke semantics  d‐persistency  Strong completeness  Modal Logic
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DOI 10.1002/malq.19960420140
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