Tense logics formulated in the bimodal propositional language are investigated with respect to Kripke-completeness (completeness) and decidability. It is proved that all minimal tense extensions of modal logics of finite width (in the sense of K. Kine) as well as all minimal tense extensions of cofinal subframe logics (in the sense of M. Zakharyaschev) are complete. The decidability of all finitely axiomatizable minimal tense extensions of cofinal subframe logics is shown. A number of variations and extensions of these results are (...) also presented. (shrink)

We shall describe the set of strongly meet irreducible logics in the lattice ϵLin.t of normal tense logics of weak orderings. Based on this description it is shown that all logics in ϵLin.t are independently axiomatizable. Then the description is used in order to investigate tense logics with respect to decidability, finite axiomatizability, axiomatization problems and completeness with respect to Kripke semantics. The main tool for the investigation is a translation of bimodal formulas into a language talking about partitions of (...) general frames into intervals so that relative to both Kripke frames and descriptive frames the expressive power of both languages coincides. (shrink)

Tense logics formulated in the bimodal propositional language are investigated with respect to Kripke-completeness and decidability. It is proved that all minimal tense extensions of modal logics of finite width as well as all minimal tense extensions of cofinal subframe logics are complete. The decidability of all finitely axiomatizable minimal tense extensions of cofinal subframe logics is shown. A number of variations and extensions of these results are also presented.