论文信息 - Tense Logic Without Tense Operators

Tense Logic Without Tense Operators

We shall describe the set of strongly meet irreducible logics in the lattice ϵLin.t of normal tense logics (in the bimodal propositional language) 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. Mathematics Subject Classification: 03B45, 03B25.

Frank Wolter | F. Wolter

[1] R. A. Bull. That All Normal Extensions of S4.3 Have the Finite Model Property , 1966 .

[2] W. Blok. The lattice of varieties of modal algebras is not strongly atomic , 1980 .

[3] Frank Wolter,et al. Completeness and decidability of tense logics closely related to logics above K4 , 1997, Journal of Symbolic Logic.

[4] Michael Zakharyaschev,et al. On the Independent Axiomatizability of Modal and Intermediate Logics , 1995, J. Log. Comput..

[5] S. K. Thomason,et al. The logical consequence relation of propositional tense logic , 1975, Math. Log. Q..

[6] Johan van Benthem,et al. The Logic of Time , 1983 .

[7] J. Kruskal. Well-quasi-ordering, the Tree Theorem, and Vazsonyi’s conjecture , 1960 .

[8] R. Goldblatt. Logics of Time and Computation , 1987 .

[9] Michael Zakharyaschev,et al. Canonical formulas for K4. Part I: Basic results , 1992, Journal of Symbolic Logic.

[10] R. A. Bull. An Algebraic Study of Tense Logics with Linear Time , 1968, J. Symb. Log..