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Tense Logic Without Tense Operators
Author(s) -
Wolter Frank
Publication year - 1996
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19960420113
Subject(s) - mathematics , decidability , kripke semantics , completeness (order theory) , intermediate logic , linguistics , discrete mathematics , description logic , computer science , artificial intelligence , philosophy , mathematical analysis
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.