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...

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Bibliographic Details
Published inMathematical logic quarterly Vol. 42; no. 1; pp. 145 - 171
Main Author Wolter, Frank
Format Journal Article
LanguageEnglish
Published Berlin WILEY-VCH Verlag Berlin GmbH 1996
WILEY‐VCH Verlag Berlin GmbH
Subjects
Decidability
Independent axiomatizability
Kripke semantics
Modal logic
Tense logic
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ISSN0942-5616
1521-3870
DOI10.1002/malq.19960420113

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Summary: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.
Bibliography:ark:/67375/WNG-4GHT6J5T-S
istex:49322DD1C472BC935037EBA43C418325DD38E0C6
ArticleID:MALQ19960420113
I should like to thank M. Kracht for several helpful suggestions.
ISSN:0942-5616
1521-3870
DOI:10.1002/malq.19960420113