ML-1997-02: Complexity of Modal Logics of Relations

ML-1997-02: Marx, Maarten (1997) Complexity of Modal Logics of Relations. [Report]

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We consider two families of modal logics of relations: arrow logic and cylindric modal logic and several natural expansions of these, interpreted on a range of (relativised) model­classes. We give a systematic study of the complexity of the validity problem of these logics, obtaining price tags for various features as assumptions on the universe of the models, similarity types, and number of variables involved. The general picture is that the process of relativisation turns an undecidable logic into one whose validity problem is exptime­complete. There are interesting deviations to this though, which we also discuss. The numerous results in this paper are all directed to obtain a better understanding why relativisation can turn an undecidable modal logic of relations into a decidable one. We connect the semantic way of ``taming logic'' by relativisation with the syntactic approach of isolating decidable so­called guarded fragments by showing that validity of loosely guarded formulas is preserved under relativisation.

Item Type: Report
Report Nr: ML-1997-02
Series Name: Mathematical Logic and Foundations (ML)
Year: 1997
Date Deposited: 12 Oct 2016 14:40
Last Modified: 12 Oct 2016 14:40

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