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On combinations of propositional dynamic logic and doxastic modal logics

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Abstract

We prove completeness and decidability results for a family of combinations of propositional dynamic logic and unimodal doxastic logics in which the modalities may interact. The kind of interactions we consider include three forms of commuting axioms, namely, axioms similar to the axiom of perfect recall and the axiom of no learning from temporal logic, and a Church–Rosser axiom. We investigate the influence of the substitution rule on the properties of these logics and propose a new semantics for the test operator to avoid unwanted side effects caused by the interaction of the classic test operator with the extra interaction axioms.

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Authors and Affiliations

  1. School of Computer Science, University of Manchester, Manchester, UK

    Renate A. Schmidt

  2. Department of Computer Science, University of Liverpool, Liverpool, UK

    Dmitry Tishkovsky

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  1. Renate A. Schmidt
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  2. Dmitry Tishkovsky
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Correspondence to Renate A. Schmidt.

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This paper is a revised and extended version of Schmidt and Tishkovsky (2003).

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Schmidt, R.A., Tishkovsky, D. On combinations of propositional dynamic logic and doxastic modal logics. J of Log Lang and Inf 17, 109–129 (2008). https://doi.org/10.1007/s10849-007-9041-6

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  • DOI: https://doi.org/10.1007/s10849-007-9041-6

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