On combinations of propositional dynamic logic and doxastic modal logics

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.
Keywords Combinations of modal logics  Dynamic logic  Doxastic logic  Epistemic logic  Reasoning about actions  Belief and knowledge
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Reprint years 2008
DOI 10.1007/s10849-007-9041-6
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References found in this work BETA
Reasoning About Knowledge.Ronald Fagin (ed.) - 2003 - MIT Press.
Logics of Public Communications.Jan Plaza - 2007 - Synthese 158 (2):165 - 179.
Products of Modal Logics, Part 1.D. Gabbay & V. Shehtman - 1998 - Logic Journal of the IGPL 6 (1):73-146.
Properties of Independently Axiomatizable Bimodal Logics.Marcus Kracht & Frank Wolter - 1991 - Journal of Symbolic Logic 56 (4):1469-1485.

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Citations of this work BETA
Reasoning About Games.Melvin Fitting - 2011 - Studia Logica 99 (1-3):143-169.
Reasoning with Protocols Under Imperfect Information.Eric Pacuit & Sunil Simon - 2011 - Review of Symbolic Logic 4 (3):412-444.
Updating Knowledge Using Subsets.Konstantinos Georgatos - 2011 - Journal of Applied Non-Classical Logics 21 (3-4):427-441.

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