On combinations of propositional dynamic logic and doxastic modal logics

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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DOI 10.1007/s10849-007-9041-6
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Melvin Fitting (2011). Reasoning About Games. Studia Logica 99 (1-3):143-169.
Konstantinos Georgatos (2011). Updating Knowledge Using Subsets. Journal of Applied Non-Classical Logics 21 (3-4):427-441.

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