Journal of Logic, Language and Information

, Volume 17, Issue 1, pp 109–129

On combinations of propositional dynamic logic and doxastic modal logics

Original Article

DOI: 10.1007/s10849-007-9041-6

Cite this article as:
Schmidt, R.A. & Tishkovsky, D. J of Log Lang and Inf (2008) 17: 109. doi:10.1007/s10849-007-9041-6


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.


Combinations of modal logics Dynamic logic Doxastic logic Epistemic logic Reasoning about actions Belief and knowledge 

Copyright information

© Springer Science+Business Media 2007

Authors and Affiliations

  1. 1.School of Computer ScienceUniversity of ManchesterManchesterUK
  2. 2.Department of Computer ScienceUniversity of LiverpoolLiverpoolUK

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