Journal of Logic, Language and Information

, Volume 17, Issue 1, pp 109–129

On combinations of propositional dynamic logic and doxastic modal logics

Authors

    • School of Computer ScienceUniversity of Manchester
  • Dmitry Tishkovsky
    • Department of Computer ScienceUniversity of Liverpool
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

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 logicsDynamic logicDoxastic logicEpistemic logicReasoning about actionsBelief and knowledge

Copyright information

© Springer Science+Business Media 2007