On combinations of propositional dynamic logic and doxastic modal logics (Q1006486)

The paper explores some logics between the fusion and the product of PDL on the one hand, and logics between K45 and S5 on the other, mainly presenting completeness and decidability results. These results are established for both the strong and the weak version of each logic, where the weak version does not have uniform substitution for actions (alias programs). The authors show in particular that the strong versions of the logics they investigate trivialize due to the presence of PDL tests, and propose and study an alternative test operator (that is different from the public announcement operator as studied in dynamic epistemic logics). They show that standard PDL can be embedded into the new logic.