  We describe a family of decidable propositional dynamic logics, where atomic
modalities satisfy some extra conditions (for example, given by axioms of the
logics K5, S5, or K45 for different atomic modalities). It follows from recent
results (Kikot, Shapirovsky, Zolin, 2014; 2020) that if a modal logic $L$
admits a special type of filtration (so-called definable filtration), then its
enrichments with modalities for the transitive closure and converse relations
also admit definable filtration. We use these results to show that if logics
$L_1, \ldots , L_n$ admit definable filtration, then the propositional dynamic
logic with converse extended by the fusion $L_1*\ldots * L_n$ has the finite
model property.
