Strong Completeness for Iteration-Free Coalgebraic Dynamic Logics

Abstract

We present a (co)algebraic treatment of iteration-free dynamic modal logics such as Propositional Dynamic Logic (PDL) and Game Logic (GL), both without star. The main observation is that the program/game constructs of PDL/GL arise from monad structure, and the axioms of these logics correspond to certain compatibilty requirements between the modalities and this monad structure. Our main contribution is a general soundness and strong completeness result for PDL-like logics for T-coalgebras where T is a monad and the ”program” constructs are given by sequential composition, test, and pointwise extensions of operations of T.KeywordsModal LogicAtomic PropositionDynamic LogicPropositional Dynamic LogicWeak PreconditionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.