IPDL: a new modal logic of computation

We propose a new perspective on logics of computation by combining instantial neighborhood logic INL with bisimulation safe operations adapted from PDL and dynamic game logic. INL is a recently proposed modal logic, based on a richer extension of neighborhood semantics which permits both universal and existential quantification over individual neighborhoods. We show that a number of game constructors from game logic can be adapted to this setting to ensure invariance for instantial neighborhood bisimulations, which give the appropriate bisimulation concept for INL. We also prove that our extended logic IPDL is a conservative extension of dual-free game logic, and its semantics generalizes the monotone neighborhood semantics of game logic. Finally, we provide a sound and complete system of axioms for IPDL, and establish its finite model property and decidability.