A propositional dynamic logic for instantial neighborhood semantics
Johan van Benthem, Nick Bezhanishvili, Sebastian Enqvist

Abstract:
We propose a new perspective on logics of computation by combining instantial neighborhood logic INL with bisimulation safe operations adapted from PDL. 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. This language has a natural interpretation as a logic of computation in open systems. Motivated by this interpretation, we show that a number of familiar programs constructors can be adapted to the setting of instantial neighborhood semantics to preserve 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.