A Distributed Kripke Semantics

Abstract

An intuitionistic, hybrid modal logic suitable for reasoning about distribution of resources was introduced in [10]. We extend the Kripke semantics of intuitionistic logic, enriching each possible Kripke state with a set of places, and show that this semantics is both sound and complete for the logic. In the semantics, resources of a distributed system are interpreted as atoms, and placement of atoms in a possible state corresponds to the distribution of the resources. The modalities of the logic allow us to validate properties in a particular place, in some place and in all places. We extend the logic with disjunctive connectives, and refine our semantics to obtain soundness and completeness for extended logic. The extended logic can be seen as an instance of Hybrid IS5 [2, 18]