Intuitionistic Layered Graph Logic

Abstract

Models of complex systems are widely used in the physical and social sciences, and the concept of layering, typically building upon graph-theoretic structure, is a common feature. We describe an intuitionistic substructural logic that gives an account of layering. As in other bunched systems, the logic includes the usual intuitionistic connectives, together with a non-commutative, non-associative conjunction (used to capture layering) and its associated implications. We give a soundness and completeness theorem for a labelled tableaux system with respect to a Kripke semantics on graphs. To demonstrate the utility of the logic, we show how to represent systems and security examples, illuminating the relationship between services/policies and the infrastructures/architectures to which they are applied.