Docherty, S; Pym, D; (2016) Intuitionistic layered graph logic. In: Olivetti, N and Tiwari, A, (eds.) Automated Reasoning: 8th International Joint Conference, IJCAR 2016, Proceedings. (pp. pp. 469-486). Springer International Publishing: Coimbra, Portugal.

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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 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 soundness and completeness theorems for labelled tableaux and Hilbert-type systems with respect to a Kripke semantics on graphs. To demonstrate the utility of the logic, we show how to represent a range of systems and security examples, illuminating the relationship between services/policies and the infrastructures/architectures to which they are applied.

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