Systems Modelling via Resources and Processes: Philosophy, Calculus, Semantics, and Logic

We describe a programme of research in resource semantics, concurrency theory, bunched logic, and stochastic processes, as applied to mathematical systems modelling. Motivated by a desire for structurally and semantically rigorous discrete event modelling tools, applicable to enterprise-scale as well as component-scale systems, we introduce a new approach to compositional reasoning based on a development of SCCS with an explicit model of resource. Our calculus models the co-evolution of resources and processes with synchronization constrained by the availability of resources. We provide a simple denotational semantics as a parametrization of Abramsky's synchronization trees semantics for SCCS. We also provide a logical characterization, analogous to Hennessy-Milner logic's characterization of bisimulation in CCS, of bisimulation between resource processes which is compositional in the concurrent and local structure of systems. We discuss applications to ideas such as location and access control