Brian Monahan

A Logical and Computational Theory of Located Resource

Experience of practical systems modelling suggests that the key conceptual components of a model of a system are processes. resources, locations and environment. In recent work, we have given a process-theoretic account of this view in which resources as well as processes are first-class citizens. This process calculus, SCRP, captures the structural aspects of the semantics of the Demos2k (D2K) modelling tool. D2K represents environment stochastically using a wide range of probability distributions and queue-like data structures. Associated with SCRP is I (bunched) modal logic. MBI, which combines the usual additive connectives of Hennessy-Milner logic with their multiplicative counterparts. In this article, we complete our conceptual framework by adding to SCRP and MBI an account of a notion of location that is simple, yet sufficiently expressive to capture naturally a wide range of forms of location, both spatial and logical. We also provide a description of an extension of the D2K tool to incorporate this notion of location.

Semantics for structured systems modelling and simulation

Simulation modelling is an important tool for exploring and reasoning about complex systems. Many supporting languages are available. Commonly occurring features of these languages are constructs capturing concepts such as process, resource, and location. We describe a mathematical framework that supports a modelling idiom based on these core concepts, and which adopts stochastic methods for representing the environments within which systems exist. We explain how this framework can be used to give a semantics to a simulation modelling language, Core Gnosis, that includes basic constructs for process, resource, and location. We include a brief discussion of a logic for reasoning about models that is compositional with respect to their structure. Our mathematical analysis of systems in terms of process, resource, location, and stochastic environment, together with a language that captures these concepts quite directly, yields an efficient and robust modelling framework within which natural mathematical reasoning about systems is captured.