Infinite Behaviour and Fairness Inconcurrent

In concurrent constraint programming, divergence (i.e. an innnite computation) and failure are often identiied. This is undesirable when modelling systems in which innnite behaviour arises naturally. This paper sets out a framework for an axiomatic and denotational view of concurrent constraint programming, and considers the relationship of both views as an instance of Stone duality. We propose a construction of a constraint system which allows both nite and innnite constraints. Subsequently, we provide semantic, topological deenitions of safety, liveness and fairness properties in a given constraint system. The process language considered is parametrized by the constraint system. It allows the actions ask and tell, the preex operator !, the (angelic) non-deterministic choice operator , the procedure call p(X), and the concurrency operator k.