Nondeterminism and infinite computations in constraint programming

We investigate the semantics of concurrent constraint programming and of various sublanguages, with particular emphasis on nondeterminism and infinite behavior. The aim is to find out what is the minimal structure which a domain must have in order to capture these two aspects. We show that a notion of observables, obtained by the upward-closure of the results of computations, is relatively easy to model even in presence of synchronization. On the contrary, modeling the exact set of results is problematic, even for the simple sublanguage of constraint logic programming. We show that most of the standard topological techniques fail in capturing this more precise notion of observables. The analysis of these failed attempts leads us to consider a categorical approach.