Generalizing previous work on determinate constraint programming we describe the semantics for such a language based on modelling a process as a set of constraints, with parallel composition (conjunction) given by set intersection and or-parallel search (disjunction) given by set union. This is achieved by viewing processes as continuous linear closure operators on the Smyth power-domain of the underlying constraint system. The model is shown to be fully abstract for the observation of finite approximants to the limits of fair execution sequences. We also give a model for the ``non-ground success set'' semantics---a model fully abstract for the observation of the minimal final stores in terminated execution sequences.