Semantic models for concurrent logic languages

In this paper we develop semantic models for a class of concurrent logic languages. We give two operational semantics based on a transition system, a declarative semantics and a denotational semantics. One operational and the declarative semantics model the success set, that is, the set of computed answer substitutions corresponding to all successfully terminating computations. The other operational and the denotational semantics also model deadlock and infinite computations. For the declarative and the denotational semantics we extend standard notions such as unification in order to cope with the synchronization mechanism of the class of languages we study. The basic mathematical structure for the declarative semantics is the complete lattice of sets of finite streams of substitutions. In the denotational semantics, we use a complete metric space of tree-like structures that are labelled with functions that represent the basic unification step. We look at the relations between the different models. We relate first the two operational semantics and next the declarative and denotational semantics with their respective operational counterparts.