Phase semantics and verification of concurrent constraint programs

The class CC of concurrent constraint programming languages and its non-monotonic extension LCC based on linear constraint systems can be given a logical semantics in Girard's intuitionistic linear logic for a variety of observables. In this paper we settle basic completeness results and we show how the phase semantics of linear logic can be used to provide simple and very concise "semantical" proofs of safety properties for GC or LCC programs.