  One approach to attempting a sound and complete semantics for fragments of linear logic associates to a formula the set of all contexts that can be used to prove that formula. Of course, such a collection may need to be more abstract and to be given various closure properties. The phase semantics of Girard  (1987)  provides one such semantics: some uses of such semantics have been made in computer science to provide counterexamples and as a tool that can help establish that a given concurrent system cannot evolve into another with certain properties  (Fages et al. 2001).  Similarly, Kripke-style semantics have been provided in  Allwein &amp; Dunn 1993  and  Hodas &amp; Miller 1994.  Quantales, certain kind of partially ordered algebraic structures, have also been used to provide early semantic models for parts of linear logic  (Yetter 1990).