Fuzzy Semantics of Contract Language

Abstract

In this paper, we focus on investigation of the predicate transformer semantics of the contract language introduced by Back and von Wright in their book titled as “Refinement Calculus: A Systematic Introduction” (Springer-Verlag, New York, 1998) in the framework of fuzziness. In order to define fuzzy operations, i.e., fuzzy logic connectives, we take into account implicator → and its associated based on residuated lattice theory. Based on these basic fuzzy operations, we introduce the angelic and demonic updates of fuzzy relations. They are the basis of fuzzy predicate transformers in the sense of that any strongly monotone fuzzy predicate transformer can be represented as the sequential composition of the angelic and demonic updates. Together with the standard strong negation , we set up the duality between the angel and demon. The fuzzy predicate transformers semantics of contract statements is established and a simple example of contract statements is given.