A constraint diagram reasoning system

Abstract

The Unified Modeling Language (UML) is a collection of notations which are mainly diagrammatic. These notations are used by software engineers in the process of object oriented modelling. The only textual notation in the UML is the Object Constraint Language (OCL). The OCL is used to express logical constraints such as system invariants. Constraint diagrams are designed to provide a diagrammatic alternative to the OCL. Since constraint diagrams are visual they complement existing notations in the UML. Spider diagrams form the basis of constraint diagrams and sound and complete reasoning systems have been developed. Spider diagrams allow subset relations between sets and cardinality constraints on sets to be expressed. In addition to this, constraint diagrams allow universal quantification and relational navigation and hence are vastly more expressive. In this paper we present the first constraint diagram reasoning system. We give syntax and semantics for constraint diagrams we call CD1 diagrams. We identify syntactic criteria that allow us to determine whether a CD1 diagram is satisfiable. We give descriptions of a set of sound and complete reasoning rules for CD1 diagrams.