Constructive Negation of Arithmetic Constraints Using Dataflow Graphs

A system which extracts a dataflow graph from sets of arithmetic constraints is described. This information is used to simplify constraints and to extract positive information from negations of constraints. The context for this work is a Prolog implementation where intervals are used to represent the underlying arithmetic variables. The system uses simple information about the existence of solutions of primitive constraints to derive the dataflow graph. This makes the system easily extensible to new primitives and domains. A practical implementation over both real and integer arithmetic is described and an extended example of its application given.