Executable specifications for hypothesis-based reasoning with Prolog and Constraint Handling Rules

Constraint Handling Rules (CHR) is an extension to Prolog which opens up a spectrum of hypothesis-based reasoning in logic programs without additional interpretation overhead. Abduction with integrity constraints is one example of hypothesis-based reasoning which can be implemented directly in Prolog and CHR with a straightforward use of available and efficiently implemented facilities.The present paper clarifies the semantic foundations for this way of doing abduction in CHR and Prolog as well as other examples of hypothesis-based reasoning that is possible, including assumptive logic programming, hypotheses with priority and scope, and nonmonotonic reasoning.Examples are presented as executable code so the paper may also serve the additional purpose of a practical guide for developing such programs, and it is demonstrated that the approach provides a seamless integration with existing constraint solvers.