An inference system for horn clause logic with equality

Abstract

In this extended abstract of a full paper we present an inference system for Horn clause logic with equality which is complete not only refutationally but also with respect to the answer substitutions returned, without using functional reflexivity axioms or paramodulating at variable positions. It is goal directed in the sense that—as in SLD resolution—inference rules are only applied to the goal statement. We present the inference system (which subsumes those used for SLD-resolution and for general E-unification), prove its soundness and completeness, and then suggest how this approach forms the appropriate foundation for the study of inference systems (like logic programming interpreters) which return answer substitutions.