Perfect Model Semantics for Logic Programs with Equality
Leo Bachmair, Harald Ganzinger · Max Planck Digital Library · 1991
We develop a perfect model semantics for logic programs with negation and equality. Our approach is based on ordered rewriting, a fundamental technique used in equational programming. A logic program in our sense is a set of first-order clauses with equality together with a well-founded ordering on terms and atoms. We show that any consistent logic program has a unique perfect model, provided the ordering is total on ground expressions. The key to this result is a notion of saturation of a set of formulas (under certain inference rules) together with a related concept of redundancy. Our techniques can be applied to Prolog-programs (without equality), in which case a class of programs can be characterized via the notion of stratification up to redundancy for which unique perfect models exist. This extends previous results on (local and weak) stratification.