Abstract

The well-founded semantics and stable model semantics have proven popular semantics for logic programs. However, these semantics (and others) are not directly amenable to logical reasoning since logically equivalent logic programs may have different stable or well-founded models. Many natural simplifications are not universally valid. Furthermore, in some semantics -- including the stable model semantics -- the definition of a new predicate in terms of old predicates can affect the semantics of the old predicates. We provide valid transformation systems for the well-founded, stable model and Clark-completion semantics. We give restrictions on the application of the simplifications which make them valid, and restrictions on the form of new definitions which avoid unwelcome side-effects on other predicates. The resulting transformation systems form a basis for reasoning in these unstable semantics.

Citations