Logic Programming Semantics Made Easy

TL;DR: A new model-theoretic semantics for logic programs is proposed, called pure semantics, based on the notions of unfounded set and assumption set, which unifies previous approaches and explains how partial model semantics follows from a weaker closed world assumption.

Abstract: We propose a new model-theoretic semantics for logic programs, called pure semantics, based on the notions of unfounded set and assumption set. The pure semantics emerges from the observation that major logic programming semantics have the following feature in common: given an ’intended model’ M, the set of negative literals in M corresponds exactly with the greatest unfounded set w.r.t. the set of positive literals in M. In other words, a model contains redundant information as its negative part can be described in function of its positive part. Thus, the total models and the partial models of programs can now be characterized by a set of positive literals. Based on this idea, we develop the pure semantics for logic programs. The result is a remarkably simple semantics that unifies previous approaches and explains how partial model semantics follows from a weaker closed world assumption.