Unfounded Sets and Well-Founded Semantics for General Logic Programs

Abstract

A general logic program (abbreviated to "program"hereafter) is a set of rules that have both positive and negative subgoals It is common to view a deductive database as a general logic program consisting of rules (IDB) sitting above elementary relations (EDB, facts) It is desirable to associate one Herbrand model with a program and think of that model as the "meaning of the program,"or its "declarative semantics."Ideally, queries directed to the program would be answered in accordance with this model We introduce unfounded sets and well-founded partiai models, and define the well-founded semantics of a program to be its well-founded partial model If the well-founded partial model is in fact a model, we call it the well-founded model, and say the program is "well-behaved "We show that the class of well-behaved programs properly includes previously studied classes of "stratified"and "locally stratified"programs Gelfond and Lifschitz have proposed a definition of "unique stable model"for general logic programs We show that a program has a unique stable model if it has a well-founded model, in which case they are the same We discuss why the converse is not true.