The well-founded semantics for general logic programs

Abstract

A general logic (abbreviated to hereafter) is a set of roles that have both positive and negative subgoals. It is common to view a deductive database as a general logic consisting of rules (IDB) slttmg above elementary relations (EDB, facts). It is desirable to associate one Herbrand model with a and think of that model as the meaning of the program, or Its declarative semantics. Ideally, queries directed to the would be answered in accordance with this model. Recent research indicates that some programs do not have a satisfactory total model; for such programs, the question of an appropriate partial model arises. Unfounded sets and well-founded partial are introduced and the well-founded semantics of a are defined to be its well-founded partial model. If the well-founded partial model is m fact a total model. it is called the well-founded model. It n shown that the class of programs possessing a total well-founded model properly includes previously studied classes of and locally stratified programs, The method in this paper is also compared with other proposals in the literature, including Clark's program completion, Fitting's and Kunen's 3-vahred interpretations of it, and the stable models of Gelfond and Lifschitz.