The well-founded semantics for general logic programs

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. Recent research indicates that some programs do not have a "satisfactory" total model; for such programs, the question of an appropriate partial model arises. We introduce unfounded sets and well-founded partial 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 total model, we call it the well-founded model. We show that the class of programs possessing a total well-founded model properly in...