Chapter 4 - On the Declarative Semantics of Logic Programs with Negation

Abstract

A logic program can be viewed as a set of predicate formulas, and its declarative meaning can be defined by specifying a certain Herbrand model of that set. For programs without negation, this model is defined either as the Herbrand model with the minimal set of positive ground atoms, or, equivalently, as the minimal fixed point of a certain operator associated with the program (van Emden and Kowalski). These solutions do not apply to general logic programs, because a program with negation may have many minimal Herbrand models, and the corresponding operator may have many minimal fixed points. Apt, Blair, and Walker and, independently, Van Gelder, introduced a class of stratified programs which disallows certain combinations of recursion and negation and showed how to use the fixed point approach to define a declarative semantics for such programs. Using the concept of circumscription, we extend the minimal model approach to stratified programs and show that it leads to the same semantics.