We survey here various approaches which were proposed to incorporate negation in logic programs. We concentrate on the proof-theoretic and model-theoretic issues and the relationships between them.

In this paper, we review recent work aimed at the application of declarative logic programming to knowledge representation in artificial intelligence. We consider exten- sions of the language of definite logic programs by classical (strong) negation, disjunc- tion, and some modal operators and show how each of the added features extends the representational power of the language.

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Background material is presented on deductive and normal deductive databases. A historical review is presented of work in disjunctive deductive databases, starting from 1982. The semantics of alternative classes of disjunctive databases is reviewed with their model and fixpoint characterizations. Algorithms are developed to compute answers to queries in the alternative theories using the concept of a model tree. Open problems in this area are discussed.

. Recently Brass and Dix have introduced the semantics D-WFS for general disjunctive logic programs. The interesting feature of this approach is that it is both semantically and proof-theoretically founded. Any program \Phi is associated a normalform res(\Phi), called the residual program, by a non-trivial bottom-up construction using least fixpoints of two monotonic operators. We show in this paper, that the original calculus, consisting of some simple transformations, has a very strong and appealing property: it is confluent and terminating. This means that all the transformations can be applied in any order: we always arrive at an irreducible program (no more transformation is applicable) and this program is already uniquely determined. Moreover, it coincides with the normalform res(\Phi) of the program we started with. The semantics D-WFS can be read off from res(\Phi) immediately. No proper subset of the calculus has these properties --- only when we restrict to certain subclasse...

. In this paper we consider the basic semantics of stable and partial stable models for disjunctive deductive databases (with default negation), cf. [9,16]. It is well--known that there are disjunctive deductive databases where no stable or partial stable models exist, and these databases are called inconsistent w.r.t. the basic semantics. We define a consistent variant of each class of models, which we call evidential stable and partial evidential stable models. It is shown that if a database is already consistent w.r.t. the basic semantics, then the class of evidential models coincides with the basic class of models. Otherwise, the set of evidential models is a subset of the set of minimal models of the database. This subset is non-empty, if the database is logically consistent. It is determined according to a suitable preference relation, whose underlying idea is to minimize the amount of reasoning by contradiction. The technical ingredients for the construction of the new classes...

Ordered Model trees were introduced as a normal form for disjunctive deductive databases. They were also used to facilitate the computation of minimal models for disjunctive theories by exploiting the order imposed on the Herbrand base of the theory. In this work we show how the order on the Herbrand base can be used to compute perfect models of a disjunctive stratified finite theory. We are able to compute the stable models of a general finite theory by combining the order on the elements of the Herbrand base with previous results that had shown that the stable models of a theory T can be computed as the perfect models of a corresponding disjunctive theory ET resulting from applying the so called evidential transformation to T . While other methods consider many models that are rejected at the end, the use of atom ordering allows us to guarantee that every model generated belongs to the class of models being computed. As for negation-free databases, the ordered tree serves a...