On the Relationship Between CWA ,

The purpose of this paper is to compare three types of non-monotonic semantics: (a) proof-theoretic semantics based on the closed world assumption, (b) model-theoretic semantics based on the notion of a minimal model and (c) model-theoretic semantics based on the notion of a minimal Herbrand model. All of these semantics capture the non-monotonicity of common sense reasoning, i.e. the ability to withdraw conclusions after some new information is added to the original theories, and proved to be powerful enough to handle most examples of such reasoning presented in the literature. However, since these formalizations are based on diierent intuitions and often produce diierent results, the problem of understanding the relationship between them is especially important. In the rst part of the paper we concentrate on the class of positive logic programs, also called deenite theories. Although the three semantics usually diier for universal sentences, our main result shows that they always coincide for existential queries. This result is particularly 1 signiicant in view of the fact that in many applications existential queries are of main interest. It also plays an important role in the problem of nding a suitable declarative semantics for logic programs. In the second part we investigate arbitrary universal theories and we show that subtle diierences exist between the three approaches and therefore no straightforward generalization of the results from the rst part can be obtained.