We introduce the stable model semantics for disjunctive logic programs and deductive databases, which generalizes the stable model semantics, defined earlier for normal (i.e., non-disjunctive) programs. Depending on whether only total (2-valued) or all partial (3-valued) models are used we obtain the disjunctive stable semantics or the partial disjunctive stable semantics, respectively. The proposed semantics are shown to have the following properties: ffl For normal programs, the disjunctive (respectively, partial disjunctive) stable semantics coincides with the stable (respectively, partial stable) semantics. ffl For normal programs, the partial disjunctive stable semantics also coincides with the well-founded semantics. ffl For locally stratified disjunctive programs both (total and partial) disjunctive stable semantics coincide with the perfect model semantics. ffl The partial disjunctive stable semantics can be generalized to the class of all disjunctive logic programs. ffl B...

1 Introduction The perfect model semantics [ABW88, VG89b, Prz88a, Prz89b] provides an attractive alternative to the traditionally used semantics of logic programs based on Clark's completion of the program [Cla78, Llo84, Fit85, Kun87]. Perfect models are minimal models of the program, which can be equivalently described as iterated least fixed points of natural operators [ABW88, VG89b], as iterated least models of the program [ABW88, VG89b] or as preferred models with respect to a natural priority relation [Prz88a, Prz89b]. As a result, the perfect model semantics is not only very intuitive, but it also has been proven equivalent to suitable forms of all four major formalizations of non-monotonic reasoning in AI (see [Prz88b]) and is used in existing database [Zan88] and truth maintenance systems. Additionally, the perfect model semantics eliminates some serious drawbacks of Clark's semantics [Prz89b] and admits a natural sound and complete procedural mechanism, called SLSresolution [...

We introduce 3-valued stable models which are a natural generalization of standard (2-valued) stable models. We show that every logic program P has at least one 3-valued stable model and that the wellfounded model of any program P [VGRS90] coincides with the smallest 3-valued stable model of P. We conclude that the well-founded semantics of an arbitrary logic program coincides with the 3-valued stable model semantics. The 3-valued stable semantics is closely related to non-monotonic formalisms in AI. Namely, every program P can be translated into a suitable autoepistemic (resp. default) theory P so that the 3-valued stable semantics of P coincides with the (3-valued) autoepistemic (resp. default) semantics of P . Similar results hold for circumscription and CWA. Moreover, it can be shown that the 3-valued stable semantics has a natural extension to the class of all disjunctive logic programs and deductive databases. The author acknowledges support from the National Science Foundat...

The most general notion of canonical model for a logic program with negation is the one of stable model [9]. In [7] the stable models of a logic program are characterized by the well-supported Herbrand models of the program, and a new fixed point semantics that formalizes the bottom-up truth maintenance procedure of [4] is based on that characterization. Here we focus our attention on the abstract notion of well-supportedness in order to derive sufficient conditions for the existence of stable models. We show that if a logic program \Pi is positive-order-consistent (i.e. there is no infinite decreasing chain w.r.t. the positive dependencies in the atom dependency graph of \Pi) then the Herbrand models of comp(\Pi) coincide with the stable models of \Pi. From this result and the ones of [10] [17] [2] on the consistency of Clark's completion, we obtain sufficient conditions for the existence of stable models for positive-order-consistent programs. Then we show that a negative cycle free ...

The area of deductive databases has matured in recent years, and it now seems appropriate to re ect upon what has been achieved and what the future holds. In this paper, we provide an overview of the area and briefly describe a number of projects that have led to implemented systems.

The LDL system provides a declarative logic-based language and integrates relational database and logic programming technologies so as to support advanced data and knowledge-based applications. This paper contains a comprehensive overview of the system and contains a description of the LDL language and the compilation techniques employed to translate LDL queries into target queries on the stored data. The paper further contains a description of the architecture and runtime environment of the system and the optimization techniques employed in order to improve the performance and assure the safety of the compiled queries. The paper concludes with an account of the experience gained so far with the system, and discusses application areas where the LDL approach appears to be particularly effective.

this paper we show, however, that stationary expansions can be equivalently defined in terms of classical, 2-valued logic. As a byproduct, we obtain a simpler and more natural description of stationary expansions.

One of the most important and difficult problems in logic programming is the problem of finding a suitable declarative or intended semantics for logic programs. The importance of this problem stems from the declarative character of logic programming, whereas its difficulty can be largely attributed to the non-monotonic character of the negation operator used in logic programs. The problem can therefore be viewed as the problem of finding a suitable formalization of the type of non-monotonic reasoning used in logic programming. In this paper we introduce a semantics of logic programs based on the class PERF(P) of all, not necessarily Herbrand, perfect models of a program P and we show that the proposed semantics is not only natural but it also combines many of the desirable features of previous approaches, at the same time eliminating some of their drawbacks. For a positive program P, the class PERF(P) of perfect models coincides with the class MIN(P) of all minimal models of P. The per...

this paper. In particular, the paper reports on a very significant progress made recently in this area. It also presents some results which have not yet appeared in print. The paper is organized as follows. In the next two sections we define deductive databases and logic programs. Subsequently, in Sections 4 and 5, we discuss model theory and fixed points, which play a crucial role in the definition of semantics. Section 6 is the main section of the paper and is entirely devoted to a systematic exposition and comparison of various proposed semantics. In Section 7 we discuss the relationship between declarative semantics of deductive databases and logic programs and non-monotonic reasoning. Section 8 contains concluding remarks. 2 Deductive Databases

In recent years, much work has been directed towards evaluating logic programs and queries on deductive databases by using an iterative bottom-up fixpoint computation. The resulting techniques offer an attractive alternative to Prolog-style top-down evaluation in several situations. They are sound and complete for positive Horn clause programs, are well-suited to applications with large volumes of data (facts), and can support a variety of extensions to the standard logic programming paradigm. We present the basics of database query evaluation and logic programming evaluation, and then discuss bottom-up fixpoint evaluation. We discuss an approach based upon using a program transformation ("Magic Templates") to restrict search, followed by fixpoint computation using a technique ("Semi-naive evaluation") that avoids repeated inferences. The program transformation technique focuses the fixpoint evaluation, which is a forward-chaining strategy, by propagating bindings in the goal in a ma...