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.

. At a workshop held in Toulouse, France in 1977, Gallaire, Minker and Nicolas stated that logic and databases was a field in its own right (see [131]). This was the first time that this designation was made. The impetus for this started approximately twenty years ago in 1976 when I visited Gallaire and Nicolas in Toulouse, France, which culminated in a workshop held in Toulouse, France in 1977. It is appropriate, then to provide an assessment as to what has been achieved in the twenty years since the field started as a distinct discipline. In this retrospective I shall review developments that have taken place in the field, assess the contributions that have been made, consider the status of implementations of deductive databases and discuss the future of work in this area. 1 Introduction As described in [234], the use of logic and deduction in databases started in the late 1960s. Prominent among the developments was the work by Levien and Maron [202, 203, 199, 200, 201] and Kuhns [1...

Our aim in this article is to supplement the set of strong properties introduced in the preceding article ([Dix94]) with a set of weak principles in order to characterize semantics of logic programs. In [Dix94] we introduced our point of view: we observed that all semantics induce in a natural way a sceptical non-monotonic entailment relation SEM scept . We ask for the properties of these sceptical relations and use them to describe all possible semantics. We collect in this paper serious shortcomings of some semantics proposed recently. Their strange behaviour led us to formulate in a natural way certain principles to avoid these problems. We argue that any well-behaved semantics should satisfy these principles. The main results state that our list of weak principles is complete in the following sense: any well-behaved-semantics is an extension of the well-founded semantics WFS and coincides for stratified programs with Apt, Blair, and Walker's supported model M supp P . We also...

. 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 tutorial-overview, which resulted from a lecture course given by the authors at

The present prolegomena consist, as all indeed do, in a critical discussion serving to introduce and interpret the extended works that follow in this book. As a result, the book is not a mere collection of excellent papers in their own specialty, but provides also the basics of the motivation, background history, important themes, bridges to other areas, and a common technical platform of the principal formalisms and approaches, augmented with examples. In the

Recently, considerable interest and research e#ort has been given to the problem of finding a suitable extension of the logic programming paradigm beyond the class of normal logic programs. In order to demonstrate that a class of programs can be justifiably called an extension of logic programs one should be able to argue that: . the proposed syntax of such programs resembles the syntax of logic programs but it applies to a significantly broader class of programs; . the proposed semantics of such programs constitutes an intuitively natural extension of the semantics of normal logic programs; . there exists a reasonably simple procedural mechanism allowing, at least in principle, to compute the semantics; . the proposed class of programs and their semantics is a special case of a more general non-monotonic formalism which clearly links it to other well-established non-monotonic formalisms. In this paper we propose a specific class of extended logic programs which will be (modestly) called super logic programs or just super-programs. We will argue that the class of super-programs satisfies all of the above conditions, and, in addition, is su#ciently flexible to allow various application-dependent extensions and modifications. We also provide a brief description of a Prolog implementation of a query-answering interpreter for the class of super-programs which is available via FTP and WWW. Keywords: Non-Monotonic Reasoning, Logics of Knowledge and Beliefs, Semantics of Logic Programs and Deductive Databases. # An extended abstract of this paper appeared in the Proceedings of the Fifth International Conference on Principles of Knowledge Representation and Reasoning (KR'96), Boston, Massachusetts, 1996, pp. 529--541. + Partially supported by the National Science Fou...

We describe the elds of disjunctive logic programming and disjunctive deductive databases from the time of their inception to the current time. Contributions with respect to semantics, implementations and applications are surveyed.

. Quite recently Brass/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. We show in this paper, that the original calculus, consisting of some simple transformations, has a very strong and appealing property: it is confluent . This means that all the transformations can be applied in any order: if we arrive at an irreducible program (no more transformation is applicable) then this is already the unique normalform. No proper subset of the calculus has this property. We also give an equivalent characterization of D-WFS in terms of iterated minimal model reasoning. This construction is a generalization of a description of the wellfounded semantics: we introduce a very simple and neat construction of a sequence D i that eventually stops and represents the set of derivable...

. In recent years, much work was devoted to the study of theoretical foundations of Disjunctive Logic Programs and Disjunctive Deductive Databases. While the semantics of non-disjunctive programs is fairly well understood the declarative and computational foundations of disjunctive programming proved to be much more elusive and difficult. Quite recently, two new and very promising semantics have been proposed for the class of disjunctive logic programs. Both of them extend the well-founded semantics of normal programs. The first one is the static semantics proposed by Przymusinski and the other is the D-WFS semantics proposed by Brass and Dix. Although the two semantics are based on very different ideas, we show in this paper that they turn out to be very closely related. In fact, we show that it is possible to restrict the underlying language of STATIC to get D-WFS. We also show how to use this characterization for an efficient implementation based on a prover for computing minimal ...