Disjunctive Logic Programming (DLP) is an advanced formalism for knowledge representation and reasoning, which is very expressive in a precise mathematical sense: it allows to express every property of finite structures that is decidable in the complexity class ΣP 2 (NPNP). Thus, under widely believed assumptions, DLP is strictly more expressive than normal (disjunction-free) logic programming, whose expressiveness is limited to properties decidable in NP. Importantly, apart from enlarging the class of applications which can be encoded in the language, disjunction often allows for representing problems of lower complexity in a simpler and more natural fashion. This paper presents the DLV system, which is widely considered the state-of-the-art implementation of disjunctive logic programming, and addresses several aspects. As for problem solving, we provide a formal definition of its kernel language, function-free disjunctive logic programs (also known as disjunctive datalog), extended by weak constraints, which are a powerful tool to express optimization problems. We then illustrate the usage of DLV as a tool for knowledge representation and reasoning, describing a new declarative programming methodology which allows one to encode complex problems (up to ∆P 3-complete problems) in a declarative fashion. On the foundational side, we provide a detailed analysis of the computational complexity of the language of

In this paper we give a short introduction to logic programming approach to knowledge representation and reasoning. The intention is to help the reader to develop a 'feel' for the field's history and some of its recent developments. The discussion is mainly limited to logic programs under the answer set semantics. For understanding of approaches to logic programming build on well-founded semantics, general theories of argumentation, abductive reasoning, etc., the reader is referred to other publications.

. 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...

Database reformulation is the process of rewriting the data and rules of a deductive database in a functionally equivalent manner.

We give a general framework for developing the least model semantics, xpoint semantics, and SLD-resolution calculi for logic programs in multimodal logics whose frame restrictions consist of the conditions of seriality (i.e. 8x 9y R i (x; y)) and some classical rst-order Horn formulas. Our approach is direct and no restriction on occurrences of 2 i and 3 i is required. We apply the framework for a large class of basic serial multimodal logics, which are parameterized by an arbitrary combination of generalized versions of axioms T , B, 4, 5 (in the form, e.g., 4 : 2 i ! 2 j 2k) and I : 2 i ! 2 j . Another part of the work is devoted to programming in multimodal logics intended for reasoning about multi-degree belief, for use in distributed systems of belief, or for reasoning about epistemic states of agents in multi-agent systems.

After brie y reviewing the basic notions and terminology of active rules and relating them to production rules and deductive rules, respectively, we survey a number of formal approaches to active rules. Subsequently, we present our own state-oriented logical approach to active rules which combines the declarative semantics of deductive rules with the possibility to de ne updates in the style of production rules and active rules. The resulting language Statelog is surprisingly simple, yet captures many features of active rules including composite event detection and di erent coupling modes. Thus, it can be used for the formal analysis of rule properties like termination and expressive power. Finally, we showhow nested transactions can be modeled in Statelog, both from the operational and the model-theoretic perspective.

We give a general framework for developing the least model semantics, xpoint semantics, and SLD-resolution calculi for logic programs in multimodal logics whose frame restrictions consist of the conditions of seriality (i.e. 8x 9y R i (x; y)) and some classical rst-order Horn formulas. Our approach is direct and no restriction on occurrences of 2 i and 3 i is required. We apply the framework for a large class of basic serial multimodal logics, which are parameterized by an arbitrary combination of generalized versions of axioms T , B, 4, 5 (in the form, e.g., 4 : 2 i ! 2 j 2k) and I : 2 i ! 2 j . Another part of the work is devoted to programming in multimodal logics intended for reasoning about multi-degree belief, for use in distributed systems of belief, or for reasoning about epistemic states of agents in multi-agent systems. For that we also use the framework, and although these latter logics belong to the mentioned class of basic serial multimodal logics, the special SLD-resolution calculi proposed for them are more eective.