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.

We introduce HEX programs, which are nonmonotonic logic programs admitting higher-order atoms as well as external atoms, and we extend the wellknown answer-set semantics to this class of programs. Higher-order features are widely acknowledged as useful for performing meta-reasoning, among other tasks. Furthermore, the possibility to exchange knowledge with external sources in a fully declarative framework such as Answer-Set Programming (ASP) is nowadays important, in particular in view of applications in the Semantic Web area. Through external atoms, HEX programs can model some important extensions to ASP, and are a useful KR tool for expressing various applications. Finally, complexity and implementation issues for a preliminary prototype are discussed. 1

Abstract. We give a logic programming based account of probability and describe a declarative language P-log capable of reasoning which combines both logical and probabilistic arguments. Several non-trivial examples illustrate the use of P-log for knowledge representation. 1

Abstract. We describe the conflict-driven answer set solver clasp, whichis based on concepts from constraint processing (CSP) and satisfiability checking (SAT). We detail its system architecture and major features, and provide a systematic empirical evaluation of its features. 1

is relatively straightforward. Another advantage of the ultimate approximation is that in cases where TP is monotone the ultimate well-founded model will be 2-valued and will coincide with the least fixpoint of TP . This is not the case for the standard well-founded semantics. For example in the standard well-founded model of the program: # p. p. p is undefined while the associated TP operator is monotone and p is true in the ultimate well-founded model. One disadvantage of using the ultimate semantics is that it has a higher computational cost even for programs without aggregates. The complexity goes one level higher in the polynomial hierarchy to # 2 for the well-founded model and to 2 for a stable model which is also complete for this class [2]. Fortunately, by adding aggregates the complexity does not increase further. To give an example of a logic program with aggregates we consider the problem of computing the length of the shortest path between two nodes in a direc

Disjunctive Logic Programming (DLP) is a very expressive formalism: it allows to express every property of nite structures that is decidable in the complexity class ). Despite the high expressiveness of DLP, there are some simple properties, often arising in real-world applications, which cannot be encoded in a simple and natural manner. Among these, properties requiring to apply some arithmetic operators (like sum, times, count) on a set of elements satisfying some conditions, cannot be naturally expressed in DLP. To overcome this de ciency, in this paper we extend DLP by aggregate functions. We formally de ne the semantics of the new language, named DLP . We show the usefulness of the new constructs on relevant knowledge-based problems. We analyze the computational complexity of DLP , showing that the addition of aggregates does not bring a higher cost in that respect. We provide an implementation of the DLP language in DLV{ the state-of-the-art DLP system { and report on experiments which con rm the usefulness of the proposed extension also for the eciency of the computation.

Abstract. We consider the simplification of logic programs under the stablemodel semantics, with respect to the notions of strong and uniform equivalence between logic programs, respectively. Both notions have recently been considered for nonmonotonic logic programs (the latter dates back to the 1980s, though) and provide semantic foundations for optimizing programs with input. Extending previous work, we investigate syntactic and semantic rules for program transformation, based on proper notions of consequence. We furthermore provide encodings of these notions in answer-set programming, and give characterizations of programs which are semantically equivalent to positive and Horn programs, respectively. Finally, we investigate the complexity of program simplification and determining semantical equivalence, showing that the problems range between coNP and Π P 2 complexity, and we present some tractable cases. 1

We introduce a new proof procedure for abductive logic programming and present two soundness results. Our procedure extends that of Fung and Kowalski by integrating abductive reasoning with constraint solving and by relaxing the restrictions on allowed inputs for which the procedure can operate correctly. An implementation of our proof procedure is available and has been applied successfully in the context of multiagent systems.

We propose a new technique for approximate ABox reasoning with OWL DL ontologies. Essentially, we obtain substantially improved reasoning performance by disregarding non-Horn features of OWL DL. Our approach comes as a side-product of recent research results concerning a new transformation of OWL DL ontologies into negation-free disjunctive datalog [1,2,3,4], and rests on the idea of performing standard resolution over disjunctive rules by treating them as if they were non-disjunctive ones. We analyse our reasoning approach by means of non-monotonic reasoning techniques, and present an implementation, called Screech.