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 chapter, we summarize the research on querying inconsistent databases we have been conducting over the last five years. The formal framework we have used is based on two concepts: repair and consistent query answer. We describe different approaches to the issue of computing consistent query answers: query transformation, logic programming, inference in annotated logics, and specialized algorithms. We also characterize the computational complexity of this problem. Finally, we discuss related research in artificial intelligence, databases, and logic programming.

Abstract. We present a novel combination of disjunctive logic programs under the answer set semantics with description logics for the Semantic Web. The combination is based on a well-balanced interface between disjunctive logic programs and description logics, which guarantees the decidability of the resulting formalism without assuming syntactic restrictions. We show that the new formalism has very nice semantic properties. In particular, it faithfully extends both disjunctive programs and description logics. Furthermore, we describe algorithms for reasoning in the new formalism, and we give a precise picture of its computational complexity. We also provide a special case with polynomial data complexity. 1

In this paper, we address the issue of how Gelfond and Lifschitz's answer set semantics for extended logic programs can be suitably modified to handle prioritized programs. In such programs an ordering on the program rules is used to express preferences. We show how this ordering can be used to define preferred answer sets and thus to increase the set of consequences of a program. We define a strong and a weak notion of preferred answer sets. The first takes preferences more seriously, while the second guarantees the existence of a preferred answer set for programs possessing at least one answer set. Adding priorities

Data complexity of reasoning in description logics (DLs) estimates the performance of reasoning algorithms measured in the size of the ABox only. We show that, even for the very expressive DL SHIQ, satisfiability checking is data complete for NP. For applications with large ABoxes, this can be a more accurate estimate than the usually considered combined complexity, which is EXPTIMEcomplete. Furthermore, we identify an expressive fragment, Horn-SHIQ, which is data complete for P, thus being very appealing for practical usage.

There has been significant recent progress in reasoning and constraint processing methods. In areas such as planning and finite model-checking, current solution techniques can handle combinatorial problems with up to a million variables and five million constraints. The good scaling behavior of these methods appears to defy what one would expect based on a worst-case complexity analysis. In order to bridge this gap between theory and practice, we propose a new framework for studying the complexity of these techniques on practical problem instances. In particular, our approach incorporates general structural properties observed in practical problem instances into the formal complexity

We address the problem of minimal-change integrity maintenance in the context of integrity constraints in relational databases. We assume that integrity-restoration actions are limited to tuple deletions. We focus on two basic computational issues: repair checking (is a database instance a repair of a given database?) and consistent query answers [3] (is a tuple an answer to a given query in every repair of a given database?). We study the computational complexity of both problems, delineating the boundary between the tractable and the intractable cases. We consider denial constraints, general functional and inclusion dependencies, as well as key and foreign key constraints. Our results shed light on the computational feasibility of minimal-change integrity maintenance. The tractable cases should lead to practical implementations. The intractability results highlight the inherent limitations of any integrity enforcement mechanism, e.g., triggers or referential constraint actions, as a way of performing minimal-change integrity maintenance. 1

The paper discusses an architecture for intelligent agents based on the use of A-Prolog - a language of logic programs under the answer set semantics. A-Prolog is used to represent the agent's knowledge about the domain and to formulate the agent's reasoning tasks. We outline how these tasks can be reduced to answering questions about properties of simple logic programs and demonstrate the methodology of constructing these programs. Keywords: Intelligent agents, logic programming and nonmonotonic reasoning. 1 INTRODUCTION This paper is a report on the attempt by the authors to better understand the design of software components of intelligent agents capable of reasoning, planning and acting in a changing environment. The class of such agents includes, but is not limited to, intelligent mobile robots, softbots, immobots, intelligent information systems, expert systems, and decision-making systems. The ability to design intelligent agents (IA) is crucial for such diverse tasks as ...

Research on information extraction from Web pages (wrapping) has seen much activity in recent times (particularly systems implementations), but little work has been done on formally studying the expressiveness of the formalisms proposed or on the theoretical foundations of wrapping. In this paper, we first study monadic datalog as a wrapping language (over ranked or unranked tree structures). Using previous work by Neven and Schwentick, we show that this simple language is equivalent to full monadic second order logic (MSO) in its ability to specify wrappers. We believe that MSO has the right expressiveness required for Web information extraction and thus propose MSO as a yardstick for evaluating and comparing wrappers. Using the above result, we study the kernel fragment Elog- of the Elog wrapping language used in the Lixto system (a visual wrapper generator). The striking fact here is that Elog- exactly captures MSO, yet is easier to use. Indeed, programs in this language can be entirely visually specified. We also formally compare Elog to other wrapping languages proposed in the literature.

Monadic query languages over trees currently receive considerable interest in the database community, as the problem of selecting nodes from a tree is the most basic and widespread database query problem in the context of XML. Partly a survey of recent work done by the authors and their group on logical query languages for this problem and their expressiveness, this paper provides a number of new results related to the complexity of such languages over so-called axis relations (such as "child" or "descendant") which are motivated by their presence in the XPath standard or by their utility for data extraction (wrapping).