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

The implementation of effective reasoning tools for deciding the satisfiability of Quantified Boolean Formulas (QBFs) is an important research issue in Artificial Intelligence. Many decision procedures have been proposed in the last few years, most of them based on the Davis, Logemann, Loveland procedure (DLL) for propositional satisfiability (SAT). In this paper we show how it is possible to extend the conflict-directed backjumping schema for SAT to QBF: when applicable, it allows to jump over existentially quantified literals while backtracking. We introduce solution-directed backjumping, which allows the same for universally quantified literals. Then, we show how it is possible to incorporate both conflict-directed and solution-directed backjumping in a DLL-based decision procedure for QBF satisfiability. We also implement and test the procedure: The experimental analysis shows that, because of backjumping, significant speed-ups can be obtained. While there have been several proposals for backjumping in SAT, this is the first time --as far as we know-- this idea has been proposed, implemented and experimented for QBFs.

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Answer Set Programming (ASP) is a novel programming paradigm, which allows to solve problems in a simple and highly declarative way. The language of ASP (function-free disjunctive logic programming) is very expressive, and allows to represent even problems of high complexity (every problem in the complexity class 2 = NP ).

The generalization of the satisfiability problem with arbitrary quantifiers is a challenging problem of both theoretical and practical relevance. Being PSPACE-complete, it provides a canonical model for solving other PSPACE tasks which naturally arise in AI.

Conditional knowledge bases have been proposed as belief bases that include defeasible rules (also called defaults) of the form " ! ", which informally read as "generally, if then ." Such rules may have exceptions, which can be handled in different ways. A number of entailment semantics for conditional knowledge bases have been proposed in the literature. However, while the semantic properties and interrelationships of these formalisms are quite well understood, about their computational properties only partial results are known so far. In this paper, we fill these gaps and first draw a precise picture of the complexity of default reasoning from conditional knowledge bases: Given a conditional knowledge base KB and a default ! , does KB entail ! ? We classify the complexity of this problem for a number of well-known approaches (including Goldszmidt et al.'s maximum entropy approach and Geffner's conditional entailment), where we consider the general propositional case as well as natural syntactic restrictions (in particular, to Horn and literal-Horn conditional knowledge bases). As we show, the more sophisticated semantics for conditional knowledge bases are plagued with intractability in all these fragments. We thus explore cases in which these semantics are tractable, and find that most of them enjoy this property on feedback-free Horn conditional knowledge bases, which constitute a new, meaningful class of conditional knowledge bases. Furthermore, we generalize previous tractability results from Horn to q-Horn conditional knowledge bases, which allow for a limited use of disjunction. Our results complement and extend previous results, and contribute in refining the tractability/intractability frontier of default reasoning from conditional know...

The work aims at extending Answer Set Programming (ASP) with the possibility of quickly introducing new predefined constructs and to deal with compound data structures. We show how ASP can be extended with `template' predicate's definitions by introducing a wellsuited form of second order logics. We present language syntax and give its operational semantics. We show that the theory supporting our ASP extension is sound, and that program encodings are evaluated as e#ciently as ASP programs. Examples show how the extended language increases declarativity, readability, compactness of program encodings and code reusability.

In this paper, we present a novel formalism of hybrid MKNF knowledge bases, which allows us to seamlessly integrate an arbitrary decidable description logic with logic programming rules. We thus obtain a powerful hybrid formalism that combines the best features of both description logics, such as the ability to model taxonomic knowledge, and logic programming, such as the ability to perform nonmonotonic reasoning. Extending DLs with unrestricted rules makes reasoning undecidable. To obtain decidability, we apply the well-known DL-safety restriction that makes the rules applicable only to explicitly named individuals, and thus trade some expressivity for decidability. We present several reasoning algorithms for different fragments of our logic, as well as the corresponding complexity results. Our results show that, in many cases, the data complexity of reasoning with hybrid MKNF knowledge bases is not higher than the data complexity of reasoning

We give a graph theoretical characterization of answer sets of normal logic programs. We show that there is a one-to-one correspondence between answer sets and a special, non-standard graph coloring of so-called block graphs of logic programs. This leads us to an alternative implementation paradigm to compute answer sets, by computing non-standard graph colorings. Our approach is rule-based and not atom-based like most of the currently known methods. We present an implementation for computing answer sets which works on polynomial space. 1

This paper presents a general, consistency-based framework for expressing belief change.