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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

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We extend the answer set semantics to a class of logic programs with nested expressions permitted in the bodies and heads of rules. These expressions are formed from literals using negation as failure, conjunction (,) and disjunction (;) that can be nested arbitrarily. Conditional expressions are introduced as abbreviations. The study of equivalent transformations of programs with nested expressions shows that any such program is equivalent to a set of disjunctive rules, possibly with negation as failure in the heads. The generalized answer set semantics is related to the LloydTopor generalization of Clark's completion and to the logic of minimal belief and negation as failure.

Abstract. Disjunctive Deductive Databases (DDDBs)-- function-free disjunctive logic programs with negation in rule bodies allowed-- have been recently recognized as a powerful tool for knowledge representation and commonsense reasoning. Much research as been spent on issues like semantics and complexity of DDDBs, but the important area of imple-menting DDDBs has been less addressed so far. However, a thorough investigation thereof is a basic requirement for building systems which render previous foundational work on DDDBs useful for practice. This paper presents the architecture ofa DDDB system currently devel-oped at TU Vienna in the FWF project P11580-MAT '~A Query System for Disjunctive Deductive Databases". 1 In t roduct ion The study of integrating databases with logic programming opened in the past the field of deductive databases. Basically, a deductive database is a function-free logic program, i.e., a datalog program (possibly extended with negation). Several advanced eductive database systems utilize logic programming and extensions thereof or querying relational databases, e.g. [14, 21, 24]. The need for representing disjunctive (or incomplete) information led to Dis-junctive Deductive Databases (DDDBs) [18]. They can be seen as function-free disjunctive logic programs, i.e., disjunctive datalog programs [19, 12]. DDDBs are nowadays widely recognized as a valuable tool for knowledge representation a d reasoning [1, 17, 30, 13, 19]. The strong interest in enhancing deductive databases by disjunction is documented by a number of publications (cf. [17]) and special workshops dedicated to this subject (cf. [30]). An important merit of DDDBs over normal (i.e., disjunction-free) logic programming is its capability to model incomplete knowledge [1, 17].

In Part I of this series of papers, we have proposed a new logic-based planning language, called K. This language facilitates the description of transitions between states of knowledge and it is well suited for planning under incomplete knowledge. Nonetheless, K also supports the representation of transitions between states of the world (i.e., states of complete knowledge) as a special case, proving to be very flexible. In the present Part II, we describe the DLV planning system, which implements K on top of the disjunctive logic programming system DLV. This novel planning system allows for solving hard planning problems, including secure planning under incomplete initial states (often called conformant planning in the literature), which cannot be solved at all by other logic-based planning systems such as traditional satisfiability planners. We present a detailed comparison of the system to several state-of-the-art conformant planning systems, both at the level of system features and on benchmark problems. Our results indicate that, thanks to the power of knowledge-state problem encoding, the DLV system is competitive even with special purpose conformant planning systems, and it often supplies a more natural and simple representation of the planning problems.

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.

Despite considerable advancements in the area of access control and authorization languages, cur-rent approaches to enforcing access control are all based on monolithic and complete specifications. This assumption is too restrictive when access control restrictions to be enforced come from the combination of different policy specifications, each possibly under the control of independent authorities, and where the specifics of some component policies may not even be known a priori. Turning individual specifications into a coherent policy to be fed into the access control system requires a nontrivial combination and translation process. This article addresses the problem of combining authorization specifications that may be independently stated, possibly in different lan-guages and according to different policies. We propose an algebra of security policies together with its formal semantics and illustrate how to formulate complex policies in the algebra and reason about them. A translation of policy expressions into equivalent logic programs is illustrated, which provides the basis for the implementation of the algebra. The algebra’s expressiveness is analyzed through a comparison with first-order logic.

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. Equilibrium logic, introduced by David Pearce, extends the concept of an answer set from logic programs to arbitrary sets of formulas. Logic programs correspond to the special case in which every formula is a “rule ” — an implication that has no implications in the antecedent (body) and consequent (head). The semantics of equilibrium logic looks very different from the usual definitions of an answer set in logic programming, as it is based on Kripke models. In this paper we propose a new definition of equilibrium logic which uses the concept of a reduct, as in the standard definition of an answer set. Second, we apply the generalized concept of an answer set to the problem of defining the semantics of aggregates in answer set programming. We propose, in particular, a semantics for weight constraints that covers the problematic case of negative weights. Our semantics of aggregates is an extension of the approach due to Faber, Leone, and Pfeifer to a language with choice rules and, more generally, arbitrary rules with nested expressions. 1