In this paper we present a study of the problem of handling constraints made by conjunctions of positive and negative literals based on the predicate symbols =, ∈,∪ and || (i.e., disjointness of two sets) in a (hybrid) universe of finite sets . We also review and compare the main techniques considered to represent finite sets in the context of logic languages. The resulting contraint algorithms are embedded in a Constraint Logic Programming (CLP) language which provides finite sets—along with basic set-theoretic operations—as first-class objects of the language. The language—called CLP( SET )—is an instance of the general CLP framework, and as such it inherits all the general features and theoretical results of this scheme. We provide, through programming examples, a taste of the expressive power offered by programming in CLP( SET ).

The field of multi-agent system (MAS) is an active area of research within artificial intelligence, with an increasingly important impact in industrial and other real-world applications. In a MAS, autonomous agents interact to pursue personal interests and/or to achieve common objectives. Distributed Constraint Optimization Problems (DCOPs) have emerged as a prominent agent model to govern the agents' autonomous behavior, where both algorithms and communication models are driven by the structure of the specific problem. During the last decade, several extensions to the DCOP model have been proposed to enable support of MAS in complex, real-time, and uncertain environments.This survey provides an overview of the DCOP model, offering a classification of its multiple extensions and addressing both resolution methods and applications that find a natural mapping within each class of DCOPs. The proposed classification suggests several future perspectives for DCOP extensions, and identifies challenges in the design of efficient resolution algorithms, possibly through the adaptation of strategies from different areas.

Since the early days of logic programming, researchers in the field realized the potential for exploitation of parallelism present in the execution of logic programs. Their high-level nature, the presence of non-determinism, and their referential transparency, among other characteristics, make logic programs interesting candidates for obtaining speedups through parallel execution. At the same time, the fact that the typical applications of logic programming frequently involve irregular computations, make heavy use of dynamic data structures with logical variables, and involve search and speculation, makes the techniques used in the corresponding parallelizing compilers and run-time systems potentially interesting even outside the field. The objective of this paper is to provide a comprehensive survey of the issues arising in parallel execution of logic programming languages along with the most relevant approaches explored to date in the field. Focus is mostly given to the challenges emerging from the parallel execution of Prolog programs. The paper describes the major techniques used for shared memory implementation of Or-parallelism, Andparallelism, and combinations of the two. We also explore some related issues, such as memory management, compile-time analysis, and execution visualization.

This technical note describes a monotone and continuous fixpoint operator to compute the answer sets of programs with aggregates. The fixpoint operator relies on the notion of aggregate solution. Under certain conditions, this operator behaves identically to the three-valued immediate consequence operator Φ aggr P for aggregate programs, independently proposed in Pelov (2004) and Pelov et al. (2004). This operator allows us to closely tie the computational complexity of the answer set checking and answer sets existence problems to the cost of checking a solution of the aggregates in the program. Finally, we relate the semantics described by the operator to other proposals for logic programming with aggregates.

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Abstract. We provide new perspectives on the semantics of logic programs with constraints. To this end we introduce several notions of computation and propose to use the results of computations as answer sets of programs with constraints. We discuss the rationale behind different classes of computations and study the relationships among them and among the corresponding concepts of answer sets. The proposed semantics generalize the answer set semantics for programs with monotone, convex and/or arbitrary constraints described in the literature.

In this paper, we present two alternative approaches to defining answer sets for logic programs with arbitrary types of abstract constraint atoms (c-atoms). These approaches generalize the fixpoint-based and the level mapping based answer set semantics of normal logic programs to the case of logic programs with arbitrary types of c-atoms. The results are four different answer set definitions which are equivalent when applied to normal logic programs. The standard fixpoint-based semantics of logic programs is generalized in two directions, called answer set by reduct and answer set by complement. These definitions, which differ from each other in the treatment of negation-as-failure (naf) atoms, make use of an immediate consequence operator to perform answer set checking, whose definition relies on the notion of conditional satisfaction of c-atoms w.r.t. a pair of interpretations. The other two definitions, called strongly and weakly well-supported models, are generalizations of the notion of well-supported models of normal logic programs to the case of programs with c-atoms. As for the case of fixpoint-based semantics, the difference between these two definitions is rooted in the treatment of naf atoms. We prove that answer sets by reduct (resp. by complement) are equivalent to weakly (resp. strongly) well-supported models of a program, thus generalizing the theorem on the correspondence between stable models and well-supported models of a normal logic program to the class of programs with c-atoms. We show that the newly defined semantics coincide with previously introduced semantics for logic programs with monotone c-atoms, and they extend the original answer set semantics of normal logic programs. We also study some properties of answer sets of programs with c-atoms, and relate our definitions to several semantics for logic programs with aggregates presented in the literature