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We provide a new perspective on the semantics of logic programs with arbitrary abstract constraints. To this end, we introduce several notions of computation. We use the results of computations to specify answer sets of programs with constraints. We present the rationale behind the classes of computations we consider, and discuss the relationships among(More)
The paper introduces the notion of off-line justification for Answer Set Programming (ASP). Justifications provide a graph-based explanation of the truth value of an atom w.r.t. a given answer set. The paper extends also this notion to provide justification of atoms during the computation of an answer set (on-line justification), and presents an integration(More)
An extended logic programming language is presented, that embodies the fundamental form of set designation based on the (nesting) element insertion operator. The kind of sets to be handled is characterized both by adaptation of a suitable Herbrand universe and via axioms. Predicates 2 and = designating set membership and equality are included in the base(More)
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(More)
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(More)
Logic programming is a paradigm of programming based on a subset of rst order logic. An important property of logic programming languages, such as Prolog, is that their declarative semantics is largely independent of the order in which diierent operations are performed during execution of the program. The diierent operations can also be performed in(More)
Comparative analysis is used throughout biology. When entities under comparison (e.g. proteins, genomes, species) are related by descent, evolutionary theory provides a framework that, in principle, allows N-ary comparisons of entities, while controlling for non-independence due to relatedness. Powerful software tools exist for specialized applications of(More)
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 =, <inline-equation> <f> &#8712;,<hsp sp="0.265">&#8746;</f> </inline-equation> and <inline-equation> <f> &dvbm0;</f> </inline-equation> (i.e., disjointness of two sets) in a (hybrid) universe of <?Pub(More)