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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)
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 notion of justification accounts for the specifics of answer set semantics. The paper extends also this notion to provide justification of atoms during the(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)
This paper presents the design, implementation and application of a Constraint Programming framework on 3D crystal lattices. The framework provides the flexibility to express and resolve constraints dealing with structural relationships of entities placed in a 3D lattice structure in space. The paper describes both sequential and parallel implementations of(More)