Answer Sets for Logic Programs with Arbitrary Abstract Constraint Atoms

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

Clinamen : Entre libertad y determinismo en De Rerum Natura de Lucrecio

En el presente trabajo se trabaja principalmente en la noción de clinamen, el cual debe entenderse como una desviación azarosa que ocurre en el átomo. Lucrecio argumenta, siguiendo la tradición atomista que lo precede, que el fundamento ontológico de la realidad, es que toda la naturaleza está compuesta de átomos y vacío. El filósofo adhiere a una concepción esencialmente mecanicista del cosmos: el hecho de que el mundo no es una creación de los dioses, hace que la naturaleza sea una constante repetición de los hechos. El concepto de clinamen lleva a Lucrecio plantear, además, el problema del determinismo y la libertad: si todo movimiento es siempre una relación causal con un antes, ¿de dónde viene este poder independiente del destino, a través del cual nos movemos hacia donde la voluntad de cada uno conduce? En segundo lugar, si todos los movimientos de los átomos son inflexiblemente determinados, la capacidad humana para decidir y asumir la responsabilidad de su accionar no podrían explicarseIn this paper is mainly work the notion of swerve, that concept is understood as some random deviation that occurs in the atom. lucretius argues, as atomistic tradition that precedes it, that the ontological foundation of reality, is that all nature is made up of atoms and empty. He adheres to an essentially mechanistic evolution of the cosmos: the fact that the world is not a creation of gods, implies that the nature is a constant repetition of events. The notion of swerve leads to Lucretius to raise, in addition, the problem of determinism and freedom: if all movement is always causally linked to an earlier, where does this power independent of fate, through which we move towards where the will to each leads? Secondly, if all the motions of atoms are inflexibly determined, the human ability to decide and take responsibility for their actions can not be explaine

Logic Programming for Finding Models in the Logics of Knowledge and its Applications: A Case Study

The logics of knowledge are modal logics that have been shown to be effective in representing and reasoning about knowledge in multi-agent domains. Relatively few computational frameworks for dealing with computation of models and useful transformations in logics of knowledge (e.g., to support multi-agent planning with knowledge actions and degrees of visibility) have been proposed. This paper explores the use of logic programming (LP) to encode interesting forms of logics of knowledge and compute Kripke models. The LP modeling is expanded with useful operators on Kripke structures, to support multi-agent planning in the presence of both world-altering and knowledge actions. This results in the first ever implementation of a planner for this type of complex multi-agent domains.Comment: 16 pages, 1 figure, International Conference on Logic Programming 201

Set Unification

The unification problem in algebras capable of describing sets has been tackled, directly or indirectly, by many researchers and it finds important applications in various research areas--e.g., deductive databases, theorem proving, static analysis, rapid software prototyping. The various solutions proposed are spread across a large literature. In this paper we provide a uniform presentation of unification of sets, formalizing it at the level of set theory. We address the problem of deciding existence of solutions at an abstract level. This provides also the ability to classify different types of set unification problems. Unification algorithms are uniformly proposed to solve the unification problem in each of such classes. The algorithms presented are partly drawn from the literature--and properly revisited and analyzed--and partly novel proposals. In particular, we present a new goal-driven algorithm for general ACI1 unification and a new simpler algorithm for general (Ab)(Cl) unification.Comment: 58 pages, 9 figures, 1 table. To appear in Theory and Practice of Logic Programming (TPLP