A fibrational semantics for logic programs

In his paper [12] Ross extends the well-founded semantics for normal logic programs [16] to disjunctive logic programs. His definition is top-down and it is closer to a procedural semantics than to the elegant fixpoint definition of the well-founded semantics for normal logic programs. In the present paper, we propose a declarative, bottom-up fixpoint definition of the well-founded semantics for disjunctive logic programs. Our construction of the greatest unfounded set of extended literals is similar with the construction of the greatest unfounded set for normal programs. As a consequence, the connection between the well-founded semantics for normal programs and the well-founded semantics for disjunctive programs is made clearer.KeywordsLogic ProgramDeductive DatabaseNormal ProgramDisjunctive ProgramExtended AtomThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Game semantics for non-monotonic intensional logic programming

Over recent years, various semantics have been proposed for dealing with updates in the setting of logic programs. The availability of different semantics naturally raises the question of which are most adequate to model updates. A systematic approach to face this question is to identify general principles against which such semantics could be evaluated. In this paper we motivate and introduce a new such principle – the refined extension principle – which is complied with by the stable model semantics for (single) logic programs. It turns out that none of the existing semantics for logic program updates, even though based on stable models, complies with this principle. For this reason, we define a refinement of the dynamic stable model semantics for Dynamic Logic Programs that complies with the principle.

Most of the theoretical work on the semantics of logic programs assumes an interpreter that provides a complete resolution procedure. In contrast, for reasons of efficiency, most logic programming languages are built around incomplete procedures. This difference is rooted in Prolog, which evaluates resolvent trees in a depth-first rather than a breadth-first order. The gap is widened by some equational logic languages, which combine the incompleteness of depth-first evaluation with incomplete approximations to equational unification. Because of this gap, it is unsound to reason about logic programs using their declarative semantics. This in turn makes it difficult to develop abstraction mechanisms that can be used to partition a logic program into independently specifiable modules.

M. Bezem defined an extensional semantics for positive higher-order logic programs. Recently, it was demonstrated by Rondogiannis and Symeonidou that Bezem's technique can be extended to higher-order logic programs with negation, retaining its extensional properties, provided that it is interpreted under a logic with an infinite number of truth values. Rondogiannis and Symeonidou also demonstrated that Bezem's technique, when extended under the stable model semantics, does not in general lead to extensional stable models. In this paper, we consider the problem of extending Bezem's technique under the well-founded semantics. We demonstrate that the well-founded extensionfailsto retain extensionality in the general case. On the positive side, we demonstrate that for stratified higher-order logic programs, extensionality is indeed achieved. We analyze the reasons of the failure of extensionality in the general case, arguing that a three-valued setting cannot distinguish between certain predicates that appear to have a different behaviour inside a program context, but which happen to be identical as three-valued relations.

Three-valued completion for abductive logic programs

Given a first order language L, and a notion of a logic L w.r.t. L, we investigate the topological properties of the space of L-structures for L. We show that under a topology called the query topology which arises naturally in logic programming, the space of L-models (where L is a decent logic) of any sentence (set of clauses) in L may be regarded as a (closed, compact) T4-space. We then investigate the properties of maps from structures to structures. Our results allow us to apply various well-known results on the fixed-points of operators on topological spaces to the semantics of logic programming – in particular, we are able to derive necessary and sufficient topological conditions for the completion of covered general logic programs to be consistent. Moreover, we derive sufficient conditions guaranteeing the consistency of program completions, and for logic programs to be determinate. We also apply our results to characterize consistency of the unions of program completions.

We present some results on semantics for logic programs. We interpret logic programs in Kripke models. They connect the area of logic programming and that of nonclassical logics. New connectives are carried over dynamic logic to logic programs, resulting in so-called predicate programs. A wide class of predicate programs is shown to have the same meaning as formulas of dynamic logic with context-free programs. This allows to discuss the known problem of introducing the negation into logic programs in new light.

This paper extends fuzzy logic programs [12, 24] to allow the explicit representation of classical negation as well as non-monotonic negation, by introducing the notion of extended fuzzy logic programs. We present the fuzzy answer set semantics for the extended fuzzy logic programs, which is based on the classical answer set semantics of classical extended logic programs [7]. We show that the proposed semantics is a natural extension to the classical answer set semantics of classical extended logic programs [7]. Furthermore, we define fixpoint semantics for extended fuzzy logic programs with and without non-monotonic negation, and study their relationship to the fuzzy answer set semantics. In addition, we show that the fuzzy answer set semantics is reduced to the stable fuzzy model semantics for normal fuzzy logic programs introduced in [42]. The importance of that is computational methods developed for normal fuzzy logic programs can be applied to the extended fuzzy logic programs. Moreover, we show that extended fuzzy logic programs can be intuitively used for representing and reasoning about actions in fuzzy environment.

The Herbrand model H of a definite logic program P is an initial model among the class of all the models of P, interpreting P as an initial theory. Such a theory (program) proves (computes) only positive literals (atoms) in P, so it does not deal with negation. In this paper, we introduce isoinitial semantics for logic programs and show that it can provide a rich semantics for logic programs, which can deal with not just negation, but also incomplete information, parametricity and compositionality.KeywordsLogic ProgramLogic ProgrammingOpen ProgramConstant SymbolGround AtomThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Part of the theory of logic programming and nonmonotonic reasoning concerns the study of fixed-point semantics for these paradigms. Several different semantics have been proposed during the last two decades, and some have been more successful and acknowledged than others. The rationales behind those various semantics have been manifold, depending on one's point of view, which may be that of a programmer or inspired by commonsense reasoning, and consequently the constructions which lead to these semantics are technically very diverse, and the exact relationships between them have not yet been fully understood. In this paper, we present a conceptually new method, based on level mappings, which allows to provide uniform characterizations of different semantics for logic programs. We will display our approach by giving new and uniform characterizations of some of the major semantics, more particular of the least model semantics for definite programs, of the Fitting semantics, and of the well-founded semantics. A novel characterization of the weakly perfect model semantics will also be provided.

A game semantics for disjunctive logic programming

The problem of determining the correct declarative semantics for generalized logic programs is still open. In generalized logic programs the body of a rule may contain negated goals. Using a logical equivalence these programs may be viewed as disjunctive logic programs where the head of a rule may contain a disjunction of goals. We hope that a careful study of the declarative semantics of disjunctive logic programs will produce criteria for evaluating the different candidates for the semantics of generalized logic programs.A conceptual analysis leads to a semantical definition of the notion of a disjunctive deductive database as a generalization of the notion of a deductive database. It will be shown that the notion of a disjunctive deductive database is equivalent to the syntactical definition of a disjunctive logic program. We have characterized disjunctive deductive databases, i. e. theories which admit in each irreducible component a minimal Herbrand model and for which this property is preserved under the addition of new facts, as disjunctive logic programs. As a special case the result yields the known characterization of deductive databases, i. e. theories which admit a minimal Herbrand model and for which this property is preserved under the addition of new facts, as logic programs. In the presence of equations term structures i. e. extended Herbrand structures replace the Herbrand structures and h-core models replace the minimal models. Actually, the results could be proved in a more general context where pseudo term structures replace the term structures. In addition, there is an intermediate case where the irreducible components coincide with the connected components. Moreover, there are characterization results for the cases where the uniformity condition is not present.KeywordsLogic ProgramIrreducible ComponentTerm StructureCanonical ModelDeductive DatabaseThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

In this paper we show the embedding of Hybrid Probabilistic Logic Programs into the rather general framework of Residuated Logic Programs, where the main results of (definite) logic programming are validly extrapolated, namely the extension of the immediate consequences operator of van Emden and Kowalski. The importance of this result is that for the first time a framework encompassing several quite distinct logic programming semantics is described, namely Generalized Annotated Logic Programs, Fuzzy Logic Programming, Hybrid Probabilistic Logic Programs, and Possibilistic Logic Programming. Moreover, the embedding provides a more general semantical structure paving the way for defining paraconsistent probabilistic reasoning with a logic programming semantics.

On the equivalence between logic programming semantics and argumentation semantics