Considering different implication operators, such as Lukasiewicz, Gödel or product implication in the same logic program, naturally leads to the allowance of several adjoint pairs in the lattice of truth-values. In this paper we apply this idea to introduce multi-adjoint logic programs as an extension of monotonic logic programs. The continuity of the immediate consequences operators is proved and the assumptions required to get continuity are further analysed.

In a previous work we have de ned Monotonic Logic Programs which extend definite logic programming to arbitrary complete lattices of truth-values with an appropriate notion of implication. We have shown elsewhere that this framework is general enough to capture Generalized Annotated Logic Programs, Probabilistic Deductive Databases, Possibilistic Logic Programming, Hybrid Probabilistic Logic Programs and Fuzzy Logic Programming [3, 4]. However, none of these semantics define a form of non-monotonic negation, which is fundamental for several knowledge representation applications. In the spirit of our previous work, we generalise our framework of Monotonic Logic Programs to allow for rules with arbitrary antitonic bodies over general complete lattices, of which normal programs are a special case. We then show that all the standard logic programming theoretical results carry over to Antitonic Logic Programs, defining Stable Model and Well-founded Model alike semantics.

Multi-adjoint logic program generalise monotonic logic programs introduced in [1] in that simultaneous use of several implications in the rules and rather general connectives in the bodies are allowed.

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.

In this paper we present a logic programming-based language allowing for the combination of several lattices of truth-values under arbitrary monotonic operators. A model and xpoint theory are presented, but the main contributions of the paper are the embedding results of a series of existing logic programming semantics dealing with uncertainty, vagueness, or probabilistic reasoning. A major bene t of this work is to provide a comparative overview of the several proposals, all of which are translate into a single uni- ed general framework. This paves the way for the construction of integrated logic programming-based systems capturing several facets of human/formal uncertainty reasoning. We overview, and compare more than twenty dierent proposals in the extant literature.

The aim of this paper is to build a formal model for fuzzy unification in multi-adjoint logic programs containing both a declarative and a procedural part, and prove its soundness and completeness. Our approach is based on a general framework for logic programming, which gives a formal model of fuzzy logic programming extended by fuzzy similarities and axioms of first-order logic with equality.

A general framework of logic programming allowing for the combination of several adjoint lattices of truth-values is presented. The main contribution is a new sufficient condition which guarantees termination of all queries for the fixpoint semantics for an interesting class of programs. Several extensions of these conditions are presented and related to some well-known formalisms for probabilistic logic programming.

Managing uncertainty and/or vagueness is starting to play an important role in Semantic Web representation languages. Our aim is to overview basic concepts on representing uncertain and vague knowledge in current Semantic Web ontology and rule languages (and their combination).

We propose a framework which extends Antitonic Logic Programs [13] to an arbitrary complete bilattice of truth-values, where belief and doubt are explicitly represented. Inspired by Ginsberg and Fitting 's bilattice approaches, this framework allows a precise de nition of important operators found in logic programming, such as explicit and default negation. In particular, it leads to a natural semantical integration of explicit and default negation through the Coherence Principle [38], according to which explicit negation entails default negation. We then de ne Coherent Answer Sets, and the Paraconsistent Well-founded Model semantics, generalising many paraconsistent semantics for logic programs. In particular, Paraconsistent Well-Founded Semantics with eXplicit negation (WFSXp ) [3, 11]. The framework is an extension of Antitonic Logic Programs for most cases, and is general enough to capture Probabilistic Deductive Databases, Possibilistic Logic Programming, Hybrid Probabilistic Logic Programs, and Fuzzy Logic Programming. Thus, we have a powerful mathematical formalism for dealing simultaneously with default, paraconsistency, and uncertainty reasoning. Results are provided about how our semantical framework deals with inconsistent information and with its propagation by the rules of the program.

In this work, we define a new framework in order to improve the knowledge representation power of Answer Set Programming paradigm. Our proposal is to use notions from possibility theory to extend the stable model semantics by taking into account a certainty level, expressed in terms of necessity measure, on each rule of a normal logic program. First of all, we introduce possibilistic definite logic programs and show how to compute the conclusions of such programs both in syntactic and semantic ways. The syntactic handling is done by help of a fix-point operator, the semantic part relies on a possibility distribution on all sets of atoms and we show that the two approaches are equivalent. In a second part, we define what is a possibilistic stable model for a normal logic program, with default negation. Again, we define a possibility distribution allowing to determine the stable models. 1