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 present Annotated Answer Set Programming, that extends the expressive power of disjunctive logic programming with annotation terms, taken from the generalized annotated logic programming framework.

We use the formal model for similarity-based fuzzy unification in multi-adjoint logic programs to provide new tools for flexible querying. 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.

In this paper we relate two logical similarity-based approaches to approximate reasoning. One approach extends the framework of (propositional) classical logic programming by introducing a similarity relation in the alphabet of the language that allows for an extended unification procedure. The second approach is a many-valued modal logic approach where ✸p is understood as approximately p. Here, the similarity relations are introduced at the level of the Kripke models where possible worlds can be similar to some extent. We show that the former approach can be expressed inside the latter.

Abstract. In this paper we relate two logical similarity-based approaches to approximate reasoning. One approach extends the framework of (propositional) classical logic programming by introducing a similarity relation in the alphabet of the language that allows for an extended unification procedure. The second approach is a many-valued modal logic approach where ✸p is understood as approximately p. Here, the similarity relations are introduced at the level of the Kripke models where possible worlds can be similar to some extent. We show that the former approach can be expressed inside the latter.

this paper we present a new quasicompleteness result for the first-order theory of multi-adjoint logic programs, a new general framework for generalized and fuzzy logic programming

In this paper we relate two logical similarity-based approaches to approximate reasoning. One approach extends the framework of (propositional) classical logic programming by introducing a similarity relation in the alphabet of the language that allows for an extended unification procedure. The second approach is a many-valued modal logic approach where ✸p is understood as approximately p. Here, the similarity relations are introduced at the level of the Kripke models where possible worlds can be similar to some extent. We show that the former approach can be expressed inside the latter.

We present a model of fuzzy logic programming with best answer semantics as an optimization task and discuss various utility function problems.

Incomplete information is a problem in many aspects of actual environments. In many sceneries the knowledge is not represented in a crisp way. It is common to find fuzzy concepts or problems with some level of uncertainty. It is difficult to find practical systems which handle fuzziness and uncertainty and the few examples that we can find are minority. To extend a popular system (which many of programmers are using) with this hability seems to be an interesting issue. Our first work (Fuzzy Prolog [1]) was a language that models B([0, 1])-valued Fuzzy Logic. In the Borel Algebra, B([0, 1]), truth value is represented using unions of intervals of real numbers. It subsumed former approaches because it was more general in truth value representation and propagation than them. Now, we enhance our former approach by using default knowledge to represent incomplete information in Logic Programming. We also provide the implementation of this new framework. This new release of Fuzzy Prolog handles incomplete information and it has a complete semantics (the before one was incomplete as Prolog) which we discuss. New Fuzzy Prolog is more expressive to represent real world.

Formal concept analysis has become an important and appealing research topic. There exist a number of different fuzzy extensions of formal concept analysis and of its representation theorem, which gives conditions for a complete lattice in order to be isomorphic to a concept lattice. In this paper we concentrate on the study of operational properties of the mappings α and β required in the representation theorem.