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.

In this paper we present a logic programming-based language allowing for the combination of several adjoint lattices of truth-values. A model and xpoint theory are presented, but the main contribution of the paper is the study of general properties guaranteeing termination of all queries. New results are presented and related to other alternative formalisms.

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).

A neural approach to propositional multi-adjoint logic programming was recently introduced. In this paper we extend the neural approach to multi-adjoint deduction and, furthermore, modify it to cope with abductive multi-adjoint reasoning, where adaptations of the uncertainty factor in a knowledge base are carried out automatically so that anumber of given observations can be adequately explained.

Muki-adjoint logic programs generalise monotonic and residuated logic pro- grams [21 in that simultaneous use of several implications in the rules and rather general connectives in the bodies are allowed. As our approach has continuous fixpoint semantics, in this work, a procedural semantics is given for the paradigm of multi-adjoint logic programming and a completeness result is proved.

Residuated Logic Programs allow to capture a spate of different semantics dealing with uncertainty and vagueness. A first result states that for any definite residuated logic program the sequence of iterations of the immediate consequences operator reaches the least fixpoint after only finitely many steps. Then, a tabulation query procedure is introduced, and it is shown that the procedure terminates every definite residuated logic program.

Multi-adjoint logic programs has been recently introduced [9, 10] as a generalization of monotonic logic programs [2, 3], in that simultaneous use of several implications in the rules and rather general connectives in the bodies are allowed.

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.

Abstract — In this paper we present the operational semantics of RFuzzy, a fuzzy Logic Programming framework that represents thruth values using real numbers from the unit interval. RFuzzy provides some useful extensions: default values to represent missing information, and typed terms to intuitively restrict predicate domains. Together, they allow the system to give constructive answers in addition to truth values. RFuzzy does not confine to a particular Fuzzy Logic, but aims at being as general as possible by using the notion of aggregation operators.

This paper discusses abductive reasoning, that is, reasoning in which explanatory hypotheses are formed and evaluated. Specifically, we present a neural net based development of abductive multi-adjoint reasoning, introduced in [4], where adaptations of the uncertainty factor in a knowledge base are carried out automatically so that a number of given observations can be adequately explained