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.

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.

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.

In this paper, we develop the notion of fuzzy unification and incorporate it into a novel fuzzy argumentation framework for extended logic programming. We make the following contributions: The argumentation framework is defined by a declarative bottom-up fixpoint semantics and an equivalent goal-directed top-down proof-procedure for extended logic programming. Our framework allows one to represent positive and explicitly negative knowledge, as well as uncertainty. Both concepts are used in agent communication languages such as KQML and FIPA ACL. One source of uncertainty in open systems stems from mismatches in parameter and predicate names and missing parameters. To this end, we conservatively extend classical unification and develop fuzzy unification based on normalised edit distance over trees.

Abstract. A prospective study of the use of ordered multi-lattices as underlying sets of truth-values for a generalised framework of logic programming is presented. Specifically, we investigate the possibility of using multi-lattice-valued interpretations of logic programs and the theoretical problems that this generates with regard to its fixed point semantics. 1

A generalization of the homogenization process needed for the neural implementation of multi-adjoint logic programming (a unifying theory to deal with uncertainty, imprecise data or incomplete information) is presented here. The idea is to allow to represent a more general family of adjoint pairs, but maintaining the advantage of the existing implementation recently introduced in [6]. The soundness of the transformation is proved and its complexity is analysed. In addition, the corresponding generalization of the neural-like implementation of the fixed point semantics of multi-adjoint is presented. 1

A synthesis of results of the recently introduced paradigm of multi-adjoint logic programming is presented. These results range from a proof theory together with some (quasi)completeness results to general termination results, and from the neural-like implementation of its fix-point semantics to the more general biresiduated multi-adjoint logic programming and its relationship with other approaches.

Abstract. The theory of multi-adjoint logic programs has been introduced as a unifying framework to deal with uncertainty, imprecise data or incomplete information. From the applicative part, a neural net based implementation of homogeneous propositional multi-adjoint logic programming on the unit interval has been presented elsewhere, but restricted to the case in which the only connectives involved in the program were the usual product, Gödel and Łukasiewicz together with weighted sums. A modification of the neural implementation is presented here in order to deal with a more general family of adjoint pairs, including conjunctors constructed as an ordinal sum of a finite family of basic conjunctors. This enhancement greatly expands the scope of the initial approach, since every t-norm (the type of conjunctor generally used in applications) can be expressed as an ordinal sum of product, Gödel and Łukasiewicz conjunctors. 1

We investigate the use of multilattices as the set of truth-values underlying a general fuzzy logic programming framework. On the one hand, some theoretical results about ideals of a multilattice are presented in order to provide an ideal-based semantics; on the other hand, a restricted semantics, in which interpretations assign elements of a multilattice to each propositional symbol, is presented and analysed. Key words: Fuzzy logic programming, multilattices, fixed point semantics 1