We present a simple, yet general top-down query answering procedure for normal logic programs over lattices and bilattices, where functions may appear in the rule bodies. Its interest relies on the fact that many approaches to paraconsistency and uncertainty in logic programs with or without non-monotonic negation are based on bilattices or lattices, respectively.

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.

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

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

We present a simple, yet general top-down query answering procedure for logic programs managing uncertainty. The main features are: (i) the certainty values are taken from a certainty lattice; (ii) computable functions may appear in the rule bodies to manipulate certainties; and (iii) we solve the problem by a reduction to an equational systems, for which we device a top-down procedure.

Abstract. We show how a fuzzy answer set program can be compiled to an equivalent fuzzy propositional theory whose models correspond to the answer sets of the program. This creates a basis for constructing fuzzy answer set solvers, such as solvers based on fuzzy SAT-solvers or on linear programming. Keywords: answer set programming, fuzzy logic, Clark’s completion, fuzzy ASSAT. 1

Abstract — In the current approaches to fuzzy answer set programming (FASP) one can state preferences amongst rules to denote their relative importance. However, in many situations we need more complex preferences such as those in the answer set optimization framework proposed by Brewka for crisp answer set programming. Unfortunately, these complex preferences do not readily fit into the current FASP approaches. In this paper we propose a language to state such preferences and show that programs with these preferences can be translated into equivalent general fuzzy answer set programming (gFASP) programs. This not only provides an implementation method, but also shows that this extension can be added as syntactic sugar on top of general fuzzy answer set programming solvers.

Abstract The management of imprecise information in logic programs becomes important whenever the real world information to be represented is of an imperfect nature and the classical crisp true, false approximation is not adequate. In this work, we consider normal logic programs over complete lattices, where computable truth combination functions may appear in the rule bodies to manipulate truth values and we will provide a top-down query answering procedure. Keywords Logic programming · Nonmonotonic logic · Many-valued logic