General Fuzzy Answer Set Programs Jeroen Janssen 1 , Steven Schockaert 2 , Dirk Vermeir 1 , and Martine De Cock 2 1 Dept. of Computer Science, Vrije Universiteit Brussel {jeroen.janssen,dvermeir}@vub.ac.be 2 Dept. of Applied Mathematics and Computer Science, Universiteit Gent {steven.schockaert,martine.decock}@ugent.be Abstract. A number of generalizations of answer set programming have been proposed in the literature to deal with vagueness, uncertainty, and partial rule satisfaction. We introduce a unifying framework that entails most of the existing approaches to fuzzy answer set programming. In this framework, rule bodies are defined using arbitrary fuzzy connectives with monotone partial mappings. As an approximation of full answer sets, k–answer sets are introduced to deal with conflicting information, yielding a flexible framework that encompasses, among others, existing work on valued constraint satisfaction and answer set optimization. Keywords: Answer Set Programs, Fuzzy Logic, Valued Constraint Satisfac- tion 1 Introduction Answer set programming [1] (ASP) is a form of non-monotonic reasoning which is based on the stable model semantics for logic programming [2]. Intuitively, in calculating answer sets of a logic program (rule base), we are interested in what can be derived from given facts by applying rules (forward chaining). This corresponds to a form of skeptical reasoning, where we are only interested in well- motivated models. When there are no occurrences of negation-as-failure in the rules, there is exactly one answer set, which corresponds to the unique minimal model of the rule base. In general, with negation-as-failure, there may be several answer sets which are defined using stable model semantics. Various extensions of ASP have been proposed to deal with different facets of imperfect information, most notably probabilistic extensions to deal with un- certainty and fuzzy extensions to deal with vagueness. Consider, for example, the following rules: r 1 : bad weather rainy r 2 : bad weather sunshine r 3 : bbq bad weather hungry r 4 : sunshine true Funded by a joint Research Foundation–Flanders (FWO) project Research Assistant of the Research Foundation - Flanders (FWO)