Generic Tableaux for Answer Set Programming

Abstract. We provide a general and modular framework for describing inferences in Answer Set Programming (ASP) that aims at an easy incorporation of additional language constructs. To this end, we generalize previous work characterizing computations in ASP by means of tableau methods. We start with a very basic core fragment in which rule heads and bodies consist of atomic literals. We then gradually extend this setting by focusing on the concept of an aggregate, understood as an operation on a collection of entities. We exemplify our framework by applying it to conjunctions in rule bodies, cardinality constraints as used in smodels, and finally to disjunctions in rule heads.