On the Equivalence between Logic Programs and Bipolar Argumentation Frameworks

Abstract

Abstract Argumentation Frameworks (AAFs) and Normal Logic Programs (NLPs) are closely related formalisms for which many equivalences have already been elicited. In this paper, we extend this line of research by considering Bipolar Argumentation Frameworks (BAFs), in which arguments have an explicit support relation, independent of the attack relation. We provide direct translations from BAFs to NLPs (and vice versa) in a one-to-one correspondence between several argumentation and 3-valued logic programming semantics. This includes the equivalence involving L-stable semantics. Besides, we deepen the connection between NLPs and BAFs by finding subsets of them for which the proposed translations are each other’s inverse up to isomorphism.