On the Equivalence Between Abstract Dialectical Frameworks and Logic Programs

Abstract

AbstractAbstract Dialectical Frameworks (ADFs) are argumentation frameworks where each node is associated with an acceptance condition. This allows us to model different types of dependencies as supports and attacks. Previous studies provided a translation from Normal Logic Programs (NLPs) toADFs and proved the stable models semantics for a normal logic program has an equivalent semantics to that of the correspondingADF. However, these studies failed in identifying a semantics forADFs equivalent to a three-valued semantics (as partial stable models and well-founded models) forNLPs. In this work, we focus on a fragment ofADFs, called Attacking Dialectical Frameworks (ADF+s), and provide a translation fromNLPs toADF+s robust enough to guarantee the equivalence between partial stable models, well-founded models, regular models, stable models semantics forNLPs and respectively complete models, grounded models, preferred models, stable models forADFs. In addition, we define a new semantics forADF+s, calledL-stable, and show it is equivalent to theL-stable semantics forNLPs.