On the Equivalence Between Abstract Dialectical Frameworks and Logic Programs. Issue 5 (September 2019) - ALCÂNTARA, JOÃO; SÁ, SAMY; ACOSTA-GUADARRAMA, JUAN
Abstract: Abstract Dialectical Frameworks ( ADF s) 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 ( NLP s) to ADF s and proved the stable models semantics for a normal logic program has an equivalent semantics to that of the corresponding ADF . However, these studies failed in identifying a semantics for ADF s equivalent to a three-valued semantics (as partial stable models and well-founded models) for NLP s. In this work, we focus on a fragment of ADF s, called Attacking Dialectical Frameworks ( ADF + s), and provide a translation from NLP s to ADF + s robust enough to guarantee the equivalence between partial stable models, well-founded models, regular models, stable models semantics for NLP s and respectively complete models, grounded models, preferred models, stable models for ADF s. In addition, we define a new semantics for ADF + s, called L -stable, and show it is equivalent to the L -stable semantics for NLP s.