On the Equivalence Between Abstract Dialectical Frameworks and Logic Programs
This work addresses a theoretical gap in formal argumentation and logic programming for researchers in AI and computational logic, though it appears incremental as it builds on prior translations by extending equivalence to three-valued semantics.
The paper tackles the problem of establishing equivalence between semantics of Normal Logic Programs (NLPs) and Abstract Dialectical Frameworks (ADFs), specifically by focusing on a fragment called Attacking Dialectical Frameworks (ADF$^+$s) and providing a translation that guarantees equivalence for multiple semantics, including partial stable, well-founded, regular, stable, and L-stable models.
Abstract 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) to ADFs 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 ADFs equivalent to a three-valued semantics (as partial stable models and well-founded models) for NLPs. In this work, we focus on a fragment of ADFs, called Attacking Dialectical Frameworks (ADF$^+$s), and provide a translation from NLPs to ADF$^+$s robust enough to guarantee the equivalence between partial stable models, well-founded models, regular models, stable models semantics for NLPs and respectively complete models, grounded models, preferred models, stable models for ADFs. In addition, we define a new semantics for ADF$^+$s, called L-stable, and show it is equivalent to the L-stable semantics for NLPs. This paper is under consideration for acceptance in TPLP.