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.

本研究针对一种名为ADFs的论证框架，提出ADF^ +，实现与NLP的语义等价，并定义了一种新的ADF^ +语义用于nlp的L-stable语义的等价。

关于抽象辩证框架和逻辑程序之间的等价性