On the Equivalence Between Abstract Dialectical Frameworks and Logic Programs

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.

Comparing logic programming and formal argumentation; the case of ideal and eager semantics

“…What Table 3 and Table 4 in essence show is in which case doing a particular selection on the argument level yields the same result as doing a comparable selection on the conclusion level. Our findings should also benefit some similar investigations exploring semantic correspondences between logic programming semantics and other argumentation formalisms, such as [1,36,37,42].…”

“…We round off with a discussion of the obtained results and an overview of the overall correspondences and non-correspondences between argumentation semantics and logic programming semantics in Section 6. 1 The first two correspondences are also observed in [24], though in a different way.…”

“…For instance, Caminada et al [16] used this translation to show the additional correspondence between well-founded semantics for logic programming and grounded semantics for formal argumentation, between 2-valued stable semantics for logic programming and stable semantics for formal argumentation, and between regular semantics for logic programming and preferred semantics for formal argumentation. 1 In the current paper, we identify an additional correspondence between logic programming semantics and formal argumentation semantics: the correspondence between ideal semantics for logic programming and ideal semantics for formal argumentation. To do so, we will make use of a recent reformulation of ideal semantics for logic programming [17], which brings it closer to ideal semantics for formal argumentation.…”

Argumentation frameworks with necessities and their relationship with logic programs

“…The main acceptability semantics 1 of Dung AFs are defined as follows: Definition 2.3 (Acceptability semantics). Let H = A, R be an AF and E ⊆ A. E is a complete extension iff it is admissible and contains all the elements it defends (i.e., F H (E) = E); E is the grounded extension iff it is the ⊆-minimal complete extension; E is a preferred extension iff it is a ⊆-maximal complete extension; E is a stable extension iff it is conflict-free and attacks all the arguments outside it (i.e.,…”

On the Semantics of Abstract Argumentation Frameworks: A Logic Programming Approach

“…In particular, the semantic equivalence between complete extensions in AF and 3-valued stable models in LP was first established in (Wu et al 2009). Then, the relationships of LP with AF have been further studied in (Caminada et al 2015), whereas those with Assumption-Based Argumentation (Bondarenko et al 1997;Craven and Toni 2016) have been considered in (Caminada and Schulz 2017), and those with Abstract Dialectical Frameworks have been investigated in (Alcântara et al 2019). Efficient mappings from AF to Answer Set Programming (i.e.…”