Capturing Bipolar Argumentation in Non-flat Assumption-Based Argumentation

Abstract

Bipolar Argumentation Frameworks (BAFs) encompass both attacks and supports among arguments. We study different semantic interpretations of support in BAFs, particularly necessary and deductive support, as well as argument coalitions and a recent proposal by Gabbay. We analyse the relationship of these different notions of support in BAFs with the semantics of a well established structured argumentation formalism, Assumption-Based Argumentation (ABA), which predates BAFs. We propose natural mappings from BAFs into a restricted class of (non-flat) ABA frameworks, which we call bipolar, and prove that the admissible and preferred semantics of these ABA frameworks correspond to the admissible and preferred semantics of the various approaches to BAFs. Motivated by the definition of stable semantics for BAFs, we introduce a novel set-stable semantics for ABA frameworks, and prove that it corresponds to the stable semantics of the various approaches to BAFs. Finally, as a by-product of modelling various approaches to BAFs in bipolar ABA, we identify precise semantic relationships amongst all approaches we consider

Argumentation and explainable artificial intelligence: a survey

“…(2016a); Čyras et al . (2016b), the authors use CBR to classify arguments to set possible options, and when new information is inserted to the KB, the class of the argument may change. Another study that uses CBR and Argumentation is Čyras et al .…”

Aggregating Bipolar Opinions (With Appendix)

“…Bipolar Assumption-based Argumentation [12] (Bipolar ABA) is a form of structured argumentation, where arguments and attacks are derived from assumptions, rules, and a contrary map from assumptions. Note that contrary should not be confused with negation, which may or may not occur in the underlying language [23].…”

“…To address the problem that different parties may adopt different interpretations of support in their opinions (BAFs), we use Bipolar Assumption-based Argumentation (ABA) frameworks [12] for representing opinions. Bipolar ABA is a restricted (but "non-flat") form of ABA providing a unified formalism to accommodate different interpretations of support [12]. Thus, by adopting Bipolar ABA, we let parties choose their interpretation of support before aggregation takes place.…”

On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games: 25 years later

“…The expressiveness was then extended to incorporate other argumentative notions. For instance, support was added, and nesting of support and attack [9,28,36,77,113]. We already mentioned different approaches to argument structure (Section 2.1, and see [17]), some directly building on [39], others indirectly.…”