Logical theories and abstract argumentation: A survey of existing works

Abstract

In 1995, in his seminal paper introducing the abstract argumentation framework, Dung has also established the first relationship between this framework and a logical framework (in this case: logic programming). Since that time, a lot of work have pursued this path, proposing different definitions, uses and exhibiting distinct relationships between argumentation and logic. In this paper, we present a survey of existing works about this topic and more especially those that address the following question: "How logic has been used for capturing various aspects or parts of Dung's argumentation". This survey covers many different approaches but is not intended to be totally exhaustive due to the huge quantity of papers in this scope. Moreover, due to the fact that each approach has its own specificities, sometimes antagonistic with the other approaches, and is also justified by its own context of definition or use, the aim of this survey is not to identify one approach as being better than another.

Abstract Argumentation with Qualitative Uncertainty: An Analysis in Dynamic Logic

“…Concurrently, a large number of works within formal argumentation have focused on building a suitable logical theory for reasoning about argumentation formalisms, with a special focus on AFs and their dynamics (see [13] for a recent survey on the topic). The dynamic logic of propositional assignments (DL-PA) [4] has been shown to be a useful tool for this enterprise [20][21][22].…”

On the Epistemic Logic of Incomplete Argumentation Frameworks

“…AFs were first studied by (Dung 1995), where the author proposed to capture the informal notion of argument acceptability through different argumentation semantics. For the sake of brevity, we limit ourselves to stable semantics, but our analysis applies to all semantics that can be captured in propositional logic (see (Besnard, Cayrol, and Lagasquie-Schiex 2020)). A stable extension of an AF (A, R) is a set of arguments E ⊆ A s.th.…”

Imprecise abstract argumentation as a support for forensic engineering

“…Imprecise probability argumentation system (IPAS) 2.1 Abstract argumentation framework (AAF) Formalized for the first time by Dung (1995), the AAF is a tuple < Args; Atts > where Args is a finite set of arguments and Atts a finite set of attacks (or defeats) in the form of binary relations Atts ⊆ Args 3 Args (Dung, 1995). An argument is a declarative sentence that has a truth value, which can be expressed in probabilistic terms (see Sections 2.2 and 2.3); in abstract argumentation, the internal consistency of the argument is not questioned; an argument is assumed to be valid without considering if it is a premise or a conclusion (Besnard et al, 2020).…”