Qualitative uncertainty and dynamics of argumentation through dynamic logic

Abstract

Dynamics and uncertainty are essential features of real-life argumentation, and many recent studies have focused on integrating both aspects into Dung’s well-known abstract argumentation frameworks (AFs). This paper proposes a combination of the two lines of research through a well-behaved logical tool: dynamic logic of propositional assignments (DL-PA). Our results show that the main reasoning tasks of virtually all existing formalisms qualitatively representing uncertainty about AFs are encodable in DL-PA. Moreover, the same tool is also useful for capturing dynamic structures, such as control AFs, as well as for developing more refined forms of argumentative communication under uncertainty.

How to Manage Supports in Incomplete Argumentation

“…The proofs of these lemmas are left to the reader. Then, the claim of the proposition follows from the last three bullet points, and the correctness of mkExt for our target semantics {co, st, gr, pr} (see, e.g., [45,Theorem 1]). □ Proposition 9 Let IB = ⟨A, A ?…”

“…We will now encode acceptability problems for IBAFs in DL-PA. For space reasons, we only list here the main definitions and results. For more details, the reader is referred to previous papers on abstract models of argumentation and DL-PA [19,21,20,29,45,32].…”

“…Then: Usefulness of the Encoding. Our translation of IBAFs to DL-PA follows a tradition of capturing abstract argumentation in this lightweight version of dynamic logic [19,21,20,29,45]. As such, the reasons given throughout this branch of the literature to justify the usefulness of this technique are naturally inherited by our approach.…”

“…the size of the background set of arguments A), their DL-PA analogous are polynomially long (c.f. [20,45]).…”

“…This paper moves forward in the combination of argumentative bipolarity and argumentative uncertainty by providing several contributions to the study of IBAFs: (i) we compare in detail the existing notions of completions (the hypothetical removal of uncertainty used in IBAFs to reason about argument acceptability); (ii) we motivate and define a new notion of completion, which is somehow a compromise in between the proposals made by us [32] and Fazzinga et al [27]; (iii) we throw new complexity results about argument acceptability problems in IBAFs; (iv) we encode these problems in the Dynamic Logic of Propositional Assignments (DL-PA) [3,2], a well-behaved variant of propositional dynamic logic that has been proven useful to reason about argumentation in recent years [19,21,20,29,45]. Apart from that, a significant part of the results that will be shown here were already presented in [32], so the current document can be seen as an improved and extended presentation, paper-style, of the mentioned technical report.…”