Computing ideal sceptical argumentation

Abstract

We present two dialectic procedures for the sceptical ideal semantics for argumentation. The first procedure is defined in terms of dispute trees, for abstract argumentation frameworks. The second procedure is defined in dialectical terms, for assumption-based argumentation frameworks. The procedures are adapted from (variants of) corresponding procedures for computing the credulous admissible semantics for assumption-based argumentation, proposed in [P.M. Dung, R.A. Kowalski, F. Toni, Dialectic proof procedures for assumption-based, admissible argumentation, Artificial Intelligence 170 (2006) 114-159]. We prove that the first procedure is sound and complete, and the second procedure is sound in general and complete for a special but natural class of assumption-based argumentation frameworks, that we refer to as p-acyclic. We also prove that in the case of p-acyclic assumption-based argumentation frameworks (a variant of) the procedure of [P.M. Dung, R.A. Kowalski, F. Toni, Dialectic proof procedures for assumption-based, admissible argumentation, Artificial Intelligence 170 (2006) 114-159] for the admissible semantics is complete. Finally, we present a variant of the procedure of [P.M. Dung, R.A. Kowalski, F. Toni, Dialectic proof procedures for assumption-based, admissible argumentation, Artificial Intelligence 170 (2006) 114-159] that is sound for the sceptical grounded semantics

Graph-Based Dispute Derivations in Assumption-Based Argumentation

“…Theorem 4.2 in [3] proves that GB-DDs are sound: if there is a GB-DD of ∆ for s then s is grounded and ∆ is admissible and contained in the grounded set of assumptions.…”

“…There are parallel, equivalent notions for sets of assumptions rather than arguments [3,14]. A set of assumptions B attacks a set of assumptions A iff there is some an argument forā supported by some B ⊆ B, for some a ∈ A.…”

“…see [2,3]). Here, we focus on GB-dispute derivations [3] (GBDDs in short). Given a selection function (taking a multi-set and returning an element occurring in it) a GB-DD of a defence set ∆ ⊆ A for a sentence s ∈ L is a finite sequence of tuples 2 …”

“…Assumption-Based Argumentation (ABA) [1][2][3][4][5] is a well-known framework for structured argumentation where, in contrast to abstract argumentation [6], arguments and attacks are not primitives but are derived from the rules of a given deductive system, assumptions and contraries. 1 ABA has been applied in several settings (e.g.…”

“…to support medical decision-making [7] and e-procurement [8]). ABA's applicability relies on the existence of computational mechanisms, based on various kinds of dispute derivations [2,3,5] that are formally proven to be correct procedures for conducting structured argumentation under various semantics. For example, [3] proposes GB-dispute derivations (GB-DDs in short) for determining whether sentences can be justified by grounded sets of arguments and assumptions.…”