A Logical Theory about Dynamics in Abstract Argumentation

Abstract

International audienceWe address dynamics in abstract argumentation using a logical theory where an agent's belief state consists of an argumentation framework (AF, for short) and a constraint that encodes the outcome the agent believes the AF \emph{should} have. Dynamics enters in two ways: (1) the constraint is strengthened upon learning that the AF should have a certain outcome and (2) the AF is expanded upon learning about new arguments/attacks. A problem faced in this setting is that a constraint may be inconsistent with the AF's outcome. We discuss two ways to address this problem: First, it is still possible to form consistent \emph{fallback beliefs}, i.e., beliefs that are most plausible given the agent's AF and constraint. Second, we show that it is always possible to find AF expansions to restore consistency. Our work combines various individual approaches in the literature on argumentation dynamics in a general setting

Argument Revision

“…For instance, several works have incorporated dynamics into abstract argumentation by considering the outcome of an abstract argumentation framework [10,17,21]. Briefly, the outcome of a framework is a description of which arguments should be accepted and those which should now (under some semantics).…”

“…Briefly, the outcome of a framework is a description of which arguments should be accepted and those which should now (under some semantics). The models proposed in [10,21] permit only expansions of (or additions to) a framework and do not include contractions. Postulates for the revision of an argumentation system are presented in in [17], but these conflate revision and contraction; an outcome can describe arguments to be both accepted and not accepted.…”

Conflict-free and conflict-tolerant semantics for constrained argumentation frameworks

“…Thus, for instance, the addition of the (non-admissible) constraint A ∨ B ∨ C to the argumentation framework AF 2 of Fig. 2 would yield, according to [13], three extensions {A}, {B}, {C}, each one is conflict-free, but neither of them is admissible.…”

“…This assures Propositions 33 and 37 below, which do not hold in the case of [17], where non-empty extensions for CAFs may not exist. Recently, Booth et al [13] provided a method for generating non-empty conflict-free extensions for constrained argumentation frameworks, but the price for that is a waiving of the principle of admissibility, so in their formalism not only the integrity constraints, but also the extensions themselves may not be admissible. Thus, for instance, the addition of the (non-admissible) constraint A ∨ B ∨ C to the argumentation framework AF 2 of Fig.…”

“…The incorporation of constraints may be useful in handling scenarios where an argumentation framework is viewed as a dynamic process [13]. For instance, constraints may encode the expected outcome of an argumentation framework, or may help to evaluate the consequences of an argumentation framework in light of new arguments (see [16]).…”