Argumentation update in YALLA (Yet Another Logic Language for Argumentation)

Abstract

International audienceThis article proposes a complete framework for handling the dynamics of an abstract argumentation system. This frame can encompass several belief bases under the form of several argumentation systems, more precisely it is possible to express and study how an agent who has her own argumentation system can interact on a target argumentation system (that may represent a state of knowledge at a given stage of a debate). The two argumentation systems are defined inside a reference argumentation system called the universe which constitutes a kind of “common language”. This paper establishes three main results. First, we show that change in argumentation in such a framework can be seen as a particular case of belief update. Second, we have introduced a new logical language called YALLA in which the structure of an argumentation system can be encoded, enabling to express all the basic notions of argumentation theory (defense, conflict-freeness, extensions) by formulae of YALLA. Third, due to previous works about dynamics in argumentation we have been in position to provide a set of new properties that are specific for argumentation update

Logical theories and abstract argumentation: A survey of existing works

“…Section 6 is mainly devoted to an approach called YALLA [55], 3 whose language permits not only to express an argumentation framework by means of specific formulae of first-order logic but also to express properties of update operators in dynamic argumentation. As an aside, a distinctive feature of YALLA is that a reference universe of argumentation is assumed, which makes it possible to capture cases of incomplete knowledge.…”

Logical Encoding of Argumentation Frameworks with Higher-Order Attacks

“…Let us recall that dstructures are particular structures in which acceptable attacks are forced to be valid. So, we consider the base Σ(RAF ) augmented with the formula that expresses the reinstatement principle for attacks, that is formula (14).…”

“…Then, the standard defence, reinstatement and stability principles are encoded with simplified versions of formulae (11), (13) and (15) (as attacks are never attacked, formulae (12), (14) and (16) would be tautologies). Let AF = A, R .…”

“…[13], or defined a logical language for expressing the dynamics of a framework e.g. [14]. To the best of our knowledge, all these works consider only attacks between two arguments.…”

A Dynamic Logic Framework for Abstract Argumentation: Adding and Removing Arguments

“…In [6], the use of a dynamic logic (DL-PA-Dynamic Logic of Propositional Assignments [1]) furthermore allows us to model updates of the argument system, such as addition or removal of an attack, or modification of extensions. [6] is not the only approach which has tackled the question of the dynamics of argument systems (see [5,15] for instance), but this one provides a single framework which encompasses at the same time the argument system, the logical definition of the change to enforce, and the change operations to perform. Moreover, the logic it is based on is non-specific to argumentation since it has already been applied in various contexts [8,12].…”