Weighted Abstract Dialectical Frameworks

Abstract

Dialectical Frameworks (ADFs) generalize Dung's argumentation frameworks allowing various relationships among arguments to be expressed in a systematic way. We further generalize ADFs so as to accommodate arbitrary acceptance degrees for the arguments. This makes ADFs applicable in domains where both the initial status of arguments and their relationship are only insufficiently specified by Boolean functions. We define all standard ADF semantics for the weighted case, including grounded, preferred and stable semantics. We illustrate our approach using acceptance degrees from the unit interval and show how other valuation structures can be integrated. In each case it is sufficient to specify how the generalized acceptance conditions are represented by formulas, and to specify the information ordering underlying the characteristic ADF operator. We also present complexity results for problems related to weighted ADFs.

Solving Advanced Argumentation Problems with Answer-Set Programming

“…As shown in (Brewka et al 2013) these semantics generalize the corresponding notions defined for AFs. For σ ∈ {adm, com, prf}, σ(D) denotes the set of all admissible (resp.…”

“…We focus on two such generalizations, namely ADFs (Brewka and Woltran 2010;Brewka et al 2013) and GRAPPA , which are expressive enough to capture many of the other available frameworks. Reasoning in ADFs spans the first three levels of the polynomial hierarchy (Strass and Wallner 2015).…”

Argumentation frameworks with necessities and their relationship with logic programs

“…The work developed in [20,22,75] introduced abstract dialectical frameworks (ADF), a powerful generalization of Dung's AFs that formalizes the idea of proof standards, widely studied in legal reasoning domain. This idea is captured in ADFs by linking each argument to a set of arguments (its parents) and introducing the notion of acceptance conditions that determine whether an argument is accepted or not according to the acceptance status of its parents.…”

“…Extensive research has been done to generalize this model (see e.g. [8,19,21,22,[38][39][40][41]44,46,47,[69][70][71][72]). Besides, one interesting research topic, which goes back to Dung's seminal work [53], is to explore links between Argumentation Frameworks (AFs) and Logic Programs (LPs) [29,30,73].…”

“…In the deductive support approach, a supports b if the acceptance of a suffices to accept b. The abstract dialectical frameworks [22] extend Dung AFs by generalizing the acceptability conditions of an argument according to the acceptability of other arguments related to it. Finally, the backing relation approach [43,44] captures the meaning of support used in Toulmin's model of argumentation (see [45] for a survey on the different approaches on support in argumentation and Section 6 for a discussion of these approaches and some of their extensions).…”