An approach to abstract argumentation with recursive attack and support

Cohen, Andrea; Gottifredi, Sebastián; García, Alejandro Javier; Simari, Guillermo Ricardo

doi:10.1016/j.jal.2014.12.001

Cited by 26 publications

(72 citation statements)

References 13 publications

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“…The meaning of N cb could be that the support from c to b is not active. A similar idea can be found in [28,12] for the more general purpose of representing recursive and defeasible attacks and supports.…”

Section: A Meta-framework Encoding Necessary Supportmentioning

confidence: 93%

An Axiomatic Approach to Support in Argumentation

Cayrol

Lagasquie-Schiex

2015

Theory and Applications of Formal Argumentation

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OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in : http://oatao.univ-toulouse.fr/ Eprints ID : 15488The contribution was presented at : http://homepages.abdn.ac.uk/n.oren/pages/TAFA-15/ Any correspondence concerning this service should be sent to the repository administrator: staff-oatao@listes-diff.inp-toulouse.fr An axiomatic approach to support in argumentationClaudette Cayrol and Marie-Christine Lagasquie-Schiex IRIT-UPS, Toulouse, France {ccayrol,lagasq}@irit.frAbstract. In the context of bipolar argumentation (argumentation with two kinds of interaction, attacks and supports), we present an axiomatic approach for taking into account a special interpretation of the support relation, the necessary support. We propose constraints that should be imposed to a bipolar argumentation system using this interpretation. Some of these constraints concern the new attack relations, others concern acceptability. We extend basic Dung's framework in different ways in order to propose frameworks suitable for encoding these constraints. By the way, we propose a formal study of properties of necessary support.

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Section: A Meta-framework Encoding Necessary Supportmentioning

confidence: 93%

An Axiomatic Approach to Support in Argumentation

Cayrol

Lagasquie-Schiex

2015

Theory and Applications of Formal Argumentation

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“…Our approach directly relies on the subargument relation which has a univocal interpretation in our context and is sufficient to develop a general theory of probabilistic labellings. The inclusion of more articulated notions, like recursive attacks and supports [3,9], is beyond the scope of this work and represents an interesting direction of future research.…”

Section: Proof 21mentioning

confidence: 99%

A labelling framework for probabilistic argumentation

Riveret

Baroni

Gao

et al. 2018

Ann Math Artif Intell

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The combination of argumentation and probability paves the way to new accounts of qualitative and quantitative uncertainty, thereby offering new theoretical and applicative opportunities. Due to a variety of interests, probabilistic argumentation is approached in the literature with different frameworks, pertaining to structured and abstract argumentation, and with respect to diverse types of uncertainty, in particular the uncertainty on the credibility of the premises, the uncertainty about which arguments to consider, and the uncertainty on the acceptance status of arguments or statements. Towards a general framework for probabilistic argumentation, we investigate a labelling-oriented framework encompassing a basic setting for rule-based argumentation and its (semi-) abstract account, along with diverse types of uncertainty. Our framework provides a systematic treatment of various kinds of uncertainty and of their relationships and allows us to back or question assertions from the literature.Definition 2.4 (Conflict relation) Given a set of literals Φ, a conflict relation 'conf lict' is a binary relation over Φ, i.e. conf lict ⊆ Φ × Φ, such that for any ϕ 1 , ϕ 2 ∈ Φ, if ϕ 1 and ϕ 2 are complementary, i.e. ϕ 1 = −ϕ 2 , then ϕ 1 and ϕ 2 are in conflict, i.e. (ϕ 1 , ϕ 2 ) ∈ conf lict.The conflict relation may be further specified. For example, the relation may be refined with asymmetric and symmetric conflicts to deal with contrary or contradictory literals as in [40]. However, treating in detail such sophistications is not necessary for our purposes.When two rules have heads in conflict, one rule may prevail over another one. Informally, a rule superiority relation r 1 ≻ r 2 states that the rule r 1 prevails over the rule r 2 .Definition 2.5 (Superiority relation) Let Rules be a set of rules. A superiority relation ≻ is a binary relation over Rules, i.e. ≻⊆ Rules × Rules, with r ≻ r ′ denoting that r is superior to r ′ .The superiority relation may enjoy some particular properties. For example, it may be antireflexive and antisymmetric, so that for a rule r it does not hold that r ≻ r and for two distinct rules r and r ′ , we cannot have both r ≻ r ′ and r ′ ≻ r. However, as for the conflict relation, treating in detail such sophistications is not necessary for our purposes.From a set of rules, a conflict relation and a superiority relation, we can define defeasible theories, cf. [22,34].Definition 2.6 (Defeasible theory) A defeasible theory is a tuple Rules, conf lict, ≻ where Rules is a set of rules, conf lict is a conflict relation over literals, and ≻ is a superiority relation over rules.

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“…Then, higher-order attacks have been considered for representing preferences between arguments (second-order attacks in [4]), or for modeling situations where an attack might be defeated by an argument, without contesting the acceptability of the source of the attack [5]. Attacks to attacks and supports have been first considered in [6] with higher level networks, then in [7]; and more generally, [8] proposes an Attack-Support Argumentation Framework which allows for nested attacks and supports, i.e. attacks and supports whose targets can be other attacks or supports, at any level.…”

Section: Introductionmentioning

confidence: 99%

“…Now the prosecutor's argumentation seems no longer sufficient for proving the intention to kill. A natural idea that has proven useful to define semantics for these frameworks, known as "flattening technique", consists in turning the original extended framework into an AF by introducing meta-arguments and a new simple (first-order) attack relation involving these meta-arguments [5], [8], [9]. More recently, alternative acceptability semantics have been defined in a direct way for argumentation frameworks with higher-order attacks [10] or for higher-order attacks and supports [11].…”

Section: Introductionmentioning

confidence: 99%