Probabilistic abstract argumentation: an investigation with Boltzmann machines

Riveret, Régis; Korkinof, Dimitrios; Draief, Moez; Pitt, Jeremy

doi:10.1080/19462166.2015.1107134

Cited by 9 publications

(3 citation statements)

References 37 publications

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“…In contrast to our work, they induce a rule-based theory and construct an AF based on conflicting rules. Riveret and Governatori (2016) studied probabilistic AF (Li, Oren, & Norman, 2011;Hunter, 2014;Riveret, Korkinof, Draief, & Pitt, 2015) learning with non-exact methods; we tackle the exact optimization problem of AF synthesis. Furthermore, Riveret (2016) considered on-the-fly computation of argumentation graphs from so-called statement acceptance labellings under the grounded semantics.…”

Section: Related Workmentioning

confidence: 99%

Synthesizing Argumentation Frameworks from Examples

Niskanen

Wallner

Järvisalo

2019

jair

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Argumentation is today a topical area of artificial intelligence (AI) research. Abstract argumentation, with argumentation frameworks (AFs) as the underlying knowledge representation formalism, is a central viewpoint to argumentation in AI. Indeed, from the perspective of AI and computer science, understanding computational and representational aspects of AFs is key in the study of argumentation. Realizability of AFs has been recently proposed as a central notion for analyzing the expressive power of AFs under different semantics. In this work, we propose and study the AF synthesis problem as a natural extension of realizability, addressing some of the shortcomings arising from the relatively stringent definition of realizability. In particular, realizability gives means of establishing exact conditions on when a given collection of subsets of arguments has an AF with exactly the given collection as its set of extensions under a specific argumentation semantics. However, in various settings within the study of dynamics of argumentation---including revision and aggregation of AFs---non-realizability can naturally occur. To accommodate such settings, our notion of AF synthesis seeks to construct, or synthesize, AFs that are semantically closest to the knowledge at hand even when no AFs exactly representing the knowledge exist. Going beyond defining the AF synthesis problem, we study both theoretical and practical aspects of the problem. In particular, we (i) prove NP-completeness of AF synthesis under several semantics, (ii) study basic properties of the problem in relation to realizability, (iii) develop algorithmic solutions to NP-hard AF synthesis using the constraint optimization paradigms of maximum satisfiability and answer set programming, (iv) empirically evaluate our algorithms on different forms of AF synthesis instances, as well as (v) discuss variants and generalizations of AF synthesis.

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Section: Related Workmentioning

confidence: 99%

Synthesizing Argumentation Frameworks from Examples

Niskanen

Wallner

Järvisalo

2019

jair

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“…To address acceptance uncertainty, we devise a sample space which is the set of possible labellings of an argumentation graph, as previously employed in [49,50,51], and resulting into what we call probabilistic labelling frames (PLFs) that we investigate in the remainder of this section.…”

Section: Acceptance Uncertainty: Probabilistic Labelling Framesmentioning

confidence: 99%

“…Since different types of probabilistic uncertainty can be discerned and argumentation can be dealt with at different level of abstraction, different families of approaches to probabilistic argumentation can be found in the literature. First probabilistic notions have been investigated at different abstraction levels, ranging from structured argumentation formalisms [47,52,48,13] to abstract argumentation frameworks [36,59,27,30,49,50,51]. Further, one can distinguish approaches based on the uncertainty concerning the arguments to actually include in the argumentation process, as in the so-called 'constellations' approach [36,27], and approaches focusing on a probabilistic notion of the acceptance status of arguments, as in the 'epistemic' approach [59,27,30].…”

Section: Introductionmentioning

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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An Imprecise Probability Approach for Abstract Argumentation Based on Credal Sets

Morveli-Espinoza

Nieves

Tacla

2019

Lecture Notes in Computer Science

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Some abstract argumentation approaches consider that arguments have a degree of uncertainty, which impacts on the degree of uncertainty of the extensions obtained from a abstract argumentation framework (AAF) under a semantics. In these approaches, both the uncertainty of the arguments and of the extensions are modeled by means of precise probability values. However, in many real life situations the exact probabilities values are unknown and sometimes there is a need for aggregating the probability values of different sources. In this paper, we tackle the problem of calculating the degree of uncertainty of the extensions considering that the probability values of the arguments are imprecise. We use credal sets to model the uncertainty values of arguments and from these credal sets, we calculate the lower and upper bounds of the extensions. We study some properties of the suggested approach and illustrate it with an scenario of decision making.

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Probabilistic abstract argumentation: an investigation with Boltzmann machines

Cited by 9 publications

References 37 publications

Synthesizing Argumentation Frameworks from Examples

Synthesizing Argumentation Frameworks from Examples

A labelling framework for probabilistic argumentation

An Imprecise Probability Approach for Abstract Argumentation Based on Credal Sets

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