Argumentation frameworks

Top PDF Argumentation frameworks:

Rich preference-based argumentation frameworks

Rich preference-based argumentation frameworks

a b s t r a c t An argumentation framework is seen as a directed graph whose nodes are arguments and arcs are attacks between the arguments. Acceptable sets of arguments, called extensions, are computed using a semantics. Existing semantics are solely based on the attacks and do not take into account other important criteria like the intrinsic strengths of arguments. The contribution of this paper is three fold. First, we study how preferences issued from differences in strengths of arguments can help in argumentation frameworks. We show that they play two distinct and complementary roles: (i) to repair the attack relation between arguments, (ii) to refine the evaluation of arguments. Despite the importance of both roles, only the first one is tackled in existing literature. In a second part of this paper, we start by showing that existing models that repair the attack relation with preferences do not perform well in certain situations and may return counter-intuitive results. We then propose a new abstract and general framework which treats properly both roles of preferences. The third part of this work is devoted to defining a bridge between the argumentation-based and the coherence-based approaches for handling inconsistency in knowledge bases, in particular when priorities between formulae are available. We focus on two well-known models, namely the preferred sub-theories introduced by Brewka and the demo-preferred sets defined by Cayrol, Royer and Saurel. For each of these models, we provide an instantiation of our abstract framework which is in full correspondence with it.
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Logical Encoding of Argumentation Frameworks with Higher-order Attacks

Logical Encoding of Argumentation Frameworks with Higher-order Attacks

lagasq@irit.fr Abstract—We propose a logical encoding of extended abstract argumentation frameworks, that is frameworks with higher- order attacks (i.e. attacks whose targets are other attacks). Our purpose is to separate the logical expression of the meaning of an attack (simple or higher-order) from the logical expression of acceptability semantics. We consider semantics which specify the conditions under which the arguments (resp. the attacks) are considered as accepted, directly on the extended framework, without translating the original framework into a Dung’s ar- gumentation framework. We characterize the output of a given framework in logical terms (namely as particular models of a logical theory). Our proposal applies to the particular case of Dung’s frameworks, enabling to recover standard extensions.
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Argumentation Frameworks with Recursive Attacks and Evidence-Based Supports

Argumentation Frameworks with Recursive Attacks and Evidence-Based Supports

b is not unacceptable because it is still supportable through α, but it is not supported (and, thus not acceptable) because α is not in the structure.  4 Relation with Recursive Argumentation Frameworks As mentioned in Section 3, our framework is a conservative generalisation of the Recursive Argumentation Framework (RAF) defined in [11] with the addition of supports and joint attacks. RAF’s attacks are similar to Dung’s attacks with the only difference that they may target, not only arguments, but also other attacks. Hence, translating RAF’s (or Dung’s) attacks into joint attacks is trivial: every attack with source a is replaced by an attack with the singleton set {a} as its source. On the other hand, like Dung’s frameworks, RAFs do not encompass the notion of support. From an evidential point of view it is as every argument or attack was externally supported, or in other words, as attacks and arguments were prima-facie. In this sense, every RAF = éA,K,s,tê can be translated into a corresponding recursive evidence-based argumentation framework of the form AF = éA,K,S,s ′ , t,Pê with S = ∅ (no supports), where every element is consid-
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Argumentation Frameworks with Higher-Order Attacks: Semantics and Complexity

Argumentation Frameworks with Higher-Order Attacks: Semantics and Complexity

Introduction Argumentation frameworks (AF) are formalisms to express argumentation problems. In Dung’s one, they are expressed as directed graph in which nodes represent argument and arrow, attack relations between arguments. Higher-order frameworks, unlike Dung’s one, allow to have attacks over attacks. RAF are such a framework (see Figures 1 and 2). Arguments are here represented by circles and attack relations by squares.

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Argumentation Frameworks with Recursive Attacks and Evidence-Based Supports

Argumentation Frameworks with Recursive Attacks and Evidence-Based Supports

RAF iff hE, Γ, ∅i is conflict-free (resp. admissible, complete, preferred, stable) w.r.t. its corresponding AF. Furthermore, there is a one-to-one correspondence between complete, preferred and stable structures in RAF’s and their corre- sponding Dung’s extensions, so this correspondence is also carried over to our argumentation frameworks with evidence-based support. In [9], it also has been shown that there is a one-to-one correspondence between RAF and AFRA [4], which is also carried over to our frameworks (when we restrict ourselves to frameworks without supports). Note that AFRA has been extended with sup- ports in [13, 14] and called Attack-Support Argumentation Framework (ASAF). However, ASAF supports are understood as necessary conditions for their tar- gets instead. This is quite different from the evidential understanding followed here as shown by the following example.
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Rationalisation of Profiles of Abstract Argumentation Frameworks: Characterisation and Complexity

Rationalisation of Profiles of Abstract Argumentation Frameworks: Characterisation and Complexity

LIPADE, Universit´ e Paris Descartes 45 rue des Saints P` eres, 75006 Paris, France Abstract Different agents may have different points of view. Following a popular approach in the artificial intelligence literature, this can be modelled by means of different abstract argu- mentation frameworks, each consisting of a set of arguments the agent is contemplating and a binary attack-relation between them. A question arising in this context is whether the diversity of views observed in such a profile of argumentation frameworks is consistent with the assumption that every individual argumentation framework is induced by a com- bination of, first, some basic factual attack-relation between the arguments and, second, the personal preferences of the agent concerned regarding the moral or social values the arguments under scrutiny relate to. We treat this question of rationalisability of a profile as an algorithmic problem and identify tractable and intractable cases. In doing so, we distinguish different constraints on admissible rationalisations, e.g., concerning the types of preferences used or the number of distinct values involved. We also distinguish two different semantics for rationalisability, which differ in the assumptions made on how agents treat attacks between arguments they do not report. This research agenda, bringing together ideas from abstract argumentation and social choice, is useful for understanding what types of profiles can reasonably be expected to occur in a multiagent system.
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Argumentation Frameworks with Recursive Attacks and Evidence-Based Supports

Argumentation Frameworks with Recursive Attacks and Evidence-Based Supports

b is not unacceptable because it is still supportable through α, but it is not supported (and, thus not acceptable) because α is not in the structure.  4 Relation with Recursive Argumentation Frameworks As mentioned in Section 3, our framework is a conservative generalisation of the Recursive Argumentation Framework (RAF) defined in [11] with the addition of supports and joint attacks. RAF’s attacks are similar to Dung’s attacks with the only difference that they may target, not only arguments, but also other attacks. Hence, translating RAF’s (or Dung’s) attacks into joint attacks is trivial: every attack with source a is replaced by an attack with the singleton set {a} as its source. On the other hand, like Dung’s frameworks, RAFs do not encompass the notion of support. From an evidential point of view it is as every argument or attack was externally supported, or in other words, as attacks and arguments were prima-facie. In this sense, every RAF = éA,K,s,tê can be translated into a corresponding recursive evidence-based argumentation framework of the form
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Rationalisation of Profiles of Abstract Argumentation Frameworks

Rationalisation of Profiles of Abstract Argumentation Frameworks

Keywords Argumentation; Social Choice Theory 1. INTRODUCTION The model of abstract argumentation introduced by Dung [12] is at the root of a vast amount of work in ar- tificial intelligence and multiagent systems. In a nutshell, this model abstracts away from the content of an argument, and thus sees argumentation frameworks as directed graphs, where the nodes are arguments and the edges are attacks between arguments—in the sense that one argument under- cuts or contradicts another argument. Different semantics provide principled approaches to selecting sets of arguments that can be viewed as coherent when taken together. The simplicity and generality of this framework, as well as its links with nonmonotonic reasoning, have stimulated a num- ber of directions of research, e.g., at the level of the definition of the semantics, of their computation, of the expressivity of such frameworks, or regarding their application in a mul- tiagent system.
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Structure-Based Semantics of Argumentation Frameworks with Higher-Order Attacks and Supports

Structure-Based Semantics of Argumentation Frameworks with Higher-Order Attacks and Supports

Keywords. Abstract argumentation, bipolar argumentation, higher-order interactions 1. Introduction Abstract argumentation frameworks have greatly eased the modelling and study of argu- mentation. Whereas Dung’s framework [12] only accounts for an attack relation between arguments, two natural generalisations have been developed in order to allow positive in- teractions (usually expressed by a support relation) and higher-order interactions (attacks or supports that target other attacks or supports). Here is an example in the legal field, bor- rowed from [1], that illustrates both generalisations (this example corresponds to a dynamic process of exchange of pieces of information, each one being considered as an “argument”). Ex. 1 The prosecutor says that the defendant has intention to kill the victim (argument b). A witness says that she saw the defendant throwing a sharp knife towards the victim (ar- gument a). Argument a can be considered as a support for argument b. The lawyer argues back that the defendant was in a habit of throwing the knife at his wife’s foot once drunk. This latter argument (argument c) is better considered attacking the support from a to b, than arguments a or b themselves. Now the prosecutor’s argumentation seems no longer sufficient for proving the intention to kill.
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Handling Support Cycles in the Logical Encoding of Argumentation Frameworks with Higher-order Attacks and Evidential Supports: An Improvement

Handling Support Cycles in the Logical Encoding of Argumentation Frameworks with Higher-order Attacks and Evidential Supports: An Improvement

Higher-order interactions. The idea of encompassing attacks to attacks in abstract argumentation frameworks has been first considered in [13] in the context of an ex- tended framework handling argument strengths and their propagation. Then, higher- order attacks have been considered for representing preferences between arguments (second-order attacks in [14]), or for modelling situations where an attack might be defeated by an argument, without contesting the acceptability of the source of the at- tack [15]. Attacks to attacks and supports have been first considered in [16] with higher level networks, then in [17]; and more generally, [18] proposes an Attack-Support Ar- gumentation Framework which allows for nested attacks and supports, i.e. attacks and supports whose targets can be other attacks or supports, at any level.
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Valid attacks in Argumentation Frameworks with Recursive Attacks (IRIT/RR--2019--02--FR)

Valid attacks in Argumentation Frameworks with Recursive Attacks (IRIT/RR--2019--02--FR)

Figure 2: Bob’s dilemma: arguments are in circle and attacks in square. More recently, recursive frameworks have been studied in [4] under the name of AFRA (Argumentation Framework with Recursive Attacks). This version describes abstract argumentation frameworks in which the interactions can be either attacks between arguments or attacks from an argument to another at- tack. A translation of an AFRA into an AF is defined by the addition of some new arguments and the attacks they produce or they receive. Note that AFRA have been extended in order to handle recursive support interactions together with recursive attacks [11, 12]. However, when supports are removed, these approaches go back to AFRA.
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A Dialectical Proof Theory for Universal Acceptance in Coherent Logic-based Argumentation Frameworks

A Dialectical Proof Theory for Universal Acceptance in Coherent Logic-based Argumentation Frameworks

A Dialectical Proof Theory for Universal Acceptance in Coherent Logic- ased Argumentation Frameworks Abdallah Arioua and Madalina Croitoru 1 Abstract. Given a logic-based argumentation framework built over a knowledge base in a logical language and a query in that language, the query is universally accepted if it is entailed from all extensions. As shown in [2, 14], universal acceptance is different from skepti- cal acceptance as a query may be entailed from different arguments distributed over all extensions but not necessarily skeptical ones. In this paper we provide a dialectical proof theory for universal accep- tance in coherent logic-based argumentation frameworks. We prove its finiteness, soundness, completeness, consistency and study its dis- pute complexity. We give an exact characterization for non-universal acceptance and provide an upper-bound for universal acceptance.
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Structure-based semantics of argumentation frameworks with higher-order attacks and supports

Structure-based semantics of argumentation frameworks with higher-order attacks and supports

1 Introduction Abstract argumentation frameworks have greatly eased the modelling and study of argu- mentation. Whereas Dung’s framework [11] only accounts for an attack relation between arguments, two natural generalisations have been developed in order to allow positive in- teractions (usually expressed by a support relation) and higher-order interactions (attacks or supports that target other attacks or supports). Here is an example in the legal field, borrowed from [1], that illustrates both generalisations (this example corresponds to a dynamic process of exchange of pieces of information, each one being considered as an “argument”).
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Structure-Based Semantics of Argumentation Frameworks with Higher-Order Attacks and Supports

Structure-Based Semantics of Argumentation Frameworks with Higher-Order Attacks and Supports

Recursive Evidence-Based Argumentation Frameworks (REBAF). Recently introduced in [6], the REBAF allows representing higher-order attacks and higher-order supports. It is a generalisation of the Evidence-Based Argumentation Framework (EBAF) [17]. In these frameworks, the “evidential” understanding of the support relation allows to distinguish be- tween two different kinds of arguments: prima-facie and standard arguments. Prima-facie arguments are justified whenever they are not defeated. On the other hand, standard ar- guments are not assumed to be justified and must inherit support from prima-facie argu- ments through a chain of supports. In the REBAF, the semantics handle both acceptability of arguments and validity of interactions (attacks or supports), and account for the fact that acceptability of arguments may depend on the validity of interactions and vice-versa. As a consequence, the standard notion of extension is replaced by a triple of a set of arguments, a set of attacks and a set of supports, called “structure”. We briefly recall the main definitions. Def. 3 (Recursive EBAF and structure) A Recursive Evidence-Based Argumentation Framework (REBAF) is a sextuple hA, R, S, s,t, Pi, where A, R and S are three pairwise disjunct sets respectively representing arguments, attacks and supports names, and where P ⊆ A ∪ R ∪ S is a set representing the prima-facie elements that do not need to be sup- ported. 3 Functions s : (R ∪ S) −→ 2 A and t : (R ∪ S) −→ (A ∪ R ∪ S) respectively map each attack and support to its source and its target.
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Valid attacks in Argumentation Frameworks with Recursive Attacks (IRIT-2017-16)

Valid attacks in Argumentation Frameworks with Recursive Attacks (IRIT-2017-16)

a α b β Figure 7: A RAF in which preferred and arg-preferred structures do not coincide are preferred structures of RAF, but only the former contains a maximal set of arguments and thus A is the unique arg-preferred structure.  We show now 5 that, as in Dung’s argumentation theory, there is also a kind of Fundamental Lemma for argumentation frameworks with recursive attacks. For the sake of compactness, we will adopt the following notations: Given a structure A = hS, Γi and a set T ⊆ (A ∪ K) containing arguments and attacks, by A ∪ T def

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Preventing Manipulation in Aggregating Audiences in Value-Based Argumentation Frameworks

Preventing Manipulation in Aggregating Audiences in Value-Based Argumentation Frameworks

3. Aggregation of Audiences in Value-Based Argumentation Frameworks One of the intuitions behind the claim that the structure of argumentation can be viewed in distinctive ways is that agents might not agree on whether particular arguments are indeed in conflict with each other. Possible explanations for such a situation involve a scenario in which particular agents disagree on the relative strength of arguments. As it was argued earlier, it is plausible to assume that if an agent believes that some strong argument is attacked by a weak one, she might decide to disregard this attack. However, decisions about which arguments are stronger than another are at the discretion of in- dividual assessors. Therefore, structures of successful attacks between arguments might vary among the group of agents.
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Preventing Manipulation in Aggregating Audiences in Value-Based Argumentation Frameworks

Preventing Manipulation in Aggregating Audiences in Value-Based Argumentation Frameworks

3. Aggregation of Audiences in Value-Based Argumentation Frameworks One of the intuitions behind the claim that the structure of argumentation can be viewed in distinctive ways is that agents might not agree on whether particular arguments are indeed in conflict with each other. Possible explanations for such a situation involve a scenario in which particular agents disagree on the relative strength of arguments. As it was argued earlier, it is plausible to assume that if an agent believes that some strong argument is attacked by a weak one, she might decide to disregard this attack. However, decisions about which arguments are stronger than another are at the discretion of in- dividual assessors. Therefore, structures of successful attacks between arguments might vary among the group of agents.
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Initial Sets in Abstract Argumentation Frameworks

Initial Sets in Abstract Argumentation Frameworks

Our aim is to introduce a new extension-based semantics, named initial sets semantics, into the study of argumentation frameworks so as to analyse the structural feature of other known extensions. Firstly, we generalize the notion of initial arguments by proposing initial-like arguments and initial sets of argumentation frameworks. In the literature, initial arguments play a basic role in describing the grounded extension. That is one incrementally starts from the initial arguments and suppresses the arguments attacked by them. If new initial arguments arise, the arguments attacked by them are suppressed and so on. The process will stop when no new initial argument appears after a deletion step. The set of all initial arguments in the final argumentation framework is the grounded extension, which is the least complete extension. An initial-like argument is an argument which attacks each attacker of it. From the view of directed graph, an initial-like argument can be regarded as a starting point. This idea can be further extended to the notion of initial set. An initial set is a minimal conflict-free set of arguments, which attacks each attacker of it. In fact, an initial set is exactly a minimal (non-empty) admissible set. Secondly, we investigate the properties of initial sets and show the relationship between initial sets and other known extensions such as complete, preferred and stable extensions.
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Initial Sets in Abstract Argumentation Frameworks

Initial Sets in Abstract Argumentation Frameworks

Since initial sets are exactly the minimal non-empty admissible sets and are the bases for gen- erating complete, preferred and stable extensions, the determination of initial sets is an extremely important work in argumentation theory. One of our future works is to investigate the comput- ing approaches on initial sets. Another direction of further research concerns the application of grounded-like extensions and initial sets for dynamics in argumentation frameworks. Several works have proposed efficient ways for handling dynamics, such as [Lia11] which introduces the division- based method, and [Xu15] where a matrix approach allows for a decomposition of traditional ex- tensions, using unattacked sets of arguments. We are going to investigate the role of initial sets in the construction of the extensions of an updated argumentation framework. Finally, it also would be interesting to situate the new semantics within the equivalence classes discussed in [Bau15].
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The matrix approach for abstract argumentation frameworks

The matrix approach for abstract argumentation frameworks

works and the operation of dual interchange of matrices. This operation makes the matrix representation be a powerful tool for the study of argumentation frameworks. Section 4 describes the characterization theorems for stable, admissible and complete extensions. Furthermore, we integrate these theorems and obtain two kinds of standard forms for ma- trices by dual interchange. Section 5 presents the reduced matrix of an argumentation framework with respect to conflict-free subsets. We discuss three basic types of reduced matrix depending on the number of conflict-free subsets and the relationship between them. Section 6 proposes the division-based reduction and its applications. We first consider the determination of grounded and preferred extensions. Then, we consider an application to the study of dynamics of argumentation frameworks. Two types of updated argumentation frameworks are considered corresponding to the addition and the removal of arguments (or attacks). All the proofs are given in Appendix except for the trivial ones.
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