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112
An abstract framework for argumentation with structured arguments
 IN INFORMATION TECHNOLOGY & LAWYERS: ADVANCED TECHNOLOGY IN THE
, 2009
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Abstract Argumentation
 ARTIFICIAL INTELLIGENCE AND LAW
, 1996
"... In this paper we explore the thesis that the role of argumentation in practical reasoning in general and legal reasoning in particular is to justify the use of defeasible rules to derive a conclusion in preference to the use of other defeasible rules to derive a conflicting conclusion. The defeasib ..."
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Cited by 107 (30 self)
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In this paper we explore the thesis that the role of argumentation in practical reasoning in general and legal reasoning in particular is to justify the use of defeasible rules to derive a conclusion in preference to the use of other defeasible rules to derive a conflicting conclusion. The defeasibility of rules is expressed by means of nonprovability claims as additional conditions of the rules. We outline an abstract approach to defeasible reasoning and argumentation which includes many existing formalisms, including default logic, extended logic programming, nonmonotonic modal logic and autoepistemic logic, as special cases. We show, in particular, that the “admissibility ” semantics for all these formalisms has a natural argumentationtheoretic interpretation and proof procedure, which seem to correspond well with informal argumentation. In the admissibility semantics there is only one way for one argument to attack another, namely by undermining one of its nonprovability claims. In this paper, we show how other kinds of attack between arguments, specifically how rebuttal and priority attacks, can be reduced to the undermining of nonprovability claims.
Proof burdens and standards
 In Guillermo Simari and Iyad Rahwan, editors, Argumentation in Artificial Intelligence
, 2009
"... This chapter explains the role of proof burdens and standards in argumentation, illustrates them using legal procedures, and surveys the history of research on computational models of these concepts. It also presents an original computational model which aims to integrate the features of these pri ..."
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Cited by 31 (4 self)
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This chapter explains the role of proof burdens and standards in argumentation, illustrates them using legal procedures, and surveys the history of research on computational models of these concepts. It also presents an original computational model which aims to integrate the features of these prior systems.
Weighted Argument Systems: Basic Definitions, Algorithms, and Complexity Results
, 2010
"... We introduce and investigate a natural extension of Dung’s wellknown model of argument systems in which attacks are associated with a weight, indicating the relative strength of the attack. A key concept in our framework is the notion of an inconsistency budget, which characterises how much inconsi ..."
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Cited by 31 (3 self)
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We introduce and investigate a natural extension of Dung’s wellknown model of argument systems in which attacks are associated with a weight, indicating the relative strength of the attack. A key concept in our framework is the notion of an inconsistency budget, which characterises how much inconsistency we are prepared to tolerate: given an inconsistency budget β, we would be prepared to disregard attacks up to a total weight of β. The key advantage of this approach is that it permits a much finer grained level of analysis of argument systems than unweighted systems, and gives useful solutions when conventional (unweighted) argument systems have none. We begin by reviewing Dung’s abstract argument systems, and motivating weights on attacks (as opposed to the alternative possibility, which is to attach weights to arguments). We then present the framework of weighted argument systems. We investigate solutions for weighted argument systems and the complexity of computing such solutions, focussing in particular on weighted variations of grounded extensions. Finally, we relate our work to the most relevant examples of argumentation frameworks that incorporate strengths.
A general account of argumentation with preferences
 ARTIFICIAL INTELLIGENCE
, 2012
"... This paper builds on the recent ASPIC+ formalism, to develop a general framework for argumentation with preferences. We motivate a revised definition of conflict free sets of arguments, adapt ASPIC+ to accommodate a broader range of instantiating logics, and show that under some assumptions, the re ..."
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Cited by 27 (5 self)
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This paper builds on the recent ASPIC+ formalism, to develop a general framework for argumentation with preferences. We motivate a revised definition of conflict free sets of arguments, adapt ASPIC+ to accommodate a broader range of instantiating logics, and show that under some assumptions, the resulting framework satisfies key properties and rationality postulates. We then show that the generalised framework accommodates Tarskian logic instantiations extended with preferences, and then study instantiations of the framework by classical logic approaches to argumentation. We conclude by arguing that ASPIC+’s modelling of defeasible inference rules further testifies to the generality of the framework, and then examine and counter recent critiques of Dung’s framework and its extensions to accommodate preferences.
Instantiating Abstract Argumentation with Classical Logic Arguments: Postulates and Properties
, 2011
"... ... argumentation frameworks. In the first part, we propose desirable properties of attack relations in the form of postulates and classify several wellknown attack relations from the literature with regards to the satisfaction of these postulates. Furthermore, we provide additional postulates that ..."
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Cited by 22 (0 self)
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... argumentation frameworks. In the first part, we propose desirable properties of attack relations in the form of postulates and classify several wellknown attack relations from the literature with regards to the satisfaction of these postulates. Furthermore, we provide additional postulates that help us prove characterisation results for these attack relations. In the second part of the paper, we present postulates regarding the logical content of extensions of argument graphs that may be constructed with classical logic. We then conduct a comprehensive study of the status of these postulates in the context of the various combinations of attack relations and extension semantics.
Inconsistency Tolerance in Weighted Argument Systems
"... We introduce and investigate a natural extension of Dung’s wellknown model of argument systems in which attacks are associated with a weight, indicating the relative strength of the attack. A key concept in our framework is the notion of an inconsistency budget, which characterises how much inconsis ..."
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Cited by 21 (3 self)
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We introduce and investigate a natural extension of Dung’s wellknown model of argument systems in which attacks are associated with a weight, indicating the relative strength of the attack. A key concept in our framework is the notion of an inconsistency budget, which characterises how much inconsistency we are prepared to tolerate: given an inconsistency budget β, we would be prepared to disregard attacks up to a total cost of β. The key advantage of this approach is that it permits a much �ner grained level of analysis of argument systems than unweighted systems, and gives useful solutions when conventional (unweighted) argument systems have none. We begin by reviewing Dung’s abstract argument systems, and present the model of weighted argument systems. We then investigate solutions to weighted argument systems and the associated complexity of computing these solutions, focussing in particular on weighted variations of grounded extensions.
Bridging the gap between abstract argumentation systems and logic
"... Abstract. Dung’s argumentation system takes as input a set of arguments and a binary relation encoding attacks among these arguments, and returns different extensions of arguments. However, no indication is given on how to instantiate this setting, i.e. how to build arguments from a knowledge base ..."
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Cited by 18 (10 self)
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Abstract. Dung’s argumentation system takes as input a set of arguments and a binary relation encoding attacks among these arguments, and returns different extensions of arguments. However, no indication is given on how to instantiate this setting, i.e. how to build arguments from a knowledge base and how to choose an appropriate attack relation. This leads in some cases to undesirable results like inconsistent extensions (i.e. the set of formulas forming an extension is inconsistent). This is due to the gap between the abstract setting and the knowledge base from which it is defined. The purpose of this paper is twofold: First it proposes to fill in this gap by extending Dung’s system. The idea is to consider all the ingredients involved in an argumentation problem. We start with an abstract monotonic logic which consists of a set of formulas and a consequence operator. We show how to build arguments from a knowledge base using the consequence operator of the logic. Second, we show that the choice of an attack relation is crucial for ensuring consistent results, and should not be arbitrary. In particular, we argue that an attack relation should be at least grounded on the minimal conflicts contained in the knowledge base. Moreover, due to the binary character of this relation, some attack relations may lead to unintended results. Namely, symmetric relations are not suitable when ternary (or more) minimal conflicts are in the knowledge base. We propose then the characteristics of attack relations that ensure sound results. 1
On the Equivalence of LogicBased Argumentation Systems
 Proceedings of the 5th International Conference on Scalable Uncertainty Management (SUM 2011), volume 6929 of Lecture Notes in Computer Science
, 2011
"... Abstract. Equivalence between two argumentation systems means mainly that the two systems return the same outputs. It can be used for different purposes, namely in order to show whether two systems that are built over the same knowledge base but with distinct attack relations return the same output ..."
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Abstract. Equivalence between two argumentation systems means mainly that the two systems return the same outputs. It can be used for different purposes, namely in order to show whether two systems that are built over the same knowledge base but with distinct attack relations return the same outputs, and more importantly to check whether an infinite system can be reduced into a finite one. Recently, the equivalence between abstract argumentation systems was investigated. Two categories of equivalence criteria were particularly proposed. The first category compares directly the outputs of the two systems (e.g. their extensions) while the second compares the outputs of their extended versions (i.e. the systems augmented by the same set of arguments). It was shown that only identical systems are equivalent w.r.t. those criteria. In this paper, we study when two logicbased argumentation systems are equivalent. We refine existing criteria by considering the internal structure of arguments and propose new ones. Then, we identify cases where two systems are equivalent. In particular, we show that under some reasonable conditions on the logic underlying an argumentation system, the latter has an equivalent finite subsystem. This subsystem constitutes a threshold under which arguments of the system have not yet attained their final status and consequently adding a new argument may result in status change. From that threshold, the statuses of all arguments become stable. 1
Backdoors to satisfaction
 The Multivariate Algorithmic Revolution and Beyond  Essays Dedicated to Michael R. Fellows on the Occasion of His 60th Birthday, volume 7370 of Lecture
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