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93
On the evaluation of argumentation formalisms
, 2007
"... Argumentation theory has become an important topic in the field of AI. The basic idea is to construct arguments in favor and against a statement, to select the “acceptable” ones and, finally, to determine whether the original statement can be accepted or not. Several argumentation systems have been ..."
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Cited by 109 (21 self)
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Argumentation theory has become an important topic in the field of AI. The basic idea is to construct arguments in favor and against a statement, to select the “acceptable” ones and, finally, to determine whether the original statement can be accepted or not. Several argumentation systems have been proposed in the literature. Some of them, the socalled rulebased systems, use a particular logical language with strict and defeasible rules. While these systems are useful in different domains (e.g. legal reasoning), they unfortunately lead to very unintuitive results, as is discussed in this paper. In order to avoid such anomalies, in this paper we are interested in defining principles, called rationality postulates, that can be used to judge the quality of a rulebased argumentation system. In particular, we define two important rationality postulates that should be satisfied: the consistency and the closure of the results returned by that system. We then provide a relatively easy way in which these rationality postulates can be warranted for a particular rulebased argumentation system developed within a
An axiomatic account of formal argumentation
 In Proceedings of the AAAI2005
, 2005
"... Argumentation theory has become an important topic in the field of AI. The basic idea is to construct arguments in favor and against a statement, to select the “acceptable ” ones and, finally, to determine whether the statement can be accepted or not. Dung’s elegant account of abstract argumentation ..."
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Cited by 64 (21 self)
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Argumentation theory has become an important topic in the field of AI. The basic idea is to construct arguments in favor and against a statement, to select the “acceptable ” ones and, finally, to determine whether the statement can be accepted or not. Dung’s elegant account of abstract argumentation (Dung 1995) may have caused some to believe that defining an argumentation formalism is simply a matter of determining how arguments and their defeat relation can be constructed from a given knowledge base. Unfortunately, things are not that simple; many straightforward instantiations of Dung’s theory can lead to very unintuitive results, as is discussed in this paper. In order to avoid such anomalies, in this paper we are interested in defining some rules, called rationality postulates or axioms, that govern the well definition of an argumentation system. In particular, we define two important rationality postulates that any system should satisfy: the consistency and the closeness of the results returned by that system. We then provide a relatively easy way in which these quality postulates can be warranted by our argumentation system.
Abstract dialectical frameworks
 In Proc. KR2010
, 2010
"... In this paper we introduce dialectical frameworks, a powerful generalization of Dungstyle argumentation frameworks where each node comes with an associated acceptance condition. This allows us to model different types of dependencies, e.g. support and attack, as well as different types of nodes wit ..."
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Cited by 35 (6 self)
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In this paper we introduce dialectical frameworks, a powerful generalization of Dungstyle argumentation frameworks where each node comes with an associated acceptance condition. This allows us to model different types of dependencies, e.g. support and attack, as well as different types of nodes within a single framework. We show that Dung’s standard semantics can be generalized to dialectical frameworks, in case of stable and preferred semantics to a slightly restricted class which we call bipolar frameworks. We show how acceptance conditions can be conveniently represented using weights respectively priorities on the links and demonstrate how some of the legal proof standards can be modeled based on this idea.
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 32 (7 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.
AnswerSet Programming Encodings for Argumentation Frameworks
, 2008
"... We present reductions from Dung’s argumentation framework (AF) and generalizations thereof to logic programs under the answerset semantics. The reduction is based on a fixed disjunctive datalog program (the interpreter) and its input which is the only part depending on the AF to process. We discus ..."
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Cited by 25 (13 self)
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We present reductions from Dung’s argumentation framework (AF) and generalizations thereof to logic programs under the answerset semantics. The reduction is based on a fixed disjunctive datalog program (the interpreter) and its input which is the only part depending on the AF to process. We discuss the reductions, which are the basis for the system ASPARTIX in detail and show their adequacy in terms of computational complexity.
Characterizing Strong Equivalence for Argumentation Frameworks
 cf2 Semantics Revisited. Proc. COMMA 2010
, 2010
"... Since argumentation is an inherently dynamic process, it is of great importance to understand the effect of incorporating new information into given argumentation frameworks. In this work, we address this issue by analyzing equivalence between argumentation frameworks under the assumption that the f ..."
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Cited by 23 (3 self)
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Since argumentation is an inherently dynamic process, it is of great importance to understand the effect of incorporating new information into given argumentation frameworks. In this work, we address this issue by analyzing equivalence between argumentation frameworks under the assumption that the frameworks in question are incomplete, i.e. further information might be added later to both frameworks simultaneously. In other words, instead of the standard notion of equivalence (which holds between two frameworks, if they possess the same extensions), we require here that frameworks F and G are also equivalent when conjoined with any further framework H. Due to the nonmonotonicity of argumentation semantics, this concept is different to (but obviously implies) the standard notion of equivalence. We thus call our new notion strong equivalence and study how strong equivalence can be decided with respect to the most important semantics for abstract argumentation frameworks. We also consider variants of strong equivalence in which we define equivalence with respect to the sets of arguments credulously (or skeptically) accepted, and restrict strong equivalence to augmentations H where no new arguments are raised.
An algorithm for computing semistable semantics
, 2007
"... Abstract. The semistable semantics for formal argumentation has been introduced as a way of approximating stable semantics in situations where no stable extensions exist. Semistable semantics can be located between stable semantics and preferred semantics in the sense that every stable extension i ..."
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Cited by 21 (11 self)
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Abstract. The semistable semantics for formal argumentation has been introduced as a way of approximating stable semantics in situations where no stable extensions exist. Semistable semantics can be located between stable semantics and preferred semantics in the sense that every stable extension is a semistable extension and every semistable extension is a preferred extension. Moreover, in situations where at least one stable extension exists, the semistable extensions are equal to the stable extensions. In this paper we provide an outline of an algorithm for computing the semistable extensions, given an argumentation framework. We show that with a few modifications, the algorithm can also be used for computing stable and preferred semantics. 1
What does it take to enforce an argument? minimal change in abstract argumentation
 In Proceedings of the European Conference on Artificial Intelligence (ECAI’12
, 2012
"... Abstract. Argumentation is a dynamic process. The enforcing problem in argumentation, i.e. the question whether it is possible to modify a given argumentation framework (AF) in such a way that a desired set of arguments becomes an extension or a subset of an extension, was first studied in [3] and ..."
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Cited by 17 (6 self)
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Abstract. Argumentation is a dynamic process. The enforcing problem in argumentation, i.e. the question whether it is possible to modify a given argumentation framework (AF) in such a way that a desired set of arguments becomes an extension or a subset of an extension, was first studied in [3] and positively answered under certain conditions. In this paper, we take up this research and study the more general problem of minimal change. That is, in brief, i) is it possible to enforce a desired set of arguments, and if so, ii) what is the minimal number of modifications (additions or removals of attacks) to reach such an enforcement, the socalled characteristic. We show for several Dung semantics that this problem can be decided by local criteria encoded by the socalled value functions. Furthermore, we introduce the corresponding equivalence notions between two AFs which guarantee equal minimal efforts needed to enforce certain subsets, namely minimalEequivalence and the more general minimal change equivalence. We present characterization theorems for several Dung semantics and finally, we show the relations to standard and the recently proposed strong equivalence [9] for a whole range of semantics. 1
Comparing Two Unique Extension Semantics for Formal Argumentation: Ideal and Eager
"... In formal argumentation, grounded semantics is well known for yielding exactly one unique extension. Since grounded semantics has a very sceptical nature, one can ask the question whether it is possible to define a unique extension semantics that is more credulous. Recent work of Dung, Mancarella an ..."
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Cited by 17 (4 self)
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In formal argumentation, grounded semantics is well known for yielding exactly one unique extension. Since grounded semantics has a very sceptical nature, one can ask the question whether it is possible to define a unique extension semantics that is more credulous. Recent work of Dung, Mancarella and Toni proposes what they call ideal semantics, which is a unique extension semantics that is more credulous than grounded semantics. In the current paper, we define a unique extension semantics called eager semantics that is even more credulous than ideal semantics. We then examine how this semantics relates to the existing argumentation semantics proposed by Dung and others.
Splitting an argumentation framework, in
 of Lecture Notes in Computer Science
"... Abstract. Abstract argumentation frameworks (AFs) are one of the most studied formalisms in AI. In this work, we introduce a certain subclass of AFs which we call compact. Given an extensionbased semantics, the corresponding compact AFs are characterized by the feature that each argument of the AF ..."
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Cited by 16 (10 self)
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Abstract. Abstract argumentation frameworks (AFs) are one of the most studied formalisms in AI. In this work, we introduce a certain subclass of AFs which we call compact. Given an extensionbased semantics, the corresponding compact AFs are characterized by the feature that each argument of the AF occurs in at least one extension. This not only guarantees a certain notion of fairness; compact AFs are thus also minimal in the sense that no argument can be removed without changing the outcome. We address the following questions in the paper: (1) How are the classes of compact AFs related for different semantics? (2) Under which circumstances can AFs be transformed into equivalent compact ones? (3) Finally, we show that compact AFs are indeed a nontrivial subclass, since the verification problem remains coNPhard for certain semantics. 1