Pareto Optimality and Strategy Proofness in Group Argument Evaluation (Extended Version)

An inconsistent knowledge base can be abstracted as a set of arguments and a defeat relation among them. There can be more than one consistent way to evaluate such an argumentation graph. Collective argument evaluation is the problem of aggregating the opinions of multiple agents on how a given set of arguments should be evaluated. It is crucial not only to ensure that the outcome is logically consistent, but also satisfies measures of social optimality and immunity to strategic manipulation. This is because agents have their individual preferences about what the outcome ought to be. In the current paper, we analyze three previously introduced argument-based aggregation operators with respect to Pareto optimality and strategy proofness under different general classes of agent preferences. We highlight fundamental trade-offs between strategic manipulability and social optimality on one hand, and classical logical criteria on the other. Our results motivate further investigation into the relationship between social choice and argumentation theory. The results are also relevant for choosing an appropriate aggregation operator given the criteria that are considered more important, as well as the nature of agents' preferences

Complexity Properties of Critical Sets of Arguments

Abstract. In an abstract argumentation framework, there are often multiple plausible ways to evaluate (or label) the status of each argument as accepted, rejected, or undecided. But often there exists a critical set of arguments whose status is sufficient to determine uniquely the status of every other argument. Once an agent has decided its position on a critical set of arguments, then essentially the entire framework has been evaluated. Likewise, once a group, e.g. a jury, agree on the status of a critical set of arguments, all of their different views over all other arguments are resolved. Thus, critical sets of arguments are important both for efficient evaluation by individual agents and collective agreement by groups of such. To exploit this idea in practice, however, a number of computational questions must be considered. In particular, how much computational effort is needed to verify that a set is, indeed, a critical set or a minimal critical set. In this paper we determine exact bounds on the computational complexity of these and related questions. In addition we provide similar analyses of issues: a concept closely related to critical set and derived in terms of (equivalence) classes of argument related through "common" labelling behaviours

Poles Apart : Navigating the Space of Opinions in Argumentation

Formal argumentation is a popular reasoning method in knowledge representation for intelligent systems. For the past 20 years it has been based on Dung’s abstract argumentation theory. More recently several challenges have been made to this standard - for example in dynamics and aggregation of argumentation frameworks. To support these new developments in this thesis new foundations are developed based on distance measures. We introduce postulates for distance measures and we show their consistency by constructing concrete measures. In the process we develop the new notion of issue. Subsequently we use the distance measures in argumentation using distance based operators introduced by Miller and Osherson in judgment aggregation. Moreover in this thesis we also improve dialectical proof procedures for grounded semantics and study postulates of non-interference and crash resistance for Dung based non-monotonic inference

Quantifying disagreement in argument-based reasoning

An argumentation framework can be seen as expressing, in an abstract way, the conflicting information of an underlying logical knowledge base. This conflicting information often allows for the presence of more than one possible reasonable position (extension/labelling) which one can take. A relevant question, therefore, is how much these positions differ from each other. In the current paper, we will examine the issue of how to define meaningful measures of distance between the (complete) labellings of a given argumentation framework. We provide concrete distance measures based on argument-wise label difference, as well as based on the notion of critical sets, and examine their properties

Complexity Properties of Critical Sets of Arguments

Abstract. In an abstract argumentation framework, there are often multiple plausible ways to evaluate (or label) the status of each argument as accepted, rejected, or undecided. But often there exists a critical set of arguments whose status is sufficient to determine uniquely the status of every other argument. Once an agent has decided its position on a critical set of arguments, then essentially the entire framework has been evaluated. Likewise, once a group, e.g. a jury, agrees on the status of a critical set of arguments, all of their different views over all other arguments are resolved. Thus, critical sets of arguments are important both for efficient evaluation by individual agents and for collective agreement by groups of such. To exploit this idea in practice, however, a number of computational questions must be considered. In particular, how much computational effort is needed to verify that a set is, indeed, a critical set or a minimal critical set. In this paper we determine exact bounds on the computational complexity of these and related questions. In addition we provide similar analyses of issues: a concept closely related to critical set and derived in terms of (equivalence) classes of arguments related through "common" labelling behaviours

Pareto optimality and strategy-proofness in group argument evaluation

An inconsistent knowledge base can be abstracted as a set of arguments and a defeat relation among them. There can be more than one consistent way to evaluate such an argumentation graph. Collective argument evaluation is the problem of aggregating the opinions of multiple agents on how a given set of arguments should be evaluated. It is crucial not only to ensure that the outcome is logically consistent, but also satisfies measures of social optimality and immunity to strategic manipulation. This is because agents have their individual preferences about what the outcome ought to be. In the current paper, we analyze three previously introduced argument-based aggregation operators with respect to Pareto optimality and strategy proofness under different general classes of agent preferences. We highlight fundamental trade-offs between strategic manipulability and social optimality on one hand, and classical logical criteria on the other. Our results motivate further investigation into the relationship between social choice and argumentation theory. The results are also relevant for choosing an appropriate aggregation operator given the criteria that are considered more important, as well as the nature of agents' preferences