Defeat Relation Research Articles

Towards a Temporal Probabilistic Argumentation Framework

In recent years, the notion of time has been studied in different ways in Dung-style Argumentation Frameworks. For example, time intervals of availability have been added to arguments and relations. As a result, the output of Dung semantics varies over time. In this paper, we consider the situation in which arguments hold with a certain probability distribution during a given interval. To model the uncertain character of events, we propose different notions of temporal conflict between arguments according to the type of availabilities intersection (partial, inclusive, or total). Then, we refine these notions of conflict by a defeat relation, using criterion functions that evaluate an attack’s significance according to the probability over time.

Reasoning about general preference relations

Preference relations are at the heart of many fundamental concepts in artificial intelligence, ranging from utility comparisons, to defeat among strategies and relative plausibility among states, just to mention a few. Reasoning about such relations has been the object of extensive research and a wealth of formalisms exist to express and reason about them. One such formalism is conditional logic, which focuses on reasoning about the “best” alternatives according to a given preference relation. A “best” alternative is normally interpreted as an alternative that is either maximal (no other alternative is preferred to it) or optimal (it is at least as preferred as all other alternatives). And the preference relation is normally assumed to satisfy strong requirements (typically transitivity and some kind of well-foundedness assumption).Here, we generalize this existing literature in two ways. Firstly, in addition to maximality and optimality, we consider two other interpretations of “best”, which we call unmatchedness and acceptability. Secondly, we do not inherently require the preference relation to satisfy any constraints. Instead, we allow the relation to satisfy any combination of transitivity, totality and anti-symmetry.This allows us to model a wide range of situations, including cases where the lack of constraints stems from a modeled agent being irrational (for example, an agent might have preferences that are neither transitive nor total nor anti-symmetric) or from the interaction of perfectly rational agents (for example, a defeat relation among strategies in a game might be anti-symmetric but not total or transitive).For each interpretation of “best” (maximal, optimal, unmatched or acceptable) and each combination of constraints (transitivity, totality and/or anti-symmetry), we study the sets of valid inferences. Specifically, in all but one case we introduce a sound and strongly complete axiomatization, and in the one remaining case we show that no such axiomatization exists.

Normative Uncertainty and Social Choice

AbstractIn ‘Normative Uncertainty as a Voting Problem’, William MacAskill argues that positive credence in ordinal-structured or intertheoretically incomparable normative theories does not prevent an agent from rationally accounting for her normative uncertainties in practical deliberation. Rather, such an agent can aggregate the theories in which she has positive credence by methods borrowed from voting theory—specifically, MacAskill suggests, by a kind of weighted Borda count. The appeal to voting methods opens up a promising new avenue for theories of rational choice under normative uncertainty. The Borda rule, however, is open to at least two serious objections. First, it seems implicitly to ‘cardinalize’ ordinal theories, and so does not fully face up to the problem of merely ordinal theories. Second, the Borda rule faces a problem of option individuation. MacAskill attempts to solve this problem by invoking a measure on the set of practical options. But it is unclear that there is any natural way of defining such a measure that will not make the output of the Borda rule implausibly sensitive to irrelevant empirical features of decision-situations. After developing these objections, I suggest an alternative: the McKelvey uncovered set, a Condorcet method that selects all and only the maximal options under a strong pairwise defeat relation. This decision rule has several advantages over Borda and mostly avoids the force of MacAskill’s objection to Condorcet methods in general.

Experimental Assessment of Aggregation Principles in Argumentation-Enabled Collective Intelligence

On the Web, there is always a need to aggregate opinions from the crowd (as in posts, social networks, forums, etc.). Different mechanisms have been implemented to capture these opinions such as Like in Facebook, Favorite in Twitter, thumbs-up/-down, flagging, and so on. However, in more contested domains (e.g., Wikipedia, political discussion, and climate change discussion), these mechanisms are not sufficient, since they only deal with each issue independently without considering the relationships between different claims. We can view a set of conflicting arguments as a graph in which the nodes represent arguments and the arcs between these nodes represent the defeat relation. A group of people can then collectively evaluate such graphs. To do this, the group must use a rule to aggregate their individual opinions about the entire argument graph. Here we present the first experimental evaluation of different principles commonly employed by aggregation rules presented in the literature. We use randomized controlled experiments to investigate which principles people consider better at aggregating opinions under different conditions. Our analysis reveals a number of factors, not captured by traditional formal models, that play an important role in determining the efficacy of aggregation. These results help bring formal models of argumentation closer to real-world application.

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.

Reinstatement and Specificty in Argumentation Systems

Reinstatement is a principle of argumentation systems that enables the justification of a defeated argument when all its defeaters are in turn ultimately defeated. Some counterexamples to reinstatement have been offered in the literature. Specifically, counterexamples suggest that reinstatement cannot be taken as a general principle of defeasible argumentation because the reinstated arguments may support incorrect conclusions. Some authors argued that the problems are not due to reinstatement but to the formalization of those examples. Then, the solution is to make the language expressive enough to obtain the correct results. They also warn that one should avoid tinkering with the formalization in concrete examples just to get a desired outcome. Therefore, this approach should be combined with the search of general principles for choosing the proper formalization. Taking into account that finding general principles of representation could be a hard enterprise, the goal of this thesis is to identify some criterion that allows i. neutralize the counterexamples, ii. preserve the original formal language as much as possible, and iii. maintain reinstatement as a general principle. To identify that criterion, counterexamples are analyzed and possible causes of the problem are detected. As a result it is found that the preference by specificity among arguments can be used to obtain that criterion. Three approaches based on specificity are proposed and evaluated. Two of them introduce alternative defeat relations among arguments. The third one is based on filtering the non maximally specific arguments.

Valued preference-based instantiation of argumentation frameworks with varied strength defeats

A Dung-style argumentation framework aims at representing conflicts among elements called arguments. The basic ingredients of this framework is a set of arguments and a Boolean abstract (i.e., its origin is not known) binary defeat relation. Preference-based argumentation frameworks are instantiations of Dung's framework in which the defeat relation is derived from an attack relation and a preference relation over the arguments. Recently, Dung's framework has been extended in order to consider the strength of the defeat relation, i.e., to quantify the degree to which an argument defeats another argument. In this paper, we instantiate this extended framework by a preference-based argumentation framework with a valued preference relation. As particular cases, the latter can be derived from a weight function over the arguments or a Boolean preference relation. We show under some reasonable conditions that there are “less situations” in which a defense between arguments holds with a valued preference relation compared to a Boolean preference relation. Finally, we provide some conditions that the valued preference relation shall satisfy when it is derived from a weight function.

A survey of different approaches to support in argumentation systems

AbstractIn the last decades, most works in the literature have been devoted to study argumentation formalisms that focus on a defeat relation among arguments. Recently, the study of a support relation between arguments regained attention among researchers; the bulk of the research has been centered on the study of support within the context of abstract argumentation by considering support as an explicit interaction between arguments. However, there exist other approaches that take support into account in a different setting. This article surveys several interpretations of the notion of support as proposed in the literature, such as deductive support, necessary support, evidential support, subargument, and backing, among others. The aim is to provide a comprehensive study where similarities and differences among these interpretations are highlighted, as well as discuss how they are addressed by different argumentation formalisms.

Practical Argumentation Semantics for Credulously Justifying Pareto Optimal Defeasible Consequences

Dungean semantics is known as the most standard argumentation-theoretic semantics that has the ability to evaluate various kinds of nonmonotonic consequences. The fact can be seen as a theoretical basis of adequacy for evaluating consequences of theoretical argumentation, i.e., argument about what to believe, that should be analyzed in terms of truth. It, however, does not give any theoretical basis of adequacy for evaluating consequences of practical argumentation, i.e., argument about what to do, that should be analyzed in terms of goodness. In order to address adequacy for evaluating consequences of practical argumentation formally, we propose practical argumentation semantics defined on practical argumentation frameworks. A practical argumentation framework has a defeat function specifying each agent's defeat relation caused by the agent's subjective desires, aims or values in conflicting arguments. Practical argumentation semantics is constructed on the notion of acceptability, which states that a set of agents accepts an argument if every argument defeating it is defeated by some argument under an agent in the set. We analyze properties of complete, preferred, grounded, and stable extensions defined for each set of agents. The correctness of our theory is shown by the fact that the practical argumentation semantics is a generalization of both Dungean semantics and Pareto optimality, i.e., a fundamental criterion for social welfare. Finally, we stratify practical argumentation frameworks on the basis of the theoretical facts and analyze properties of the frameworks.

On Resolving Conflicts Between Arguments

Argument systems are based on the idea that one can construct arguments for propositions; i.e., structured reasons justifying the belief in a proposition. Using defeasible rules, arguments need not be valid in all circumstances, therefore, it might be possible to construct an argument for a proposition as well as its negation. When arguments support conflicting propositions, one of the arguments must be defeated, which raises the question of \emph{which (sub-)arguments can be subject to defeat}? In legal argumentation, meta-rules determine the valid arguments by considering the last defeasible rule of each argument involved in a conflict. Since it is easier to evaluate arguments using their last rules, \emph{can a conflict be resolved by considering only the last defeasible rules of the arguments involved}? We propose a new argument system where, instead of deriving a defeat relation between arguments, \emph{undercutting-arguments} for the defeat of defeasible rules are constructed. This system allows us, (\textit{i}) to resolve conflicts (a generalization of rebutting arguments) using only the last rules of the arguments for inconsistencies, (\textit{ii}) to determine a set of valid (undefeated) arguments in linear time using an algorithm based on a JTMS, (\textit{iii}) to establish a relation with Default Logic, and (\textit{iv}) to prove closure properties such as \emph{cumulativity}. We also propose an extension of the argument system that enables \emph{reasoning by cases}.