Abstract Probabilistic argumentation combines probability theory and formal models of argumentation. Given an argumentation graph where vertices are arguments and edges are attacks or supports between arguments, the approach of probabilistic labellings relies on a probability space where the sample space is any specific set of argument labellings of the graph, so that any labelling outcome can be associated with a probability value. Argument labellings can feature a label indicating that an argument is not expressed, and in previous work these labellings were constructed by exploiting the subargument-completeness postulate according to which if an argument is expressed then its subarguments are expressed and through the use of the concept of ‘subargument-complete subgraphs’. While the use of such subgraphs is interesting to compare probabilistic labellings with other works in the literature, it may also hinder the comprehension of a relatively simple framework. In this short communication, we revisit the construction of probabilistic labellings and demonstrate how labellings can be specified without reference to the concept of subargument-complete subgraphs. By doing so, the framework is simplified and yields a more natural model of argumentation.

In this paper we provide an account of the burden of persuasion in the context of structured argumentation. A formal model for the burden of persuasion is defined, discussed, and used to capture the role of the burden of persuasion in adjudicating conflicts between conflicting arguments and in determining the dialectical status of arguments. We consider how our model can also capture adversarial burdens of proof, namely, those cases in which failure to establish an argument for a proposition burdened with persuasion entails establishing the complementary proposition.

Neural-symbolic systems combine the strengths of neural networks and symbolic formalisms. In this paper, we introduce a neural-symbolic system which combines restricted Boltzmann machines and probabilistic semi-abstract argumentation. We propose to train networks on argument labellings explaining the data, so that any sampled data outcome is associated with an argument labelling. Argument labellings are integrated as constraints within restricted Boltzmann machines, so that the neural networks are used to learn probabilistic dependencies amongst argument labels. Given a dataset and an argumentation graph as prior knowledge, for every example/case K in the dataset, we use a so-called K-maxconsistent labelling of the graph, and an explanation of case K refers to a K-maxconsistent labelling of the given argumentation graph. The abilities of the proposed system to predict correct labellings were evaluated and compared with standard machine learning techniques. Experiments revealed that such argumentation Boltzmann machines can outperform other classification models, especially in noisy settings.

This paper presents a framework for modelling legislative deliberation in the form of dialogues. Roughly, in legislative dialogues coalitions can dynamically change and propose rule-based theories associated with different utility functions, depending on the legislative theory the coalitions are trying to determine.

In computational models of argumentation, the justification of statements has drawn less attention than the construction and justification of arguments. Significant losses of sensitivity or expressibility on statement statuses can be incurred by otherwise appealing formalisms. In order to reappraise statement statuses and, more generally, to support a uniform modelling of different phases of the argumentation process we introduce multi-labelling systems, a generic formalism devoted to represent reasoning processes consisting of a sequence of labelling stages. In the argumentation context, two families of multi-labelling systens, called argument-focused and statement-focused approach are identified and compared. Then they are shown to be able to encompass several prominent literature proposals as special cases, thereby enabling a systematic comparison evidencing their merits and limits. Further, we show that the proposed model supports tunability of statement justification by specifying a few alternative statement justification labellings, and we illustrate how they can be seamlessly integrated into different formalisms.

Dung-like argumentation framework ASPIC+and Defeasible Logic (DL) arebothwell-studiedrule-basedformalismsfordefeasiblereasoning.Wecomparethe two frameworks and establish a linkage between an instantiation of ASPIC+and a DL variant, which leads to a better understanding and cross-fertilization – in particular our work sheds light on features such as ambiguity propagating/blocking, team defeat and strict rules for argumentation, while emphasizing the argumentation-theoretic features of DL.

In computational models of argumentation, argument justification has attracted more attention than statement justification, and significant sensitivity losses are identifiable when dealing with the justification of statements by otherwise appealing formalisms. This paper reappraises statement justification as a formalism-independent component in argument-based reasoning. We introduce a novel general model of argument-based reasoning based on multiple stages of labellings, the last one being devoted to statement justification, identify two alternative paths from argument acceptance to statement justification, and compare their expressiveness. We then show that this model encompasses several prominent literature proposals as special cases, thereby enabling a systematic comparison of existing approaches to statement justification, evidencing their merits and limits. Finally we illustrate our model by specifying a generic ignorance-aware statement justification and showing how it can be seamlessly integrated into different formalisms.

In this paper, we investigate the problem of finding argumentation graphs consistent with some observed statement labellings. We consider a general abstract framework, where the structure of arguments is left unspecified, and we focus on particular grounded argument labellings where arguments can be omitted. The specification of such grounded labellings, the Principle of Multiple Explanations and the Principle of Parsimony lead us to a simple and efficient anytime algorithm to induce 'on the fly' all the 'argument-parsimonious' argumentation graphs consistent with an input stream of statement labellings.

We propose a model of vicarious reinforcement in rule-based learning agents. The influence of this reinforcement is investigated in a population where a law is enforced ex ante. The norm-governed population of learning agents is formalised and simulated in an executable probabilistic rule-based argumentation framework. Vicarious experiences are expressed with rules and their learning effects are integrated into reinforcement learning. So, agents learn not only from their own experiences but also by taking into account the experiences of others. We show that simulation results differ from traditional calculus based on expected utilities.

This paper proposes to integrate an argumentation framework with techniques from Temporal Constraint Satisfaction. Temporal constraints are thus embedded into legal argumentation to account for temporal aspects of legal reasoning. Through the accommodation of temporal constraints, the validity of arguments and of their conclusions is made relative to the time-points when the applied norms are alive, according to the adopted temporal perspective. A fixed-point semantics and an associated dialogue game are given.

This contribution introduces a novel approach to study legal interactions, legal professions, and legal institutions, by combining argumentation, game theory and evolution. We consider a population of lawyers, having different postures, who engage in adversarial argumentation with other lawyers, obtaining outcomes according the existing context and their chosen strategies. We examine the resulting games and analyse the evolution of the population.

This paper proposes some variants of Temporal Defeasible Logic (TDL) to reason about normative modifications. These variants make it possible to differentiate cases in which, for example, modifications at some time change legal rules but their conclusions persist afterwards from cases where also their conclusions are blocked.

Argumentation is modelled as a game where the payoffs are measured in terms of the probability that the claimed conclusion is, or is not, defeasibly provable, given a history of arguments that have actually been exchanged, and given the probability of the factual premises. The probability of a conclusion is calculated using a standard variant of Defeasible Logic, in combination with standard probability calculus. It is a new element of the present approach that the exchange of arguments is analysed with game theoretical tools, yielding a prescriptive and to some extent even predictive account of the actual course of play. A brief comparison with existing argument-based dialogue approaches confirms that such a prescriptive account of the actual argumentation has been almost lacking in the approaches proposed so far.