Argumentation theory is a powerful paradigm that formalizes a type of commonsense reasoning that aims to simulate the human ability to resolve a specific problem in an intelligent manner. A classical argumentation process takes into account only the properties related to the intrinsic logical soundness of an argument in order to determine its acceptability status. However, these properties are not always the only ones that matter to establish the argument's acceptabilitythere exist other qualities, such as strength, weight, social votes, trust degree, relevance level, and certainty degree, among others.In this work, we redefine the argumentative process to improve the analysis of arguments by considering their special features in order to obtain more refined results. Towards this end, we propose adding meta-level information to the arguments in the form of labels representing quantifiable data ranking over a range of fuzzy valuations. These labels are propagated through an argumentative graph according to the relations of support, conflict, and aggregation between arguments. Through this process we obtain final labels that are useful in determining argument acceptability. We redefine the argumentative process improving the argumentation analysis considering special features of the arguments.We add meta-level information to arguments as labels representing quantifiable data ranking over a fuzzy valuations range.Labels are propagated through an argumentative graph according to the relations of support, conflict, and aggregation.Label information is used to establish the arguments' acceptability according to different acceptance levels.We define an acceptability threshold to determine whether an argument satisfies certain conditions to be accepted.
In a similar fashion, probabilistic argumentation frameworks can be divided into those that arise from extending abstract models @cite_17 @cite_57 @cite_31 and others based on incorporating probabilities in structured frameworks---the earliest such works appeared almost two decades ago @cite_2 @cite_18 , followed by a period of inactivity and a recent resurgence of interest in the topic @cite_6 @cite_19 @cite_76 . Clearly, our work is closest in spirit to the latter, since labels can be seen as a generalization of probability values associated with items in the knowledge base---the generalization is not, however, a complete subsumption since the algebra in this case would simply model a probabilistic space; the modeling of the corresponding probability distribution needs to reside elsewhere, as done in the works mentioned above.
@cite_18 @cite_6 @cite_57 @cite_19 @cite_2 @cite_31 @cite_76 @cite_17
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Combining computational models of argumentation with probability theory has recently gained increasing attention, in particular with respect to abstract argumentation frameworks. Approaches following this idea can be categorised into the constellations and the epistemic approach. While the former considers probability functions on the subgraphs of abstract argumentation frameworks, the latter uses probability theory to represent degrees of belief in arguments, given a fixed framework. In this paper, we investigate the case where probability functions are given on the extensions of abstract argumentation frameworks. This generalises classical semantics in a straightforward fashion and we show that our approach also complies with many postulates for epistemic probabilistic argumentation. We propose a new graded semantics for abstract argumentation frameworks that is based on the constellations approach to probabilistic argumentation. Given an abstract argumentation framework, our approach assigns uniform probability to all arguments and then ranks arguments according to the probability of acceptance wrt. some classical semantics. Albeit relying on a simple idea this approach (1) is based on the solid theoretical foundations of probability theory, and (2) complies with many rationality postulates proposed for graded semantics. We also investigate an application of our approach for inconsistency measurement in argumentation frameworks and show that the measure induced by the probabilistic graded semantics also complies with the basic rationality postulates from that area. Probabilistic abstract argumentation combines Dung’s abstract argumentation framework with probability theory in order to model uncertainty in argumentation. In this setting, we address the fundamental problem of computing the probability that a set of arguments is an extension according to a given semantics. We focus on the most popular semantics (i.e., admissible, stable, complete, grounded, preferred, ideal-set, ideal, stage, and semistable) and show the following dichotomy result: computing the probability that a set of arguments is an extension is either FP or FP#P-complete depending on the semantics adopted. Our polynomial-time results are particularly interesting, as they hold for some semantics for which no polynomial-time technique was known so far. The combination of argumentation and probability paves the way to new accounts of qualitative and quantitative uncertainty, thereby offering new theoretical and applicative opportunities. Due to a variety of interests, probabilistic argumentation is approached in the literature with different frameworks, pertaining to structured and abstract argumentation, and with respect to diverse types of uncertainty, in particular the uncertainty on the credibility of the premises, the uncertainty about which arguments to consider, and the uncertainty on the acceptance status of arguments or statements. Towards a general framework for probabilistic argumentation, we investigate a labelling-oriented framework encompassing a basic setting for rule-based argumentation and its (semi-) abstract account, along with diverse types of uncertainty. Our framework provides a systematic treatment of various kinds of uncertainty and of their relationships and allows us to back or question assertions from the literature.