Probabilistic Argumentation with Epistemic Extensions and Incomplete Information

Abstract argumentation offers an appealing way of representing and evaluating arguments and counterarguments. This approach can be enhanced by a probability assignment to each argument. There are various interpretations that can be ascribed to this assignment. In this paper, we regard the assignment as denoting the belief that an agent has that an argument is justifiable, i.e., that both the premises of the argument and the derivation of the claim of the argument from its premises are valid. This leads to the notion of an epistemic extension which is the subset of the arguments in the graph that are believed to some degree (which we defined as the arguments that have a probability assignment greater than 0.5). We consider various constraints on the probability assignment. Some constraints correspond to standard notions of extensions, such as grounded or stable extensions, and some constraints give us new kinds of extensions

Stratified Labelings for Abstract Argumentation

We introduce stratified labelings as a novel semantical approach to abstract argumentation frameworks. Compared to standard labelings, stratified labelings provide a more fine-grained assessment of the controversiality of arguments using ranks instead of the usual labels in, out, and undecided. We relate the framework of stratified labelings to conditional logic and, in particular, to the System Z ranking functions

A general approach to reasoning with probabilities

We propose a general scheme for adding probabilistic reasoning capabilities to a wide variety of knowledge representation formalisms and we study its properties. Syntactically, we consider adding probabilities to the formulas of a given base logic. Semantically, we define a probability distribution over the subsets of a knowledge base by taking the probabilities of the formulas into account accordingly. This gives rise to a probabilistic entailment relation that can be used for uncertain reasoning. Our approach is a generalisation of many concrete probabilistic enrichments of existing approaches, such as ProbLog (an approach to probabilistic logic programming) and the constellation approach to abstract argumentation. We analyse general properties of our approach and provide some insights into novel instantiations that have not been investigated yet

Summary Report of The First International Competition on Computational Models of Argumentation

Computational models of argumentation are an active research discipline within Artificial Intelligence that has grown since the beginning of the 1990s (Dung 1995). While still a young field when compared to areas such as SAT solving and Logic Programming, the argumentation community is very active, with a conference series (COMMA, which began in 2006) and a variety of workshops and special issues of journals. Argumentation has also worked its way into a variety of applications. For example, Williams et al. (2015) described how argumentation techniques are used for recommending cancer treatments, while Toniolo et al. (2015) detail how argumentation-based techniques can support critical thinking and collaborative scientific inquiry or intelligence analysis. Many of the problems that argumentation deals with are computationally difficult, and applications utilising argumentation therefore require efficient solvers. To encourage this line of research, we organised the First International Competition on Computational Models of Argumentation (ICCMA), with the intention of assessing and promoting state of the art solvers for abstract argumentation problems, and to identify families of challenging benchmarks for such solvers. The objective of ICCMA’15 is to allow researchers to compare the performance of different solvers systematically on common benchmarks and rules. Moreover, as witnessed by competitions in other AI disciplines such as planning and SAT solving, we see ICCMA as a new pillar of the community which provides information and insights on the current state of the art, and highlights future challenges and developments. This article summarises the first ICCMA held in 2015 (ICCMA’15). In this competition, solvers were invited to address standard decision and enumeration problems of abstract argumentation frameworks (Dunne and Wooldridge 2009). Solvers’ performance is evaluated based on their time taken to provide a correct solution for a problem; incorrect results were discarded. More information about the competition, including complete results and benchmarks, can be found on the ICCMA website