Abduction and Dialogical Proof in Argumentation and Logic Programming

We develop a model of abduction in abstract argumentation, where changes to an argumentation framework act as hypotheses to explain the support of an observation. We present dialogical proof theories for the main decision problems (i.e., finding hypothe- ses that explain skeptical/credulous support) and we show that our model can be instantiated on the basis of abductive logic programs.Comment: Appears in the Proceedings of the 15th International Workshop on Non-Monotonic Reasoning (NMR 2014

Building an Epistemic Logic for Argumentation

Abstract. In this paper, we study a multi-agent setting in which each agent is aware of a set of arguments. The agents can discuss and persuade each other by putting forward arguments and counter-arguments. In such a setting, what an agent will do, i.e. what argument she will utter, may depend on what she knows about the knowledge of other agents. For example, an agent does not want to put forward an argument that can easily be attacked, unless she believes that she is able to defend her argument against possible attackers. We propose a logical framework for reasoning about the sets of arguments owned by other agents, their knowledge about other agents' arguments, etc. We do this by defining an epistemic logic for representing their knowledge, which allows us to express a wide range of scenarios

Probabilistic graded semantics

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

On the Relation between Possibilistic Logic and Abstract Dialectical Frameworks

Abstract dialectical frameworks (in short, ADFs) are one of the most general and unifying approaches to formal argumentation. As the semantics of ADFs are based on three-valued interpretations, the question poses itself as to whether some and which monotonic three-valued logic underlies ADFs, in the sense that it allows to capture the main semantic concepts underlying ADFs. As an entry-point for such an investigation, we take the concept of model of an ADF, which was originally formulated on the basis of Kleene’s threevalued logic. We show that an optimal concept of a model arises when instead of Kleene’s three-valued logic, possibilistic logic is used. We then show that in fact, possibilistic logic is the most conservative three-valued logic that fulfils this property, and that possibilistic logic can faithfully encode all other semantical concepts for ADFs. Based on this result, we also make some observations on strong equivalence and introduce possibilistic ADFs

Probabilistic Abstract Argumentation Based on SCC Decomposability

In this paper we introduce a new set of general principles for probabilistic abstract argumentation. The main principle is a probabilistic analogue of SCC decomposability, which ensures that the probabilistic evaluation of an argumentation framework complies with the probabilistic (in)dependencies implied by the graph topology. We introduce various examples of probabilistic semantics and determine which principles they satisfy. Our work also provides new insights into the relationship between abstract argumentation and the theory of Bayesian networks

Revision and Conditional Inference for Abstract Dialectical Frameworks

For propositional beliefs, there are well-established connections between belief revision, defeasible conditionals and nonmonotonic inference. In argumentative contexts, such connections have not yet been investigated. On the one hand, the exact relationship between formal argumentation and nonmonotonic inference relations is a research topic that keeps on eluding researchers despite recently intensified efforts, whereas argumentative revision has been studied in numerous works during recent years. In this paper, we show that similar relationships between belief revision, defeasible conditionals and nonmonotonic inference hold in argumentative contexts as well. We first define revision operators for abstract dialectical frameworks, and use such revision operators to define dynamic conditionals by means of the Ramsey test. We show that such conditionals can be equivalently defined using a total preorder over three-valued interpretations, and study the inferential behaviour of the resulting conditional inference relations