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

On the input/output behavior of argumentation frameworks

This paper tackles the fundamental questions arising when looking at argumentation frameworks as interacting components, characterized by an Input/Output behavior, rather than as isolated monolithical entities. This modeling stance arises naturally in some application contexts, like multi-agent systems, but, more importantly, has a crucial impact on several general application-independent issues, like argumentation dynamics, argument summarization and explanation, incremental computation, and inter-formalism translation. Pursuing this research direction, the paper introduces a general modeling approach and provides a comprehensive set of theoretical results putting the intuitive notion of Input/Output behavior of argumentation frameworks on a solid formal ground. This is achieved by combining three main ingredients. First, several novel notions are introduced at the representation level, notably those of argumentation framework with input, of argumentation multipole, and of replacement of multipoles within a traditional argumentation framework. Second, several relevant features of argumentation semantics are identified and formally characterized. In particular, the canonical local function provides an input-aware semantics characterization and a suite of decomposability properties are introduced, concerning the correspondences between semantics outcomes at global and local level. The third ingredient glues the former ones, as it consists of the investigation of some semantics-dependent properties of the newly introduced entities, namely S-equivalence of multipoles, S-legitimacy and S-safeness of replacements, and transparency of a semantics with respect to replacements. Altogether they provide the basis and draw the limits of sound interchangeability of multipoles within traditional frameworks. The paper develops an extensive analysis of all the concepts listed above, covering seven well-known literature semantics and taking into account various, more or less constrained, ways of partitioning an argumentation framework. Diverse examples, taken from the literature, are used to illustrate the application of the results obtained and, finally, an extensive discussion of the related literature is provided

Conditional acceptance functions

Dung-style abstract argumentation theory centers on argumentation frameworks and acceptance functions. The latter take as input a framework and return sets of labelings. This methodology assumes full awareness of the arguments relevant to the evaluation. There are two reasons why this is not satisfactory. Firstly, full awareness is, in general, not a realistic assumption. Second, frameworks have explanatory power, which allows us to reason abductively or counterfactually, but this is lost under the usual semantics. To recover this aspect, we generalize conventional acceptance, and we present the concept of a conditional acceptance function