On the Input/Output behavior of argumentation frameworks

Abstract

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 replacementof multipoles within a traditional argumentation framework. Second, several relevant features of argumentation semantics are identified and formally characterized. In particular, the canonical local functionprovides 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-equivalenceof 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

Non-Monotonic Inference Properties for Assumption-Based Argumentation

“…As far as (ii) is concerned, argumentation dynamics has recently been studied with respect to Abstract Argumentation [15] and some other argumentation-based approaches to non-monotonic reasoning, such as DeLP [19] (see e.g. [3,12,13,18]). To the best of our knowledge, [16] is the only work in the direction of investigating structured, extension-based argumentation with regards to non-monotonic inference propertiesá la [22].…”

A General Notion of Equivalence for Abstract Argumentation

“…The issue of local evaluation of AFs was also tackled in the work on input/output AFs [Baroni et al, 2014a;Giacomin et al, 2016]. There the behavior of AFs (with dedicated input-and output-arguments) is described by the possible valuations of the output-arguments for each possible input.…”

“…In this section, we introduce argumentation frameworks [Dung, 1995] and recall the semantics we study (for an overview, see [Baroni et al, 2011]). We fix U as countably infinite domain of arguments.…”

“…As already outlined by Dung, AFs provide a formally simple basis to capture the essence of different nonmonotonic formalisms. Therefore, several so-called semantics are typically considered for AFs, see also [Baroni et al, 2011]. A semantics delivers several sets of arguments (called extensions) that can be jointly accepted in order to satisfy certain properties.…”

Change in Abstract Bipolar Argumentation Systems

“…1. The translation of BAS into AS BAS is an update 5 A second case, referred as "monotony from G ′ to G", has been described in [9]. It is not used in this paper.…”