Compact Argumentation Frameworks

The field of explainable AI has grown exponentially in recent years. Within this landscape, argumentation frameworks have shown to be helpful abstractions of some AI models towards providing explanations thereof. While existing work on argumentative explanations and their properties has focused on static settings, we focus on dynamic settings whereby the (AI models underpinning the) argumentation frameworks need to change. Specifically, for a number of notions of explanations drawn from abstract argumentation frameworks under extension-based semantics, we address the following questions: (1) Are explanations robust to extension-preserving changes, in the sense that they are still valid when the changes do not modify the extensions? (2) If not, are these explanations pseudo-robust in that can be tractably updated? In this paper, we frame these questions formally. We consider robustness and pseudo-robustness w.r.t. ordinary and strong equivalence and provide several results for various extension-based semantics.

Verification in incomplete argumentation frameworks

We introduce Incomplete Bipolar Argumentation Frameworks (iBAFs), the extension of Dung’s Abstract Argumentation Frameworks (AAFs) allowing the simultaneous presence of supports (borrowed from BAFs – Bipolar AAFs) and of uncertain elements of the argumentation graph (borrowed from iAAFs – incomplete AAFs). We investigate the computational complexity of verification problem (under the possible perspective) and the acceptance problem, by studying its sensitivity to the semantics of supports and the semantics of extensions. On the one hand, we show that adding supports on top of incompleteness does not affect the complexity of the acceptance. On the other hand, surprisingly, we show that the joint use of bipolarity and incompleteness has a deep impact on the complexity of the verification: for the semantics under which the verification over AAFs is polynomial-time solvable, although moving from AAFs to BAFs or to iAAFs does not change the complexity, the complexity of the verification over iBAFs may increase up to NP-complete.

Parametric properties of ideal semantics

We propose natural generalizations of the credulous and skeptical acceptance problems in abstract argumentation for incomplete argumentation frameworks [3]. This continues earlier work on a similar generalization of the verification problem. We provide a full analysis of the computational complexity of the generalized problems for all original semantics, showing that, in almost all cases, acceptance problems for incomplete argumentation frameworks are significantly harder than the respective problems for argumentation frameworks without uncertainty. All our hardness results for the classes NP, coNP, Πp2, and Σp2

The bipolar argumentation framework (BAF) setting is an extension of Dung’s setting for abstract argumentation, that considers an additional relation, called support relation. Several interpretations of such a support relation have been pointed out so far, including deductive, necessity, general and backing supports. These notions of support capture different kinds of interactions between arguments, that do not primarily correspond to attacks. In this paper, we propose a new notion of support, called monotonic support. Our approach is axiomatic: two postulates are introduced for capturing the intuition that underlies this notion of support in formal terms. The first postulate, monotony, prevents the support relation from downgrading the acceptance status of the supported argument. The second postulate, non-triviality, requires the existence of BAFs for which supporting an argument leads to increase its acceptance status. We present a general family of extension-based semantics for BAFs, called support score-based (SSB) semantics, that satisfy the two postulates and are parameterized by some aggregation functions. We prove a characterisation result linking the postulates that a SBB semantics satisfies with the properties of the aggregation functions used to define it. We also show that none of the previously introduced semantics for BAFs satisfies the monotony postulate.

The Verification Problem in abstract argumentation consists in checking whether a set is acceptable under a given semantics in a given argumentation graph. Explaining why the answer is so is the challenge tackled by our work. In this extended abstract, we focus on a small part of this aim considering only the defence principle and proposing explanations in order to explain why a subset of arguments defends all its elements. These explanations are visual, in the sense that they take the form of subgraphs of the initial argumentation framework. They form a class, whose properties are investigated.