Deep learning models are powerful image classifiers but their opacity hinders their trustworthiness. Explanation methods for capturing the reasoning process within these classifiers faithfully and in a clear manner are scarce, due to their sheer complexity and size. We provide a solution for this problem by defining a novel method for explaining the outputs of image classifiers with debates between two agents, each arguing for a particular class. We obtain these debates as concrete instances of Free Argumentative eXchanges (FAXs), a novel argumentation-based multi-agent framework allowing agents to internalise opinions by other agents differently than originally stated. We define two metrics (consensus and persuasion rate) to assess the usefulness of FAXs as argumentative explanations for image classifiers. We then conduct a number of empirical experiments showing that FAXs perform well along these metrics as well as being more faithful to the image classifiers than conventional, non-argumentative explanation methods. All our implementations can be found at https://github.com/koriavinash1/FAX.

This paper introduces the Hierarchical Kolmogorov-Arnold Network (HKAN), a novel network architecture that offers a competitive alternative to the recently proposed Kolmogorov-Arnold Network (KAN). Unlike KAN, which relies on backpropagation, HKAN adopts a randomized learning approach, where the parameters of its basis functions are fixed, and linear aggregations are optimized using least-squares regression. HKAN utilizes a hierarchical multi-stacking framework, with each layer refining the predictions from the previous one by solving a series of linear regression problems. This non-iterative training method simplifies computation and eliminates sensitivity to local minima in the loss function. Empirical results show that HKAN delivers comparable, if not superior, accuracy and stability relative to KAN across various regression tasks, while also providing insights into variable importance. The proposed approach seamlessly integrates theoretical insights with practical applications, presenting a robust and efficient alternative for neural network modeling.

Assumption-based Argumentation (ABA) is a well-known structured argumentation formalism, whereby arguments and attacks between them are drawn from rules, defeasible assumptions and their contraries. A common restriction imposed on ABA frameworks (ABAFs) is that they are flat, i.e., each of the defeasible assumptions can only be assumed, but not derived. While it is known that flat ABAFs can be translated into abstract argumentation frameworks (AFs) as proposed by Dung, no translation exists from general, possibly non-flat ABAFs into any kind of abstract argumentation formalism. In this paper, we close this gap and show that bipolar AFs (BAFs) can instantiate general ABAFs. To this end we develop suitable, novel BAF semantics which borrow from the notion of deductive support. We investigate basic properties of our BAFs, including computational complexity, and prove the desired relation to ABAFs under several semantics. Finally, in order to support computation and explainability, we propose the notion of dispute trees for our BAF semantics.

In many real-life situations that involve exchanges of arguments, individuals may differ on their assessment of which supports between the arguments are in fact justified, i.e., they put forward different support-relations. When confronted with such situations, we may wish to aggregate individuals' argumentation views on support-relations into a collective view, which is acceptable to the group. In this paper, we assume that under bipolar argumentation frameworks, individuals are equipped with a set of arguments and a set of attacks between arguments, but with possibly different support-relations. Using the methodology in social choice theory, we analyze what semantic properties of bipolar argumentation frameworks can be preserved by aggregation rules during the aggregation of support-relations.

Recently there has been an increasing interest in frameworks extending Dung's abstract Argumentation Framework (AF). Popular extensions include bipolar AFs and AFs with recursive attacks and necessary supports. Although the relationships between AF semantics and Partial Stable Models (PSMs) of logic programs has been deeply investigated, this is not the case for more general frameworks extending AF. In this paper we explore the relationships between AF-based frameworks and PSMs. We show that every AF-based framework $\Delta$ can be translated into a logic program $P_\Delta$ so that the extensions prescribed by different semantics of $\Delta$ coincide with subsets of the PSMs of $P_\Delta$. We provide a logic programming approach that characterizes, in an elegant and uniform way, the semantics of several AF-based frameworks. This result allows also to define the semantics for new AF-based frameworks, such as AFs with recursive attacks and recursive deductive supports. Under consideration for publication in Theory and Practice of Logic Programming.

Bipolar Argumentation Frameworks (BAFs) admit several interpretations of the support relation and diverging definitions of semantics. Recently, several classes of BAFs have been captured as instances of bipolar Assumption-Based Argumentation, a class of Assumption-Based Argumentation (ABA). In this paper, we establish the complexity of bipolar ABA, and consequently of several classes of BAFs. In addition to the standard five complexity problems, we analyse the rarely-addressed extension enumeration problem too. We also advance backtracking-driven algorithms for enumerating extensions of bipolar ABA frameworks, and consequently of BAFs under several interpretations. We prove soundness and completeness of our algorithms, describe their implementation and provide a scalability evaluation. We thus contribute to the study of the as yet uninvestigated complexity problems of (variously interpreted) BAFs as well as of bipolar ABA, and provide the lacking implementations thereof.