arXiv subjects

Arunavo Ganguly

Publications and source records attributed to Arunavo Ganguly.

3 recordsLinked to original sources

arXiv2026

Safety, Liveness, and Fairness in Quantitative Argumentation Dialogues

We introduce notions of safety, liveness, and fairness, as commonly used in temporal reasoning and distributed systems, to quantitative (bipolar) argumentation dialogues where repeated inferences are drawn from argumentation graphs with weighted nodes. Between inferences, these graphs undergo updates. Safety and liveness captures that arguments' (final) strengths attain a specific threshold of credibility and always attain the threshold eventually, respectively. Fairness notions assess how safe arguments are spread within a sequence of argumentation graphs. Additionally, we introduce the notion of oscillation to capture the stability of a topic argument with respect to the threshold of credibility. We formally show how these notions are related, and discuss some analytical challenges with respect to providing general guarantees for our properties.

cs.MA↗

arXiv2026

Dimensions of Power: A Systematic Guide to Power Indices for Explainable AI

Power indices, originating in cooperative game theory, quantify each player's influence on the outcome of a given game. Originally designed to distribute profits or costs among players and to analyse the fairness of voting systems, power indices have recently gained prominence as methods for attributing outputs of AI-based systems to inputs, thus facilitating explainability. However, selecting the appropriate power index for a given explanation task is an understudied problem. To address this, we organise power indices along three attribution dimensions: single-player, set-based, and cardinality-based. For each dimension, we review the corresponding power indices, generalise existing ones where applicable, and analyse which formal principles they satisfy. We provide proofs for properties that are missing in the literature and show that moving to the cardinality-based setting removes player-identity information while preserving some index-level distinctions. Using concrete examples, we illustrate how the choice of dimension and index affects the resulting attributions in practice, and offer guidance for practitioners seeking to select a suitable power index for a given application context.

cs.GT↗

arXiv2026

Modal Fragments

We survey systematic approaches to basis-restricted fragments of propositional logic and modal logics, with an emphasis on how expressive power and computational complexity depend on the allowed operators. The propositional case is well-established and serves as a conceptual template: Post's lattice organizes fragments via Boolean clones and supports complexity classifications for standard reasoning tasks. For modal fragments, we then bring together two historically independent lines of investigation: a general framework where modal fragments are parameterized by a basis of "connectives" defined by arbitrary modal formulas (initially proposed and studied by logicians such as Kuznetsov and Ratsa in the 1970s), and the more tractable class of what we call simple modal fragments parameterized by Boolean functions plus selected modal operators, where Post-lattice methods enable systematic decidability and dichotomy results. Along the way, we collect and extend results on teachability and exact learnability from examples for both propositional fragments and simple modal fragments, and we conclude by identifying several open problems.

cs.LO↗