On Strong and Weak Admissibility in Non-Flat Assumption-Based Argumentation

2025-08-14

AI Summary

Standard assumption-based argumentation (ABA) frameworks lack adequate semantic characterizations of acceptability for non-flat ABA, where the flatness assumption—requiring all assumptions to be atomic and conflict-free—is relaxed. This limitation hinders precise modeling of complex assumption dependencies and conflicts. Method: We systematically extend strong and weak acceptability as alternative semantics: first formalizing strong acceptability in general (non-flat) ABA, and generalizing weak acceptability beyond the flat fragment; then, leveraging abstract bipolar structured argumentation frameworks (BSAFs), we integrate assumption derivation relations and conflict structures to define corresponding preferred, complete, and grounded semantics. Contribution: We establish a comprehensive semantic framework for strong and weak acceptability in non-flat ABA; prove that all three acceptability notions—standard, strong, and weak—preserve key properties including modularity; identify shared expressive limitations relative to standard ABA semantics; and outline principled directions for overcoming these limitations.

Technology Category

• Knowledge Representation and Reasoning: Argumentation
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Multiagent Systems: Agreement, Argumentation & Negotiation

Application Category

• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

In this work, we broaden the investigation of admissibility notions in the context of assumption-based argumentation (ABA). More specifically, we study two prominent alternatives to the standard notion of admissibility from abstract argumentation, namely strong and weak admissibility, and introduce the respective preferred, complete and grounded semantics for general (sometimes called non-flat) ABA. To do so, we use abstract bipolar set-based argumentation frameworks (BSAFs) as formal playground since they concisely capture the relations between assumptions and are expressive enough to represent general non-flat ABA frameworks, as recently shown. While weak admissibility has been recently investigated for a restricted fragment of ABA in which assumptions cannot be derived (flat ABA), strong admissibility has not been investigated for ABA so far. We introduce strong admissibility for ABA and investigate desirable properties. We furthermore extend the recent investigations of weak admissibility in the flat ABA fragment to the non-flat case. We show that the central modularization property is maintained under classical, strong, and weak admissibility. We also show that strong and weakly admissible semantics in non-flat ABA share some of the shortcomings of standard admissible semantics and discuss ways to address these.

Problem

• Extending strong and weak admissibility to non-flat ABA frameworks
• Introducing preferred, complete, and grounded semantics for general ABA
• Investigating modularization properties across classical and new admissibility types

Innovation

• Strong admissibility for non-flat ABA
• Weak admissibility extended to non-flat
• Abstract bipolar frameworks represent ABA