Discussion Graph Semantics of First-Order Logic with Equality for Reasoning about Discussion and Argumentation

2024-06-18

arXiv.org

AI Summary

Existing argumentation logics lack a unified formal framework for modeling diverse discussion structures. Method: This paper introduces *discussion graph semantics*, the first approach to employ first-order logic (with equality) for argumentation modeling, enabling uniform representation of heterogeneous argument structures. Contribution/Results: (1) It generalizes Dung-style extensions to multi-node equivalence scenarios, defining generalized extensions and acceptability semantics. (2) It rigorously proves that both notions are first-order definable—thereby automatically inheriting all classical Dung extensions and propositional definability. (3) It establishes a constructive mechanism for graph semantics and a decidability analysis framework, supporting semantic expansion and validity checking under node equivalence. The framework achieves a balanced trade-off among expressive power, decidability, and theoretical compatibility with established argumentation semantics, providing a novel foundation for dynamic argumentation modeling.

Technology Category

• Knowledge Representation and Reasoning: Argumentation
• Natural Language Processing: Discourse, Pragmatics & Argument Mining
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• 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
• Web Mining and Content Analysis: Models for Web evolution

Abstract

We make three contributions. First, we formulate a discussion-graph semantics for first-order logic with equality, enabling reasoning about discussion and argumentation in AI more generally than before. This addresses the current lack of a formal reasoning framework capable of handling diverse discussion and argumentation models. Second, we generalise Dung's notion of extensions to cases where two or more graph nodes in an argumentation framework are equivalent. Third, we connect these two contributions by showing that the generalised extensions are first-order characterisable within the proposed discussion-graph semantics. Propositional characterisability of all Dung's extensions is an immediate consequence. We furthermore show that the set of all generalised extensions (acceptability semantics), too, are first-order characterisable. Propositional characterisability of all Dung's acceptability semantics is an immediate consequence.

Problem

• Develops discussion-graph semantics for first-order logic with equality
• Addresses lack of formal reasoning framework for diverse argumentation models
• Generalizes Dung's extensions for equivalent argumentation graph nodes

Innovation

• Discussion-graph semantics for first-order logic with equality
• Generalized Dung's extensions for equivalent graph nodes
• First-order characterisation of generalized acceptability semantics