Technical Report -- A Context-Sensitive Multi-Level Similarity Framework for First-Order Logic Arguments: An Axiomatic Study

2026-04-14

AI Summary

This study addresses the challenge of effectively measuring similarity between structured arguments expressed in the more expressive first-order logic (FOL) to support tasks such as argument aggregation and enthymeme reconstruction. The work proposes the first multi-level similarity framework tailored for FOL-based arguments, integrating a four-tier parametric model—spanning predicates, literals, clauses, and formulas—with a context-sensitive weighting mechanism and syntax-aware modeling enhanced by language models. Operating within the constraints of an axiomatic system, the framework enables fine-grained, interpretable similarity computations that satisfy desirable theoretical properties. By bridging formal rigor with practical applicability, this approach offers a novel and robust tool for argument analysis in higher-order logical settings.

Technology Category

• Knowledge Representation and Reasoning: Argumentation
• Natural Language Processing: Discourse, Pragmatics & Argument Mining
• Cognitive Modeling & Cognitive Systems: Analogy

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Similarity in formal argumentation has recently gained attention due to its significance in problems such as argument aggregation in semantics and enthymeme decoding. While existing approaches focus on propositional logic, we address the richer setting of First-Order Logic (FOL), where similarity must account for structured content. We introduce a comprehensive framework for FOL argument similarity, built upon: (1) an extended axiomatic foundation; (2) a four-level parametric model covering predicates, literals, clauses, and formulae similarity; (3) two model families, one syntax-sensitive via language models, both integrating contextual weights for nuanced and explainable similarity; and (4) formal constraints enforcing desirable properties.

Problem

• First-Order Logic
• Argument Similarity
• Formal Argumentation
• Structured Content
• Similarity Measurement

Innovation

• First-Order Logic
• Argument Similarity
• Context-Sensitive
• Axiomatic Framework
• Multi-Level Modeling