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

TL;DR

This paper introduces a comprehensive, axiomatic framework for measuring similarity in First-Order Logic arguments, incorporating multiple levels and contextual weights for nuanced, explainable comparisons.

Contribution

It extends existing propositional logic similarity approaches to FOL, with a four-level parametric model and formal constraints for desirable properties.

Findings

Developed a four-level similarity model for FOL arguments

Integrated contextual weights for nuanced similarity assessment

Established formal constraints for desirable similarity properties

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.