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

Victor David; Jérôme Delobelle; Jean-Guy Mailly

cs.AIApr 14, 2026

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

Authors: Victor David, Jérôme Delobelle, Jean-Guy Mailly

Organizations: University Cˆote d’Azur, Inria, CNRS, I3S, Sophia-Antipolis, France · Universit´e Paris Cit´e, LIPADE, Paris, France · Universit´e Toulouse Capitole, IRIT, Toulouse, France

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.

Figures & tables

Figure 1: Histogram explaining the formulae similarity for [ CNF_T1 , CNF_T2 ] (green line), based on weighted clause similarities (blue) and their proportion of importance (red).

Figure 2: Similarity on the premises of $A_{1}$ vs $A_{2}$ where $1=\alpha_{1}$ , $2=\alpha_{2}$ , $3=\alpha_{3}$ , $4=\alpha_{4}$ , $5=\alpha_{5}$ , $6=\alpha_{6}$ , $7=\alpha_{7}$ , $8=\alpha_{8}$ and $9=\alpha_{9}$ on the x-axis.

Figure 3: Similarity on the claims of $A_{1}$ vs $A_{2}$ where $1=\beta_{1}$ and $2=\beta_{2}$ on the x-axis.

Panel of Figure 4 — Figure 4: Influence of $\eta$ on argument similarity: higher values prioritize the support, lower values the claim.

Figure 5: Similarity on the premises of $A_{2}$ vs $A_{3}$ where $1=\alpha_{5}$ , $2=\alpha_{6}$ , $3=\alpha_{7}$ , $4=\alpha_{8}$ , $5=\alpha_{9}$ , $6=\alpha_{10}$ , $7=\alpha_{11}$ , $8=\alpha_{12}$ , $9=\alpha_{13}$ and $10=\alpha_{14}$ on the x-axis.

Figure 6: Similarity on the claims of $A_{2}$ vs $A_{3}$ where $1=\beta_{2}$ and $2=\beta_{3}$ on the x-axis.

Computational Argumentation

Computational argumentation studies how to represent, analyze, and apply arguments and their relationships using formal and computational methods.

See all 99 papers

Logical Embeddings for Argument Analysis
Aug 15, 2026Leander Heldring, Santiago TorresText Embedding Models Computational Argumentation
Kellogg School of Management Northwestern University 2211 Campus Drive, Evanston, IL 60208 · Department of Economics MIT 50 Memorial Drive, Cambridge, MA 02142
LLM-based Argument Mining meets Argumentation and Description Logics: a Unified Framework for Reasoning about Debates
Mar 3, 2026Gianvincenzo Alfano, Sergio Greco, Lucio La Cava +2Computational Argumentation Argument Mining
Department of Informatics, Modeling, Electronics and System Engineering, University of Calabria, Italy
Natural Language to First-Order Logic LLM-based Autoformalization
Oct 8, 2026Andrea Brunello, Cristian Curaba, Luca Geatti +3Autoformalization
University of Udine, Italy

Aug 15, 2026J/K move · Enter open · S save

Logical Embeddings for Argument Analysis

Leander Heldring, Santiago Torres

Kellogg School of Management Northwestern University 2211 Campus Drive, Evanston, IL 60208 · Department of Economics MIT 50 Memorial Drive, Cambridge, MA 02142

Text Embedding Models Computational Argumentation Argument Mining

Open paper AskPDF arXiv

We propose a new framework for machine-learning-oriented argument analysis tasks. Our proposal involves replacing traditional contextualized word embeddings used in most NLP tasks with logical embeddings, an alternative encoding that directly exploits argumentation structures. In essence, logical embeddings encapsulate the logical semantics of an argument, allowing for a better representation of its meaning. Supporting these embeddings is a mathematical logic-based similarity measure that offers a transparent notion of proximity and is guaranteed to satisfy several desirable theoretical properties that current cosine similarity-based contextualized word embeddings cannot assure. This similarity measure induces a positive semi-definite kernel on the set of arguments, enabling us to uniquely define logical embeddings using the theory of Reproducing Kernel Hilbert Spaces (RKHS). Moreover, we prove that this encoding is optimal, in the sense that no logical information is lost in the process. As with other RKHS applications, logical embeddings can be used in numerous supervised and unsupervised tasks. We provide an implementation of the method and aim to test it against literature benchmarks. Additionally, we demonstrate that logical embeddings outperform most standard embedding methods on a classification task.

Abstract

Computational Argumentation

Explore similar work

Logical Embeddings for Argument Analysis

LLM-based Argument Mining meets Argumentation and Description Logics: a Unified Framework for Reasoning about Debates

Natural Language to First-Order Logic LLM-based Autoformalization