The Latent Space of Equational Theories

ACL ARR 2026 January Submission7154 Authors

Keywords: Equational Theories, Implication Graph, Latent Space, Stone Pairings, Principal Component Analysis

Abstract:

Building on the collaborative
[Equational Theories](https://teorth.github.io/equational_theories)
project initiated by Terence Tao fifteen months ago,
and combining it with ideas coming from
machine learning and finite model theory,
we construct a *latent space of equational theories*
where each equational theory
is located at a specific location,
determined by its statistical behavior
with respect to
a large sample of finite magmas.
This experiment
enables us to observe for the first time
how reasoning flows
and produces surprisingly oriented
and well-structured chains
of logical implications in the latent space of equational theories.

Paper Type: Long

Research Area: Mathematical, Symbolic, Neurosymbolic, and Logical Reasoning

Research Area Keywords: Mathematical reasoning, symbolic reasoning, logical reasoning, deductive reasoning; symbolic AI; mathematical NLP;

Contribution Types: Theory

Languages Studied: Formal logic

Submission Number: 7154