Neuro-Symbolic Rule Exploration

The Problem

When an AI system interprets text or raw data, it often jumps immediately to a single "final" theory. This is methodologically unsound because it conflates the actual phenomenon with our observation of it and our linguistic report of that observation.

A direct passage from text to theory lacks the necessary discipline for managing uncertainty. This architecture aims to solve that by constructing a bounded local region of theory space around available evidence, rather than seeking a single, privileged ontology.

The Approach

Our objective is not to find the "one true theory," but to manage a family of plausible local theories under explicit uncertainty. This is meta-rational: the system doesn't treat early abstractions as final. It preserves several candidates as long as the evidence, task, or cost model does not justify stronger commitment.

These theories are organized into a neighborhood where relations of refinement, coarsening, and refactorization are explicit. We treat rewriting as a family of local transformations, studying compositionality in the sense of categorical abstract rewriting [DUVAL-2011].

Core Ruliologic Objects

We introduce three fundamental objects:

Observational Hypotheses: Hypotheses about what was observed or asserted, including causal hints and provenance links.
Local Theory: A combination of state schema, rewrite templates, and a score profile covering stability and predictive adequacy.
Local Rulial Neighborhood: A family of theories together with the transformations between them. It records how one theory evolves into another through refinement or observer shift.

The neighborhood maintains a local geometry of theory space, ensuring that observer-relative equivalence is a first-class relation [WOLFRAM-2026].

Pipeline and Roles

This division of labor uses neuro-symbolic principles:

Neural Lifting: Using language models to propose structured observational hypotheses from text, handling lexical variation and underdetermined structures.
Symbolic Induction: Generating candidate rule systems and theories. Symbolic components dominate where rules and compositions must be auditable.
Rulial Exploration: Organizing theories into neighborhoods and computing robust invariants that are stable across multiple nearby models.

By localized and auditable roles for neural components, the architecture remains disciplined and explainable [MAO-2025].

References

[WOLFRAM-2026] Stephen Wolfram. What Is Ruliology? 2026.
[MAO-2025] Jiayuan Mao, Tenenbaum, Wu. Neuro-Symbolic Concepts. 2025.
[DUVAL-2011] Dominique Duval et al. Categorical Abstract Rewriting Systems. 2011.
[FONG-SPIVAK-2019] Brendan Fong, David Spivak. Seven Sketches in Compositionality. 2019.