Delta1 with LLM: symbolic and neural integration for credible and explainable reasoning

TL;DR

This paper presents an integrated neuro-symbolic reasoning framework combining Delta1's formal theorem generation with LLMs to produce interpretable, auditable, and domain-specific explanations across various fields.

Contribution

It introduces an end-to-end explainability pipeline that deterministically generates minimal unsatisfiable clause sets and theorems, enhancing interpretability in neuro-symbolic AI.

Findings

Enables interpretable reasoning in healthcare, compliance, and regulatory domains.

Ensures soundness and minimality in theorem generation by construction.

Facilitates natural language explanations and actionable insights from formal proofs.

Abstract

Neuro-symbolic reasoning increasingly demands frameworks that unite the formal rigor of logic with the interpretability of large language models (LLMs). We introduce an end to end explainability by construction pipeline integrating the Automated Theorem Generator Delta1 based on the full triangular standard contradiction (FTSC) with LLMs. Delta1 deterministically constructs minimal unsatisfiable clause sets and complete theorems in polynomial time, ensuring both soundness and minimality by construction. The LLM layer verbalizes each theorem and proof trace into coherent natural language explanations and actionable insights. Empirical studies across health care, compliance, and regulatory domains show that Delta1 and LLM enables interpretable, auditable, and domain aligned reasoning. This work advances the convergence of logic, language, and learning, positioning constructive theorem generation as a principled foundation for neuro-symbolic explainable AI.