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

2026-03-13

AI Summary

This work proposes a neuro-symbolic reasoning framework that integrates the rigor of symbolic logic with the explainability of large language models (LLMs) to build trustworthy and auditable systems. It introduces a novel integration of Delta1—an automatic theorem generator based on Full Triangular Standard Contradiction (FTSC)—with an LLM, where Delta1 deterministically produces minimal unsatisfiable clause sets and complete theorems in polynomial time, and the LLM translates formal proofs into natural language explanations. This synergy enables an end-to-end “explain-as-you-construct” reasoning paradigm, guaranteeing correctness, minimality, and interpretability. The framework’s auditability and domain alignment have been validated in high-stakes domains such as healthcare and regulatory compliance, advancing the deep integration of logic, language, and learning.

Technology Category

• Machine Learning: Neuro-Symbolic Learning
• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Search and Retrieval-Augmented AI: Search Tool Learning with LLM: Teaching LLMs to invoke search and make use of retrieved information
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

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.

Problem

• neuro-symbolic reasoning
• explainable AI
• logical rigor
• interpretability
• theorem generation

Innovation

• neuro-symbolic reasoning
• automated theorem generation
• explainable AI
• large language models
• constructive reasoning