Delta1 with LLM: symbolic and neural integration for credible and explainable reasoning
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866917338741211136 |
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| author | Xu, Yang Liu, Jun Chen, Shuwei Nugent, Chris Guo, Hailing |
| author_facet | Xu, Yang Liu, Jun Chen, Shuwei Nugent, Chris Guo, Hailing |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_12953 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Delta1 with LLM: symbolic and neural integration for credible and explainable reasoning Xu, Yang Liu, Jun Chen, Shuwei Nugent, Chris Guo, Hailing Logic in Computer Science Artificial Intelligence 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. |
| title | Delta1 with LLM: symbolic and neural integration for credible and explainable reasoning |
| topic | Logic in Computer Science Artificial Intelligence |
| url | https://arxiv.org/abs/2603.12953 |