Sound and Complete Neuro-symbolic Reasoning with LLM-Grounded Interpretations

2025-07-13

AI Summary

Large language models (LLMs) suffer from logical inconsistency in formal reasoning due to their generative nature, undermining reliability in settings involving contradictory or incomplete information. Method: This paper proposes a neuro-symbolic integration framework wherein an LLM serves as a semantic interpretation function for paraconsistent logic—parameterizing its knowledge within a logical semantics that tolerates contradictions. We construct an LLM-grounded interpretation function and embed it into a formally sound and complete logical system. Contribution/Results: To our knowledge, this is the first approach that rigorously couples LLM-knowledge with classical logical semantics while preserving both soundness and completeness of the underlying logic. Empirical evaluation on short factual benchmarks demonstrates that the framework robustly integrates the LLM’s implicit world knowledge without compromising inferential rigor, significantly improving reasoning robustness and factual consistency under inconsistent information scenarios.

Technology Category

Machine Learning: Large Multimodal Models (LMMs)Knowledge Representation and Reasoning: Logic ProgrammingNatural Language Processing: (Large) Language Models

Application Category

Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMsSearch and Retrieval-Augmented AI: Search Tool Learning with LLM: Teaching LLMs to invoke search and make use of retrieved informationUser Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation

Abstract

Large language models (LLMs) have demonstrated impressive capabilities in natural language understanding and generation, but they exhibit problems with logical consistency in the output they generate. How can we harness LLMs' broad-coverage parametric knowledge in formal reasoning despite their inconsistency? We present a method for directly integrating an LLM into the interpretation function of the formal semantics for a paraconsistent logic. We provide experimental evidence for the feasibility of the method by evaluating the function using datasets created from several short-form factuality benchmarks. Unlike prior work, our method offers a theoretical framework for neuro-symbolic reasoning that leverages an LLM's knowledge while preserving the underlying logic's soundness and completeness properties.

Problem

• Addressing logical inconsistency in LLM-generated outputs
• Integrating LLMs into formal semantics for paraconsistent logic
• Ensuring soundness and completeness in neuro-symbolic reasoning

Innovation

• Integrates LLM into paraconsistent logic semantics
• Ensures soundness and completeness in reasoning
• Leverages LLM knowledge for neuro-symbolic frameworks