Sound and Complete Neurosymbolic Reasoning with LLM-Grounded Interpretations

• URL: http://arxiv.org/abs/2507.09751v2
• Date: Fri, 01 Aug 2025 16:30:02 GMT
• Title: Sound and Complete Neurosymbolic Reasoning with LLM-Grounded Interpretations
• Authors: Bradley P. Allen, Prateek Chhikara, Thomas Macaulay Ferguson, Filip Ilievski, Paul Groth,
• Abstract summary: Large language models (LLMs) have demonstrated impressive capabilities in natural language understanding and generation.<n>We present a method for directly integrating an LLM into the interpretation function of the formal semantics for a paraconsistent logic.
• Score: 7.81820080453498
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 neurosymbolic reasoning that leverages an LLM's knowledge while preserving the underlying logic's soundness and completeness properties.

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