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This research integrates LLMs into paraconsistent logic frameworks to address logical inconsistencies without triggering logical explosion, effectively localizing contradictions in high-stakes domains like medication safety. By leveraging bilateral factuality evaluation, the approach improves macro-F1 scores on standard benchmarks while maintaining the soundness and completeness of the underlying formal system. The work offers a practical pathway for neurosymbolic reasoning that combines the broad knowledge of neural networks with the rigor of symbolic logic.
Sound and Complete Neurosymbolic Reasoning with LLM-Grounded Interpretations
arXiv:2507.09751v3 Announce Type: replace-cross Abstract: Large language models (LLMs) have demonstrated impressive capabilities in natural language understanding and generation, but exhibit problems with logical consistency in their output. 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 evaluate the method empirically using datasets derived from the short-form factuality benchmarks GPQA and SimpleQA, showing that bilateral factuality evaluation improves macro-F1 over a unilateral baseline by roughly 6 percentage points on both benchmarks (at the cost of reduced coverage, as abstention is triggered on inconsistent or uncertain cases). We further describe a proof-of-concept tableau reasoner implementing the method, and apply it to a medication-safety knowledge base of 228 asserted and 712 inferred statements: the system detects 92 gluts corresponding to medically significant errors (e.g., opioids inferred as non-addictive, beta-blockers inferred as safe in asthma) while remaining satisfiable, demonstrating that contradictions are localized rather than causing logical explosion. Unlike prior work, our method offers a theoretical framework with a practical implementation for neurosymbolic reasoning that leverages an LLM's knowledge while preserving the underlying logic's soundness and completeness properties.
Abstract:Large language models (LLMs) have demonstrated impressive capabilities in natural language understanding and generation, but exhibit problems with logical consistency in their output. 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 evaluate the method empirically using datasets derived from the short-form factuality benchmarks GPQA and SimpleQA, showing that bilateral factuality evaluation improves macro-F1 over a unilateral baseline by roughly 6 percentage points on both benchmarks (at the cost of reduced coverage, as abstention is triggered on inconsistent or uncertain cases). We further describe a proof-of-concept tableau reasoner implementing the method, and apply it to a medication-safety knowledge base of 228 asserted and 712 inferred statements: the system detects 92 gluts corresponding to medically significant errors (e.g., opioids inferred as non-addictive, beta-blockers inferred as safe in asthma) while remaining satisfiable, demonstrating that contradictions are localized rather than causing logical explosion. Unlike prior work, our method offers a theoretical framework with a practical implementation for neurosymbolic reasoning that leverages an LLM's knowledge while preserving the underlying logic's soundness and completeness properties.
43 pages, 14 tables, 4 figures. Accepted to the 19th Conference on Neurosymbolic Learning and Reasoning (NeSy 2025); to appear Neurosymbolic Artifical Intelligence Special Issue on NeSy 2025 Extended Papers
Artificial Intelligence (cs.AI); Computation and Language (cs.CL); Logic in Computer Science (cs.LO)
arXiv:2507.09751 [cs.AI]
(or arXiv:2507.09751v3 [cs.AI] for this version)
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