Sound and Complete Neurosymbolic Reasoning with LLM-Grounded Interpretations

Researchers present a neurosymbolic reasoning method that integrates large language models into formal logic systems using paraconsistent logic, enabling sound and complete reasoning while leveraging LLM knowledge. The approach improves factuality evaluation by 6 percentage points and successfully identifies logical contradictions in medical knowledge bases without causing logical explosion.

This research addresses a fundamental challenge in AI: reconciling the broad knowledge captured by large language models with the logical consistency requirements of formal reasoning systems. LLMs excel at pattern recognition and knowledge synthesis but struggle with maintaining logical coherence, making them unreliable for applications requiring strict formal reasoning. The proposed method uses paraconsistent logic—a framework that tolerates contradictions without collapsing into logical explosion—as the foundation for integrating LLM outputs directly into formal semantics.

The significance lies in achieving theoretical soundness and completeness while preserving practical utility. Traditional approaches either sacrifice LLM capabilities to enforce strict logic or accept logical inconsistency. This work demonstrates a third path: the system detected 92 meaningful contradictions in a medication-safety database while remaining mathematically sound, indicating that errors are localized rather than system-wide. The empirical improvements on GPQA and SimpleQA benchmarks validate the approach across factuality evaluation tasks.

For the AI industry, this represents progress toward trustworthy AI systems in high-stakes domains like healthcare, legal reasoning, and finance. The theoretical framework provides a foundation for future neurosymbolic systems that must balance knowledge breadth with logical rigor. The trade-off of reduced coverage—the system abstains on inconsistent cases—is acceptable for safety-critical applications where false confidence poses greater risk than abstention.

The key challenge ahead involves scaling this approach and developing efficient implementations. The proof-of-concept tableau reasoner demonstrates feasibility, but production systems will need optimization for larger knowledge bases and real-time constraints. Industries deploying LLMs in regulated domains should monitor this line of research closely.

• →Paraconsistent logic enables LLM integration while maintaining formal soundness without logical explosion from contradictions.
• →Bilateral factuality evaluation improved macro-F1 scores by 6 percentage points over unilateral baselines on standard benchmarks.
• →System successfully isolated 92 medically significant errors in a 940-statement knowledge base without system-wide logical failure.
• →Method provides theoretical guarantees alongside practical implementation, bridging the neurosymbolic reasoning gap.
• →Coverage-accuracy trade-off shows the system abstains on uncertain cases, prioritizing precision over recall for safety-critical applications.