Sound and Complete Neuro-symbolic Reasoning with LLM-Grounded
  Interpretations
Authors: name: Bradley P. Allen, name: Prateek Chhikara, name: Thomas Macaulay Ferguson, name: Filip Ilievski, name: Paul Groth

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.