Logical reasoning, i.e., deductively inferring the truth value of a
conclusion from a set of premises, is an important task for artificial
intelligence with wide potential impacts on science, mathematics, and society.
While many prompting-based strategies have been proposed to enable Large
Language Models (LLMs) to do such reasoning more effectively, they still appear
unsatisfactory, often failing in subtle and unpredictable ways. In this work,
we investigate the validity of instead reformulating such tasks as modular
neurosymbolic programming, which we call LINC: Logical Inference via
Neurosymbolic Computation. In LINC, the LLM acts as a semantic parser,
translating premises and conclusions from natural language to expressions in
first-order logic. These expressions are then offloaded to an external theorem
prover, which symbolically performs deductive inference. Leveraging this
approach, we observe significant performance gains on FOLIO and a balanced
subset of ProofWriter for three different models in nearly all experimental
conditions we evaluate. On ProofWriter, augmenting the comparatively small
open-source StarCoder+ (15.5B parameters) with LINC even outperforms GPT-3.5
and GPT-4 with Chain-of-Thought (CoT) prompting by an absolute 38% and 10%,
respectively. When used with GPT-4, LINC scores 26% higher than CoT on
ProofWriter while performing comparatively on FOLIO. Further analysis reveals
that although both methods on average succeed roughly equally often on this
dataset, they exhibit distinct and complementary failure modes. We thus provide
promising evidence for how logical reasoning over natural language can be
tackled through jointly leveraging LLMs alongside symbolic provers. All
corresponding code is publicly available at https://github.com/benlipkin/lin