  We introduce LLM-ARC, a neuro-symbolic framework designed to enhance the
logical reasoning capabilities of Large Language Models (LLMs), by combining
them with an Automated Reasoning Critic (ARC). LLM-ARC employs an Actor-Critic
method where the LLM Actor generates declarative logic programs along with
tests for semantic correctness, while the Automated Reasoning Critic evaluates
the code, runs the tests and provides feedback on test failures for iterative
refinement. Implemented using Answer Set Programming (ASP), LLM-ARC achieves a
new state-of-the-art accuracy of 88.32% on the FOLIO benchmark which tests
complex logical reasoning capabilities. Our experiments demonstrate significant
improvements over LLM-only baselines, highlighting the importance of logic test
generation and iterative self-refinement. We achieve our best result using a
fully automated self-supervised training loop where the Actor is trained on
end-to-end dialog traces with Critic feedback. We discuss potential
enhancements and provide a detailed error analysis, showcasing the robustness
and efficacy of LLM-ARC for complex natural language reasoning tasks.
