  Though prompting LLMs with various reasoning structures produces reasoning
proofs along with answers, these proofs are not ensured to be causal and
reliable due to the inherent defects of LLMs. Tracking such deficiencies, we
present a neuro-symbolic integration method, in which a neural LLM is used to
represent the knowledge of the problem while an LLM-free symbolic solver is
adopted to do deliberative reasoning using the knowledge. Specifically, our
customized meta-interpreters allow the production of reasoning proofs and
support flexible search strategies. These reasoning proofs are ensured to be
causal and reliable because of the deterministic executing nature of the
symbolic solvers. Empirically, on ProofWriter, our method surpasses the CoT
baseline by nearly double in accuracy and more than triple in proof similarity.
On GSM8K, our method also shows accuracy improvements and nearly doubled proof
similarity. Our code is released at https://github.com/DAMO-NLP-SG/CaRing
