LogicVault: Persistent Symbolic Belief States for Cross-Query Logical Consistency in LLMs

Sarim Chaudhry

Track: long paper (up to 10 pages)

Keywords: logical reasoning, neuro-symbolic AI, belief revision, SMT solvers, cross-query consistency, large language models

TL;DR: A novel framework that enforces cross-query logical consistency in large language models by maintaining a persistent symbolic belief state verified with SMT solving and belief revision.

Abstract: Large Language Models (LLMs) answer each query in isolation with no persistent logical state. This causes contradictions across related questions. We introduce LogicVault, a framework that maintains a symbolic belief vault alongside any LLM and enforces cross-query consistency through an external SMT solver. For each response, LogicVault formalizes the output into first-order logic, checks it against all prior beliefs via Z3, and repairs contradictions by feeding the minimal unsatisfiable core back to the LLM. A belief revision module based on AGM theory handles genuine world-model updates. We release LogicBench-Cross, the first benchmark for crossquery logical consistency, containing 500 multi-query scenarios across five domains. Across six LLMs, LogicVault reduces cross-query contradictions by 78% and improves single-query accuracy on FOLIO, ProofWriter, and LogiQA 2.0. The framework requires no training and works with any LLM at inference time. Code is available at: https://github.com/Sarimsaljook/LogicVault.

Anonymization: This submission has been anonymized for double-blind review via the removal of identifying information such as names, affiliations, and identifying URLs.

Funding: No, the presenting author of this submission does *not* fall under ICLR’s funding aims, or has sufficient alternate funding.

Submission Number: 35