Open-World LLM Logical Reasoning

Large Language Models (LLMs) achieve remarkable performance but struggle with complex logical reasoning, particularly in real-world settings. Existing research is largely confined to the closed-world assumption, which posits that all premises required for reasoning are explicitly provided. However, real-world tasks frequently exhibit open-world characteristics, where the provided information is insufficient to infer a conclusion due to missing premises or implicit commonsense knowledge. To address this, we propose OpenIKLR, an Open-world Incomplete-Knowledge-aware Logical Reasoning framework that integrates symbolic logic solvers with LLMs. OpenIKLR first translates natural language into symbolic representations to pinpoint reasoning gaps via a logical solver. It then iteratively generates a minimal set of necessary missing premises using LLMs. To ensure these added premises are both logically sound and factually accurate, we introduce a dual-verification: logic verification via the solver and fact verification via the LLMs. Experiments show that OpenIKLR consistently outperforms existing logical reasoning and RAG baselines across multiple backbones and real-world datasets. The code is available at https://github.com/OpenIKLR/OpenIKLR.