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.

In many real-world reasoning problems, the provided information is not sufficient to derive the solution. To solve these problems, human intelligence often relies on background knowledge and common sense to fill in missing pieces. However, LLMs often struggle when important information is missing. In this work, we introduce a new framework that helps LLMs identify and fill these reasoning gaps. Our method first checks whether the available information is sufficient to support a conclusion. If not, it searches for the minimal set of missing facts needed to complete the reasoning process, thus achieving both sufficiency and necessity. Experiments on logical reasoning and real-world legal tasks show that our framework enables more reliable reasoning when information is incomplete. These findings provide new insights into how LLMs can handle complex open-world reasoning problems, where not all relevant knowledge is provided.