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Despite substantial advancements in aligning LLMs with human values, current safety mechanisms remain susceptible to jailbreak attacks. We attribute this vulnerability to the distributional discrepancies between alignment-oriented prompts and malicious prompts. To investigate this, and drawing inspiration from logic-driven NLP tasks, we introduce LogiBreak, a universal black-box jailbreak method that utilizes logical expression translation to bypass LLM safety mechanisms. By converting harmful natural language prompts into formal logical expressions, LogiBreak exploits the distributional gap between alignment data and logic-expressed inputs, preserving the underlying semantic intent and readability while evading safety constraints. Furthermore, to fill the gap of existing benchmarks that lack systematic resources specifically targeting logical expression-based attacks against LLM robustness, we construct a novel multilingual logical expression jailbreak dataset for evaluation. Our evaluations of LogiBreak in five languages demonstrate its effectiveness and generalizability in various linguistic contexts. The code is available at https://github.com/Applied-Machine-Learning-Lab/ACL2026_Logibreak.