Non-monotonic reasoning (NMR) refers to the fact that conclusions may be invalidated by new information.It is widely used in daily life and legal reasoning.An NMR task usually has multiple extensions, which are sets of plausible conclusions.There are two reasoning modesskeptical and credulous reasoning, depending on whether to believe facts in all extensions or any one extension.Despite some preliminary work exploring the NMR abilities of LLMs, the multi-extension NMR capabilities of LLMs remain underexplored.In this paper, we synthesize a multi-extension NMR dataset Multi-LogicNMR, and construct two variants of the dataset with more extensions or text diversity.We propose a neural-symbolic framework Mul-tiLogicNMRer for multi-extension NMR.Experimental evaluation with the datasets shows that LLMs still face significant challenges in NMR abilities, and reveal the effectiveness of our neural-symbolic framework, with an average accuracy gain of about 15% compared to prompt-based methods, and even outperforming some fine-tuning methods.All code and data are publicly available 1 .