Reasoning over Commonsense Knowledge Bases (CSKB), i.e. CSKB reasoning, has been explored as a way to acquire new commonsense knowledge based on reference knowledge in the original CSKBs and external prior knowledge. Despite the advancement of Large Language Models (LLM) and prompt engineering techniques in various reasoning tasks, they still struggle to deal with CSKB reasoning. One of the problems is that it is hard for them to acquire explicit relational constraints in CSKBs from only in-context exemplars, due to a lack of symbolic reasoning capabilities (Bengio et al., 2021). To this end, we proposed **ConstraintChecker**, a plugin over prompting techniques to provide and check explicit constraints. When considering a new knowledge instance, ConstraintChecker employs a rule-based module to produce a list of constraints, then it uses a zero-shot learning module to check whether this knowledge instance satisfies all constraints. The acquired constraint-checking result is then aggregated with the output of the main prompting technique to produce the final output. Experimental results on CSKB Reasoning benchmarks demonstrate the effectiveness of our method by bringing consistent improvements over all prompting methods. Codes and data are available at \url{https://github.com/HKUST-KnowComp/ConstraintChecker}.

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