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The success of a natural language processing (NLP) system on a task does not amount to fully understanding the complexity of the task, typified by many deep learning models. One such question is: can a black-box model make logically consistent predictions for transitive relations? Recent studies suggest that pre-trained BERT can capture lexico-semantic clues from words in the context. However, to what extent BERT captures the transitive nature of some lexical relations is unclear. From a probing perspective, we examine WordNet word senses and the IS-A relation, which is a transitive relation. That is, for senses A, B, and C, A is-a B and B is-a C entail A is-a C. We aim to quantify how much BERT agrees with the transitive property of IS-A relations, via a minimalist probing setting. Our investigation reveals that BERT’s predictions do not fully obey the transitivity property of the IS-A relation.