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[en] Named entity recognition (NER) is an essential task in natural language processing, but the internal mechanism of most NER models is a black box for users. In some high-stake decision-making areas, improving the interpretability of an NER method is crucial but challenging. In this paper, based on the existing Deterministic Talmudic Public announcement logic (TPK) model, we propose a novel binary tree model (called BTPK) and apply it to two widely used Bi-RNNs to obtain BTPK-based interpretable ones. Then, we design a counterfactual verification module to verify the BTPK-based learning method. Experimental results on three public datasets show that the BTPK-based learning outperform two classical Bi-RNNs with self-attention, especially on small, simple data and relatively large, complex data. Moreover, the counterfactual verification demonstrates that the explanations provided by the BTPK-based learning method are reasonable and accurate in NER tasks. Besides, the logical reasoning based on BTPK shows how Bi-RNNs handle NER tasks, with different distance of public announcements on long and complex sequences.