Biomedical Named entity recognition (BioNER) is a crucial initial step for biomedical information processing, serving as the cornerstone technology for identifying biomedical entities and their interactions. However, the inherent workings of most BioNER models remain opaque to users, posing a significant challenge in enhancing their interpretability. In this paper, we propose a novel interpretable learning method based on Talmudic Public announcement logic (TPK), which can learn human-readable knowledge from Bi-directional Long Short-Term Memory (BLSTM) models and generate effective explanations in the form of dichotomous TPK trees. Empirical evaluations conducted on the publicly available BioNER dataset, GENIA, demonstrate that our TPK-based deep learning method outperforms the vanilla BLSTM models in low-source settings. Furthermore, the logical reasoning based on TPK models shows how BLSTM handles BioNER tasks in real applications, providing users with rigorous and transparent logical justifications.