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During clinical practice, radiologists often use attributes, e.g. morphological and appearance characteristics of a lesion, to aid disease diagnosis. Effectively modeling attributes as well as all relationships involving attributes could boost the generalization ability and verifiability of medical image diagnosis algorithms. In this paper, we introduce a hybrid neuro-probabilistic reasoning algorithm for verifiable attribute-based medical image diagnosis. There are two parallel branches in our hybrid algorithm, a Bayesian network branch performing probabilistic causal relationship reasoning and a graph convolutional network branch performing more generic relational modeling and reasoning using a feature representation. Tight coupling between these two branches is achieved via a cross-network attention mechanism and the fusion of their classification results. We have successfully applied our hybrid reasoning algorithm to two challenging medical image diagnosis tasks. On the LIDC-IDRI benchmark dataset for benign-malignant classification of pulmonary nodules in CT images, our method achieves a new state-of-the-art accuracy of 95.36\% and an AUC of 96.54\%. Our method also achieves a 3.24\% accuracy improvement on an in-house chest X-ray image dataset for tuberculosis diagnosis. Our ablation study indicates that our hybrid algorithm achieves a much better generalization performance than a pure neural network architecture under very limited training data.