In recent years, explainable machine learning methods have been very successful. Despite their success, most explainable machine learning methods are applied to black-box models without any domain knowledge. By incorporating domain knowledge, science-informed machine learning models have demonstrated better generalization and interpretation. But do we obtain consistent scientific explanations if we apply explainable machine learning methods to science-informed machine learning models? This question is addressed in the context of monotonic models that exhibit three different types of monotonicity. To demonstrate monotonicity, we propose three axioms. Accordingly, this study shows that when only individual monotonicity is involved, the baseline Shapley value provides good explanations; however, when strong pairwise monotonicity is involved, the Integrated gradients method provides reasonable explanations on average.

AI is fast becoming an amazing asset, having achieved superhuman levels of performance in domains such as image recognition, Go, and even poker. Many are excited about the future of AI and humanity. At the same time, there is a general sense that AI does suffer from one pesky flaw: AI in its current state can be unpredictably unreliable. The classical example is the Jeopardy! IBM Challenge, during which Watson, the IBM AI, cleaned the board with ease, only to miss the "Final Jeopardy!" question, which was under the category of US Cities: "Its largest airport is named for a World War II hero; its second largest for a World War II battle."