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Learning with supervision has achieved remarkable success in numerous artificial intelligence (AI) applications. In the current literature, by referring to the properties of the labels prepared for the training dataset, learning with supervision is categorized as supervised learning (SL) and weakly supervised learning (WSL). SL concerns the situation where the training data set is assigned with ideal (complete, exact and accurate) labels, while WSL concerns the situation where the training data set is assigned with non-ideal (incomplete, inexact or inaccurate) labels. However, various solutions for SL tasks have shown that the given labels are not always easy to learn, and the transformation from the given labels to easy-to-learn targets can significantly affect the performance of the final SL solutions. Without considering the properties of the transformation from the given labels to easy-to-learn targets, the definition of SL conceals some details that can be critical to building the appropriate solutions for specific SL tasks. Thus, for engineers in the AI application field, it is desirable to reveal these details systematically. This article attempts to achieve this goal by expanding the categorization of SL and investigating the sub-type moderately supervised learning (MSL) that concerns the situation where the given labels are ideal, but due to the simplicity in annotation, careful designs are required to transform the given labels into easy-to-learn targets. From the perspectives of the definition, framework and generality, we conceptualize MSL to present a complete fundamental basis to systematically analyse MSL tasks. At meantime, revealing the relation between the conceptualization of MSL and the mathematicians' vision, this paper as well establishes a tutorial for AI application engineers to refer to viewing a problem to be solved from the mathematicians' vision.