A process discovery algorithm aims to construct a process model that represents the real-world process stored in event data well; it is precise, generalizes the data correctly, and is simple. At the same time, it is reasonable to expect that better quality input event data should lead to constructed process models of better quality. However, existing process discovery algorithms omit the discussion of this relationship between the inputs and outputs and, as it turns out, often do not guarantee it. We demonstrate the latter claim using several quality measures for event data and discovered process models. Consequently, this paper requests for more rigor in the design of process discovery algorithms, including properties that relate the qualities of the inputs and outputs of these algorithms. We present four incremental maturity stages for process discovery algorithms, along with concrete guidelines for formulating relevant properties and experimental validation. We then use these stages to review several state of the art process discovery algorithms to confirm the need to reflect on how we perform algorithmic process discovery
