The aim of a process discovery algorithm is to construct from event data a process model that describes the underlying, real-world process well. Intuitively, the better the quality of the input event data, the better the quality of the resulting discovered model should be. However, existing process discovery algorithms do not guarantee this relationship. We demonstrate this by using a range of quality measures for both event data and discovered process models. This paper is a call to the community of IS engineers to complement their process discovery algorithms with properties that relate qualities of their inputs to those of their outputs. To this end, we distinguish four incremental stages for the development of such algorithms, along with concrete guidelines for the formulation of relevant properties and experimental validation. We use these stages to reflect on the state of the art, which shows the need to move forward in our thinking about algorithmic process discovery.