The imprecisions of precision measures in process mining

In process mining, precision measures are used to quantify how much a process model overapproximates the behavior seen in an event log. Although several measures have been proposed throughout the years, no research has been done to validate whether these measures achieve the intended aim of quantifying over-approximation in a consistent way for all models and logs. This paper fills this gap by postulating a number of axioms for quantifying precision consistently for any log and any model. Further, we show through counter-examples that none of the existing measures consistently quantifies precision.