Conformance checking is becoming more important for the analysis of business processes. While the diagnosed results of conformance checking techniques are used in diverse context such as enabling auditing and performance analysis, the quality and reliability of the conformance checking techniques themselves have not been analyzed rigorously. As the existing conformance checking techniques heavily rely on the total ordering of events, their diagnostics are unreliable and often even misleading when the timestamps of events are coarse or incorrect. This paper presents an approach to incorporate flexibility, uncertainty, concurrency and explicit orderings between events in the input as well as in the output of conformance checking using partial...