There is an ongoing debate on the foundational principles of quantum theory since its formulation, the most prominent issue being the measurement problem, followed by the non-locality, contextuality, the quantum-to-classical transition to name a few. One of the formulations of quantum theory is the consistent histories approach, in the framework of which many of these issues have been addressed. An additional advantage is that there is a consistent formulation of closed systems, which is necessary in considerations of the quantum universe. In this formalism, the main object is the histories on space which should decohere in order to assign the classical probability theory rules. The sets of histories satisfying this condition are called consistent.
In this talk, I will give an example of contradictory arguments in the consistent histories approach which contains classical questions (macroscopic) and thus puts into doubt the interpretation of the consistent histories. I will explain that the existence of contrary inferences comes from the existence of zero covers of the quantum measure which consist of two coarse-grained sets and discuss the consequences of their existence at the classical level.