Conceptual analysis of quantum history theory

We give formal content to some concepts, naturally stemming from consistent history approach (CHA), which are not formalized in the standard formulation of the theory. The outcoming (extended) conceptual basis is used to perform a formal, conceptually transparent analysis of some debated questions in CHA. As results, the problems raised by contrary inferences of Kent are ruled out, whereas some prescriptions of the theory cannot be mantained.