The aim of this research is to clarify the conceptual foundations of quantum theory through a careful study of the principles which govern correct quantum reasoning. A particular focus will be the rules which determine whether or not a quantum history--that is, a series of quantum events at successive times- -makes physical sense. Previous work needs to be put into a consistent mathematical and logical framework that will make it easier for students to learn the subject, and aid in applying quantum theory to new fields, such as quantum computation and various problems in modern atomic physics. It is well known that the predictions of quantum theory violate a mathematical condition known as Bell's inequality. Situations where this occurs will be studied to see whether the violation points (as many physicists maintain) to the presence of mysterious long- range forces in nature, or whether it simply indicates that derivations of Bell's inequality do not conform to the rules for sound quantum reasoning.
