The refusal to define the conjunction or disjunction when \(PQ\neq QP\) should be thought of as a syntactical rule, analogous to that in ordinary logic that says an expression like \(P\land\lor\, Q\) is meaningless because it has not been formed according to the rules used to construct meaningful sentences. In this connection it is important to distinguish “meaningless” from “false”. A proposition which is false is meaningful and its negation is true, whereas the negation of a meaningless statement is equally meaningless. Once the commutativity restriction for meaningful combinations of quantum propositions or properties is in place the usual logical rules apply together with the intuition that goes along with them. This will be further codified using the single framework rule defined in subsection 3.4 below.