  One could engage in endless argument over the correctness or incorrectness of these and other iteration principles for \(\Box\) and \(\Diamond\). The controversy can be partly resolved by recognizing that the words ‘necessarily’ and ‘possibly’, have many different uses. So the acceptability of axioms for modal logic depends on which of these uses we have in mind. For this reason, there is no one modal logic, but rather a whole family of systems built around \(M\). The relationship between these systems is diagrammed in  Section 8,  and their application to different uses of ‘necessarily’ and ‘possibly’ can be more deeply understood by studying their possible world semantics in  Section 6.