  Each of the modal logic axioms we have discussed corresponds to a condition on frames in the same way. The relationship between conditions on frames and corresponding axioms is one of the central topics in the study of modal logics. Once an interpretation of the intensional operator \(\Box\) has been decided on, the appropriate conditions on \(R\) can be determined to fix the corresponding notion of validity. This, in turn, allows us to select the right set of axioms for that logic.