 These definitions imply that something is permissible iff (if and only if) its negation is not obligatory, impermissible iff its negation is obligatory, omissible iff it is not obligatory, optional iff neither it nor its negation is obligatory, and non-optional iff it is either obligatory or impermissible. Call this “The Traditional Definitional Scheme (TDS)”. It, or minor variants, are found as far back as Ockham in European thought, and quite explicitly in Leibniz in the modern  period.[12]  If one began with \(\OB\) alone and considered the formulas on the right above, one could easily be led to consider them as at least candidate defining conditions for those on the left. Although not uncontestable, they are natural, and this scheme has been very widely employed. Now if the reader looks back at our use of the necessity operator in defining the remaining five alethic modal operators, it will be clear that these are perfectly analogous to the five deontic definitions above. From the formal standpoint, the one is merely a syntactic variant of the other: just replace \(\OB\) with \(\Box\), \(\PE\) with \(\Diamond\), etc.