 One may wonder how much room for manoeuvre is made available by this general strategy, which, since are concentrating on connectives here, amounts to asking how many two-dimensional isotopes a given Boolean connective has. A simpler case than that of the binary connectives with which we have been preoccupied is that of the one-place connectives. A ‘unarized’ version of the whether featuring in (3) above arises by choosing the case in which ψ is ¬φ. This can be written more simply as Aφ ↔ φ, used (in effect) as the definition of what was written as Oφ on p. 119 of Humberstone (2002). (There is no intention, in using “O” here, to evoke any deontic associations.) If we took O as primitive, we could instead define A by taking Aφ to abbreviate Oφ ↔ φ if we wanted. Either way, if an epistemic operator K is treated in the same way semantically as the deontic obligation operator above (though with its own accessibility relation, of course, or even just using neighbourhood semantics here, as in Lewis 1982, p. 202), then for purely Boolean φ, KOφ, alias K(Aφ ↔ φ) ends up unrestrictedly equivalent to (Aφ ∧ Kφ) ∨ (A¬φ ∧ K¬φ) and thus not a bad approximation to something saying that our cognitive subject knows whether (or not)  φ.[54]