In "Aristotle's Megarian Maneuvers" (forthcoming in Mind)\,

Kit Fine argues that Aristotle's propositional modal logic should be

identified with the logic he calls KP2D\, where K and D are what you

expect\, and P2 is (p &\; -q) (p &\; -q). He shows\, among many

other things\, that KP2D is (1) reductive (any nested occurrence of a

modality is equivalent to a non-nested one)\, and (2) strongly

anti-Megarean (any consistent non-modal formula constitutes a genuine

possibility). In an earlier draft of the article\, Fine stated that

there were precisely two normal logics having the properties above\,

namely\, S5 and his Aristotelian system. I pointed out in an email

conversation that because of a subtlety involving D in fact there were

four. (To my grateful surprise\, Fine gives me credit for this little

observation.) So\, we have:

Theorem. There are precisely 4 reductive and strongly anti-Megarean

normal modal logics: S5\, S5 x Ver\, KP2D\, KP2 (= KP2D x Ver). \; \;

I will sketch a proof and\, time permitting\, say something more on the

similarities between S5 (S5 x Ver) and KP2D (KP2).