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There is a C axiom as mentioned at https://plato.stanford.edu/entries/logic-modal/#MapRelBetModLog in Section 8. My question is: what can be said about the formula which is the converse of the C axiom? I have been trying to find out whether the converse to C has been considered as an axiom or whether it can be formally proved in some modal axiom system.

  • I want to consider the converse to the C axiom in modal logics weaker than S5. – Monica Oct 4 '17 at 0:53
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The converse of C,

◻◊A→◊◻A,

is known as the McKinsey formula; it does not have a first-order frame condition.

It has also been discussed on Math SE.

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