I have given necessity and possibility (which used to redirect to S4-modal logc) an entry of their own.
The entry presently
first recalls the usual axioms;
then complains that these are arguably necessary but not sufficient to characterize the idea of necessity/possibility;
and then points out that if one passes from propositional logic to first-order logic (hyperdoctrines) and/or to dependent type theory, then there is a way to axiomatize modalities that actually have the correct interpretation, namely by forming the reflection (co)monads of and , respectively.
You may possibly complain, but not necessarily. Give it a thought. I was upset about the state of affairs of the insufficient axiomatics considered in modal logic for a long time, and this is my attempt to make my peace with it.
]]>started a minimum at de dicto and de re, mainly such as to have a place to point to section 4 of