Logique et Analyse. Bull and Ono have studied the model-theory of these systems. Intuitionistic mathematics starts also with notions taken over from classical matemathics, but uses only intuitionistically valid methods of proof. C , F contains only the predicates R and V, and the latter with a sentential variable as its second argument.
V is a valuation in the model-theoretic sense.
In this way using intuitionistic instead of classical logic we weaken the model an there is now place for a strong and a weak possibility. This is why we may speak of as a strong and as a weak possibility. All other cases are proved in the same way. The supplementary stability hypothesis, which are classically vacuous, are weaker intuitionistically than the corresponding assertions of decidability. Let us call MCPC the system with the same four rules but based on an axiomatisation of classical propositional logic.