>Classical Modal logic approach of classical probability theory
>are proposed as substitution of probability theory.
Please read instead:
Classical Modal logic approach of classical probability theory
are ***-NOT-**** proposed as substitution of probability theory.
(They are different motivations for using modal logic in probability
context. One is to benefit of modal's semantics to prove things
on probabilities. Mines comes from my (our!) subproblems of extracting
the probabilities (the measure) from a modal context (like the many
observer moment, we could say).
In one little sentence: modal logic is a tool for refining truth
by making it relative to context, situations, etc. Those last
notions are in general captured by some abstract mathematical
spaces, like set + binary (accessibility) relations with Kripke,
quasi topological space with Scott and Montague, etc.