On 9/20/2012 2:05 AM, Bruno Marchal wrote:
A modal logic of probability is given by the behavior of the "probability one". In Kripke terms, P(x) = 1 in world alpha means that x is realized in all worlds accessible from alpha, and (key point) that we are not in a cul-de-sac world.

What does 'accessible' mean? Generally speaking a different world is defined as not accessible. If you can go there, it's part of your same world.


This gives KD modal logics, with K: = [](p -> q)->([]p -> []q), and D: []p -> <>p. Of course with "[]" for Gödel's beweisbar we don't have that D is a theorem, so we ensure the D property by defining a new box, Bp = []p & <>t.

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