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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