On 20 Sep 2012, at 18:14, meekerdb wrote:

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?


In modal logic semantic, it is a technical world for any element in set + a binary relation on it.

When applied to probability, the idea is to interpret the worlds by the realization of some random experience, like throwing a coin would lead to two worlds accessible, one with head, the other with tail. In that modal (tail or head) is a certainty as (tail or head) is realized everywhere in the accessible worlds.



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

Yes. OK. Sorry. Logician used the term world in a technical sense, and the worlds can be anything, depending of which modal logic is used, for what purpose, etc. Kripke semantic main used is in showing the independence of formula in different systems.

Bruno




Brent


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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http://iridia.ulb.ac.be/~marchal/



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