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 meansthat x is realized in all worlds accessible from alpha, and (keypoint) 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

BrentThis gives KD modal logics, with K: = [](p -> q)->([]p -> []q),and D: []p -> <>p. Of course with "[]" for GĂ¶del's beweisbar wedon't have that D is a theorem, so we ensure the D property bydefining a new box, Bp = []p & <>t.--You received this message because you are subscribed to the GoogleGroups "Everything List" group.To post to this group, send email to everything-list@googlegroups.com.To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com.For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.

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