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

On 9/20/2012 10:31 AM, Bruno Marchal wrote: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 inset + a binary relation on it.When applied to probability, the idea is to interpret the worlds bythe realization of some random experience, like throwing a coinwould lead to two worlds accessible, one with head, the other withtail. In that modal (tail or head) is a certainty as (tail or head)is realized everywhere in the accessible worlds.Then accessible means nomologically possible.

`Accessible means only that some binary relation exists on a set. But`

`in some concrete model of a multi-world or multi-situation context,`

`nomological possibility is not excluded.`

But in the worlds of the UD there is no nomological constraint, sothere's no probability measure?

`I am not sure why there is no nomological constraints in the UD. UD*`

`is a highly structured entity. You might elaborate on this.`

Bruno

Generally speaking a different world is defined as notaccessible. 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 isused, for what purpose, etc. Kripke semantic main used is inshowing the independence of formula in different systems.BrunoBrentThis 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.http://iridia.ulb.ac.be/~marchal/--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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