On 9/20/2012 10:31 AM, Bruno Marchal wrote:

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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". InKripke terms, P(x) = 1 in world alpha means that x is realized in all worldsaccessible 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 binaryrelation on it.When applied to probability, the idea is to interpret the worlds by the realization ofsome random experience, like throwing a coin would lead to two worlds accessible, onewith head, the other with tail. In that modal (tail or head) is a certainty as (tail orhead) is realized everywhere in the accessible worlds.

`Then accessible means nomologically possible. But in the worlds of the UD there is no`

`nomological constraint, so there's no probability measure?`

Brent

Generally speaking a different world is defined as not accessible. If you can gothere, it's part of your same world.Yes. OK. Sorry. Logician used the term world in a technical sense, and the worlds can beanything, depending of which modal logic is used, for what purpose, etc. Kripke semanticmain used is in showing 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 we don't have that D is a theorem, so weensure the D property by defining a new box, Bp = []p & <>t.--You received this message because you are subscribed to the Google Groups "EverythingList" group.To post to this group, send email to everything-list@googlegroups.com.To unsubscribe from this group, send email toeverything-list+unsubscr...@googlegroups.com.For more options, visit this group athttp://groups.google.com/group/everything-list?hl=en.http://iridia.ulb.ac.be/~marchal/

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