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 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.
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, so
there'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 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.
--
You received this message because you are subscribed to the Google
Groups "Everything List" group.
To post to this group, send email to [email protected]
.
To unsubscribe from this group, send email to [email protected]
.
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 Google
Groups "Everything List" group.
To post to this group, send email to [email protected].
To unsubscribe from this group, send email to [email protected]
.
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 Google Groups
"Everything List" group.
To post to this group, send email to [email protected].
To unsubscribe from this group, send email to
[email protected].
For more options, visit this group at
http://groups.google.com/group/everything-list?hl=en.
