On 2/6/2014 12:14 PM, Bruno Marchal wrote:
In Kripke semantic all statements are relativized to the world you are in. []A can be
true in some world and false in another. The meaning of "[]" is restricted, for each
world, to the world they can access (through the accessibility relation available in the
Kripke multiverse).
[]A still keep a meaning, but only in each world. So everything is said when we define
the new meaning of "[]" by the rule
[]A is true in alpha, by definition, means that A is true in all world beta *accessible*
from alpha.
And
<>A is true in alpha iff there is a world beta; where A is true, accessible
from alpha.
Suppose A is true in alpha, but alpha is not accessible from alpha and A is not true in
any other world accessible from alpha. Does it follow that <>A is not true in alpha? I
don't see the point allowing that worlds may not be accesible from themselves? Does that
have some application?
Brent
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