On Sep 14, 2008, at 5:48 PM, Pat Hayes wrote:
> ...
> I'm still waiting to hear how to map form Kripke to Dunn. (01)
I can't see how this can be done uniquely. Consider a very simple
Kripke model with two worlds w1 and w2 where all atomic sentences true
in w0 are true in w1 (but not vice versa -- assume also that at least
one atomic sentence is true in w0) and both worlds are accessible to
themselves and w1 is accessible to w0. The problem for turning this
into a Dunn model is: when do we have a "mere" necessary truth and
when do we have a law? Nothing seems to determine an answer to this
question; it is simply stipulated in a given model. In particular,
presumably, starting with a Kripke model M, we map each world w0 of M
to a world u0 in a Dunn model whose facts are the truths of w0. Given
this, it seems we can have one Dunn model where every fact of u0 is
also a law of u0 and another model where u0 is a "lawless" world,
i.e., where no fact of u0 is a law of u0. By Dunn's definition, this
will make both worlds accessible to themselves and u1 accessible to
u0. (In both cases, suppose also that every fact of u1 is a law of u1
-- this will prevent u0 from being assessible to u1, since some of
u1's laws are not facts of u0.) (02)
I think that's right (though I'm working old memories of Dunn's
semantics). If so, there is in general no unique mapping from a Kripke
model to a Dunn model. (03)
-chris (04)
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