[Top] [All Lists]

Re: [ontolog-forum] Thing and Class

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Christopher Menzel <cmenzel@xxxxxxxx>
Date: Sun, 14 Sep 2008 23:37:49 -0500
Message-id: <2EC53003-0D63-43A0-8A3F-EAAE53D5BA6D@xxxxxxxx>
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)

Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/  
Subscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/  
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/ 
To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx    (05)

<Prev in Thread] Current Thread [Next in Thread>