On Sep 12, 2008, at 11:10 PM, John F. Sowa wrote: (01)
> Pat and Chris M.,
> We usually agree on technical details, but we often interpret
> their implications differently. But the following is a very
> clear technical point: (02)
Good! :-) (03)
> JFS>> So Kripke's semantics is a *proper subset* of Dunn's semantics.
> PH> Wrong as stated, since Dunn's semantics has no constructions
>> corresponding to Kripkean worlds.
> CM> It seems that one should be able to convert any Kripke model
>> into a Dunn model but, off the top of my head, it's not clear to
>> me that one can do so *uniquely*.
> There is an isomorphism from a Kripke model to a Dunn model:
> 1. Given a Kripke model (K,R,Phi) and for each world w in K,
> let M (a Hintikka-style model set) be the set of propositions
> true in w. (04)
Whoa. That set is not yet fully defined. What do you mean by
'proposition'? If you mean 'sentence', you have to say what formal
language your sentences are written in, because this is not specified
by a Kripke (or any other model-theoretic) structure. If you mean
something other than 'sentence', I am all ears to hear what it is that
you do mean. (05)
The rest of your construction is meaningless until this question is
> Pat claimed that Kripke's version is more "usable", but everything
> that can be done with Kripke's version can be done with Dunn's
> version. (07)
I was actually thinking of a rather looser debate, between thinking of
possible worlds as actual entities, versus thinking of them as sets of
propositions or sentences; the Kripke-vs-Dunn terminology was being
used for that, but has now in this thread been tightened up to mean
something much more precise. But to return to the original debate,
which is more relevant for ontology. My point is only that it is very
natural and "usable" to treat possible worlds of various kinds
(including possible times, possible places and possible states of
affairs) as real things which stand in relationships and can be
quantified over. And this point I will insist upon and defend, as
(unlike this semantic scholarly debate) it is of real importance for
ontology engineering. (08)
> But if the two systems are isomorphic, the next question
> is how I could claim that Dunn's version is a superset of Kripke's.
> CM> You don't get much more from Dunn except a very rarefied notion
>> of "law".
> PH> And I have never seen any useful observation or insight arise
>> from Dunn's work that was not already clear in the Kripke framework.
> My answer is that Dunn's version makes it possible to do things
> that cannot be done with Kripke's:
> 1. Unlike Kripke's "arbitrary" relation R, Dunn's version allows
> R to be derived from the choice of laws and facts.
> 2. Instead of being arbitrary, the choice can be made by principled
> arguments about which statements are more "entrenched" than
> others. For example, the ontology is usually considered more
> fundamental than just an offhand observation or assertion.
> 3. Pat made the claim that nobody in AI is using Dunn's semantics.
> But I claim that the entire Description Logic community is using
> Dunn's semantics, but they don't know it. (09)
Publish some papers explaining this to them, and see what kind of a
reception you get. If you are right about all these advantages, then
you should start a revolution in the entire DL field. If that happens,
I will bow to your prescience along with many others. In the meantime,
however, I will continue to use the same semantics that everyone else
on the planet apart from yourself seems to find the most useful. (010)
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