[Top] [All Lists]

Re: [ontolog-forum] Thing and Class

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Tue, 16 Sep 2008 00:12:27 -0400
Message-id: <48CF322B.7020501@xxxxxxxxxxx>
Pat,    (01)

PH> But now we get back to my earlier objection. Propositions, in
 > this sense, might as well be sentences: a set of propositions is
 > just a set of sentences with an equivalence defined on it.    (02)

I agree that the additional equivalence relation does not make
any critical difference.  In my note to Chris, I agreed that it
would have been better to use the word 'sentence' since it would
have avoided that distracting point.    (03)

PH> A Kripke structure does not itself define a particular language
 > to interpret against it, so your mapping from Kripke to Dunn
 > seems to be under-defined.    (04)

It certainly doesn't determine the syntax, but it definitely
determines semantics.  That's the whole point of a model.
There are two points to consider:    (05)

  1. The two basic modal operators, say Necs and Psbl,
     where Psbl is defined as ~Necs~.    (06)

  2. The nonmodal base, which could be propositional logic
     or some version of FOL.    (07)

The two operators in #1 (and the axioms that define them)
are completely determined by the accessibility relation.
For generality, the nonmodal base could be a very general
version of FOL, such as Common Logic, which includes a
very large number of other versions as subsets.  That
choice would be sufficient to determine a Dunn model
by the construction I suggested earlier.    (08)

John    (09)

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    (010)

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