On Aug 8, 2011, at 9:40 PM, John F. Sowa wrote:
>> ...it appeared clear to me it's not for nothing that Dunn suggested
>> extending his semantics with a substitutional quantification theory;
>
> Dunn published papers about truth-value semantics and substitutional
> theories for years. It's one of his main interests. (01)
Yes, but I wasn't suggesting (as this might be taken to imply) that it was his
*interest* in substitutional theories that led him to suggest a substitutional
quantification theory for extending his semantics. The claim was that it is
required by the nature of his truth-value semantics. (02)
>> you can't just tack on a classical QT onto his semantics and go on
>> your merry way the way you can with Kripke semantics.
>
> There is a one-to-one isomorphism between Kripke worlds and Dunn's
> pairs. Every theorem that applies to one applies to the other. (03)
This is just not relevant to my point. Your claim here is a fact about two
semantic theories for modal *propositional* logic. MY point was that it is
non-trivial to extend Dunn's semantics for modal propositional logic to a
semantics for full modal predicate logic. (04)
> Could you please show me anything you can "tack on" to a K model
> that you couldn't "tack on" to a D model with a line-by-line
> translation from one formalism to the other. (05)
This question seems to miss the point. You *first* have to provide a
quantificational semantics to Dunn's propositional semantics. Once you do,
there will be an immediate "line-by-line translation". The point is that adding
a classical semantics for quantification to his truth-value semantics is
non-trivial in a way that it is not for Kripke semantics. (06)
OK, that's enough for this thread. :-) (07)
-chris (08)
_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
Config Subscr: 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 join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J (09)
|