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Re: [ontolog-forum] Truth

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Michael Brunnbauer <brunni@xxxxxxxxxxxx>
Date: Sat, 7 Jul 2012 16:39:37 +0200
Message-id: <20120707143937.GA17957@xxxxxxxxxxxx>

Hello Chris,    (01)

On Fri, Jul 06, 2012 at 01:08:57PM -0500, Chris Menzel wrote:
> > So someone trying to define OWL FOL would have to be careful to stay in
> > first
> > order logic because Properties are first class entities ? Would that be a
> > difficult problem ?
> As long as one adds no special semantic requirement that there must be as
> many properties as there are sets of individuals (which, by Cantor's
> Theorem, is simply impossible to require if properties are "first-class
> entities", i.e., a species of individual), there is no risk of moving
> beyond first-order logic.    (02)

After some reading, I think I begin to understand this. As long as the 
properties I can quantify over are first class entities, I have Henkin 
semantics. Only if I can quantify over all possible properties, I get true 
second order logic.    (03)

Regards,    (04)

Michael Brunnbauer    (05)

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