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Re: [ontac-forum] Theories, Models, Reasoning, Language, and Truth

To: Chris Menzel <cmenzel@xxxxxxxx>, ONTAC-WG General Discussion <ontac-forum@xxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Wed, 21 Dec 2005 08:34:42 -0500
Message-id: <43A959F2.10204@xxxxxxxxxxx>
Chris,    (01)

Sorry, I should have added more qualifications.    (02)

 > John, I know you know that there's no complement
 > operation in set theory, at least, not in ZF.  That
 > said, in the class theories underlying, e.g., OWL
 > and SUMO, and I'm thinking perhaps your own account,
 > it does appear that classes form a Boolean algebra;
 > so I'm guessing that's what lies behind your remark here.    (03)

In my theories.htm paper, I was using the example of
a lattice of all subsets of a designated set U as the top
and the empty set as bottom.  That's what I was thinking of.    (04)

In fact, I should have mentioned that example as an excellent
reason why the empty set is needed:  In order for every element
of that lattice to have a complement, you need the empty set
as the complement of U.    (05)

John    (06)

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