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Re: [ontac-forum] Type vs. Class - last chance to vote.

To: Chris Menzel <cmenzel@xxxxxxxx>, ONTAC-WG General Discussion <ontac-forum@xxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Sun, 22 Jan 2006 21:42:50 -0500
Message-id: <43D442AA.1000704@xxxxxxxxxxx>
Chris,    (01)

A few comments:    (02)

CM> The notion of "type" in ramified type theory falls
 > within the scope of the informal senses of "type"?
 > You appear to be drawing upon the usage of a very
 > sophisticated community of speakers of informal English!    (03)

On the contrary, you can generalize a notion just by
deleting axioms.  The notion of type that I am advocating,
which I would claim is very close to the common English
meaning of the word, has the following minimal structure:    (04)

  1. For each type t, a set of axioms that define the
     conditions for any x to be an instance of t.    (05)

  2. A partial ordering called subtype, which is determined
     by the axioms for the types, not by their instances
     in any particular model.    (06)

This definition implies that types are intensional because
two types can have the same instances in a particular model,
yet their axioms might not be not provably equivalent.  That
makes them intensional according to Church's criterion.    (07)

I would also claim that this notion of type is general enough
to include the other technical uses of the word as special cases.
If I am wrong, I would like to see a counterexample.    (08)

CM> ... These languages [RDF and OWL] are expressively limited
 > and rather horrible to look at, but they have a lot of
 > important virtues, are in wide adoption, and are ignored by
 > this group at its peril.    (09)

I must confess that my feelings of nausea when I look at them
has prevented me from looking very hard.    (010)

I promise that I won't badmouth RDF and OWL, but I will use
translators that map them to dialects of Common Logic that
I find more congenial.    (011)

JS>> The word 'class' would hopelessly confuse the issue.    (012)

CM> Properly axiomatized, it simply wouldn't.    (013)

Are you claiming that anybody who hears or sees the word
'class' is expected to look up the axioms associated with
the word every time they run into it?    (014)

Why not just use the word 'type', whose common meaning
(see above) implies the axioms we want to use?    (015)

CM> I fear this group is looking less and less like a WG and
 > more and more like other ideological war zones we've seen
 > over the past 15 years.    (016)

Indeed it is.  Why do you insist on using the word 'class',
when the common English word 'type' already says what we want
to say?    (017)

John    (018)

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