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Re: [ontology-summit] First Model Bench Challenge

To: ontology-summit@xxxxxxxxxxxxxxxx
From: John F Sowa <sowa@xxxxxxxxxxx>
Date: Thu, 10 May 2012 02:02:33 -0400
Message-id: <4FAB59F9.3000605@xxxxxxxxxxx>
Dear Matthew and Doug,    (01)

> I do not know what distinction you [JR] make between class
> and type. I make none.    (02)

I sympathize.  I would prefer not to use the word 'class' because
it has been used in so many different ways that any use is an open
invitation to confusion.  In any case, my preferred definition
determines a one-to-one association between classes and types:    (03)

    A class is the set of all x of a given type, where type is
    defined by a monadic predicate.    (04)

> You define a class as "the set of all instances of a given type".  In
> order for a definition of a set to identify a timeless group of things,
> the definition must yield the same group no matter when its extent
> is calculated.    (05)

That is why I prefer to avoid the word 'class'.  The O-O people wanted
to apply set-like operators to collections that change their membership
in different contexts.  The word 'type' defined by a monadic predicate
has that property.  You can talk about subtypes and instances in the
same way that you can talk about sets and members, but the instances
can change in different contexts.    (06)

> The spatio-temporal extents [in a 4D view] are considered to exist
> simpliciter independent of time. You can of course also have the class
> "Persons alive at 2012-05-08 21:52:00".    (07)

I'm happy with that way of talking.  But I would prefer to use the word
'set' when I focus on the instances and 'type' when I focus on the
membership criteria.  There is never a case when the word 'class' is
useful -- except when talking about notations that use that word.    (08)

John    (09)

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