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Re: [ontolog-forum] Truth

To: ontolog-forum@xxxxxxxxxxxxxxxx
From: John F Sowa <sowa@xxxxxxxxxxx>
Date: Sun, 08 Jul 2012 10:46:35 -0400
Message-id: <4FF99D4B.1000308@xxxxxxxxxxx>
David,    (01)

This example shows how the level of understanding is inversely
proportional to the amount of verbiage.    (02)

> The OWL 1 Language Reference says:    (03)

OWL ref
> Classes provide an abstraction mechanism for grouping resources
> with similar characteristics. Like RDF classes, every OWL class
> is associated with a set of individuals, called the class extension.    (04)

This is a bunch of undefined gobbledygook that results from ignoring
the logic base (LBase) that Pat Hayes and R. V. Guha defined:    (05)

    http://www.w3.org/TR/lbase/    (06)

If you assume the LBase (which is a subset of Common Logic), everything
else can be defined very simply and clearly.  People don't even have to
read the LBase document.  They can just pick up any elementary intro
to math & logic.  Following is the one I wrote:    (07)

   http://www.jfsowa.com/logic/math.htm    (08)

That's all you need to translate the meaningless gobbledygook in the
W3C specs to ordinary English + elementary math.    (09)

Translation of the OWL ref sentence above:
> Every OWL class C is defined by a monadic relation R, which is called
> the intension of C.  The set S of all individuals for which R is true
> is called the extension of C.    (010)

More from the OWL ref
> The individuals in the class extension are called the instances of the class.
> A class has an intensional meaning (the underlying concept) which is related
> but not equal to its class extension. Thus, two classes may have the same
> class extension, but still be different classes.    (011)

> The individuals in the class extension are called the instances of the class.
> Equality of classes is determined by their defining relations.
> Two classes with different defining relations are different,
> even though their extensions might be the same.    (012)

Note that the first sentence of this translation is the same as the
original.  But none of the following terms are required:  'concept',
'meaning', 'abstraction mechanism', 'grouping resources', 'similar',
'characteristics', and 'associated with'.    (013)

> The OWL 2 new features document claims "More importantly, backwards
> compatibility with OWL 1 is complete, both syntactically and semantically."
> even though I can't find any mention of the intensional meaning vs.
> class extension relationship in any of the OWL 2 documents.    (014)

That is more meaningless gobbledygook.  For every version of every OWL
class there is a defining relation.  That's the intension.  The set
of all individuals in the domain is the extension.  End of story.    (015)

> So what does Pat's "assumption of extensionality" mean wrt OWL 1 and OWL 2
> and the question of whether two classes with the same extent are the same 
>class?    (016)

Pat's assumption of extensionality just means that the defining relation
for every class determines a set of individuals in the domain.    (017)

Note that the counter at the bottom of my intro to math & logic shows
that there have been 165,648 downloads.  I'd be happy to let the W3C
copy it, if they would promise to use it to expunge the gobbledygook
from their documents.    (018)

John    (019)

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