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Re: [ontolog-forum] Interpreting OWL

To: ontolog-forum@xxxxxxxxxxxxxxxx
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Sun, 17 Oct 2010 10:05:49 -0400
Message-id: <4CBB02BD.2030004@xxxxxxxxxxx>
On 10/17/2010 7:17 AM, sean barker wrote:
> The statement was made that anything that could be written in EXPRESS
> could be written in OWL. However, some of the constructs in EXPRESS,
> particularly those concerning the cardinality and structure of
> relationships are not directly obviously expressible in OWL, such as the
> distinction between a bag and a set. However, it should be possible to
> create a first order interpretation of OWL such that an EXPRESS
> relationship is a subtype of 'thing', and the relationship constraints
> are then OWL properties. EXPRESS Entity and Type also become subtypes of
> 'thing'    (01)

That first claim is false.  EXPRESS has the full power of first-order
logic, but OWL is deliberately restricted to a subset of FOL.    (02)

In particular, OWL DL, which has become OWL 2.0, is designed so that
every model has a tree structure.  This restriction ensures that 
anything that can be expressed in OWL is decidable.    (03)

That restriction is technically known as *Procrustean* .  Any part
that doesn't form a tree is chopped off to ensure that what remains
is a tree.  There are many structures routinely described by EXPRESS
that have cycles, and they cannot be completely described in OWL:    (04)

  1. A benzene molecule has six carbon atoms connected in a ring.
     In OWL, it's possible to say that a benzene molecule C6H6 has
     six carbon and six hydrogen atoms.  You can say that each H
     is connected to exactly one C.  You can even say that each C
     is connected to exactly two Cs.  But you can't say or imply
     that the Cs form a ring, because a ring is not a tree.    (05)

  2. If you look at a bridge that has beams that connect to form
     triangles, you can describe that bridge structure and all its
     interconnections in EXPRESS.  But you can't describe it in
     OWL, because a triangle forms a cycle, which is not a tree.    (06)

  3. If you look at a window with 9 windowpanes, you may notice
     that it has the shape of a large rectangle that contains
     9 smaller rectangles.  You can make that statement in OWL,
     but you can't describe all the connections of the cross
     pieces because rectangles aren't trees.    (07)

The OWL theoreticians are very well aware of this problem,
and they are proposing solutions.  One solution is to extend
OWL with finite graphs.  That would enable some future version
of OWL to represent such things.    (08)

Of course, every such research proposal makes OWL more complex
and harder to teach and learn.  But that is not a problem for OWL,
since its primary goal is to enable professors to teach graduate
students, who write PhD dissertations about decidability so that
they can become professors who teach other grad students, and so on.
And the hierarchy of professors and their grad students is a tree.    (09)

John    (010)

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