Dear John (01)
If there were an annual ontolog prize for best post I think yours below should
win it. Brilliant. (02)
Bill (03)
On Oct 17, 2010, at 9:05, "John F. Sowa" <sowa@xxxxxxxxxxx> wrote: (04)
> 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'
>
> That first claim is false. EXPRESS has the full power of first-order
> logic, but OWL is deliberately restricted to a subset of FOL.
>
> 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.
>
> 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:
>
> 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.
>
> 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.
>
> 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.
>
> 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.
>
> 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.
>
> John
>
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