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Dr. Sowa,
What is the need to support acyclic structure vs cyclic ?
In a tree, to traverse each node, one has to move both up and down.
For example, If you start at the parent node, and traverse down the
left side, after reaching each node, one has to move back to the parent node,
to traverse the right side of the nodes..
In squares, one can do the same, if one can traverse in bi directions or in uni-direction
since it is cyclic. . ( trace back..). A tree is acyclic, and a
square or triangle is cyclic But it does form a loop. Are you suppose
to avoid the loop?
Regards,
Pavithra
--- On Sun, 10/17/10, John F. Sowa <sowa@xxxxxxxxxxx> wrote:
From: John F. Sowa <sowa@xxxxxxxxxxx>
Subject: Re: [ontolog-forum] Interpreting OWL
To: ontolog-forum@xxxxxxxxxxxxxxxx
Date: Sunday, October 17, 2010, 10:05 AM
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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