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## Re: [ontolog-forum] Interpreting OWL

 To: "'[ontolog-forum] '" "Rich Cooper" Sun, 17 Oct 2010 15:21:11 -0700 <20101017222116.F257A138D11@xxxxxxxxxxxxxxxxx>

John, that is a great ending!

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.

But wouldn’t that hierarchy be a lattice instead of a tree?

Some professors teach other professors who audit their classes, and some grad students – TAs for example – teach other grad students in the introductory courses for each specialty, one per professor usually but occasionally less or more.  And the side branch of RAs would be in parallel from higher credit grad students to lower credit ones, finally joining the recently applied grad students with both streams.

JMHO,

-Rich

Sincerely,

Rich Cooper

EnglishLogicKernel.com

Rich AT EnglishLogicKernel DOT com

9 4 9 \ 5 2 5 - 5 7 1 2

From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Pavithra
Sent: Sunday, October 17, 2010 2:30 PM
To: [ontolog-forum]
Subject: Re: [ontolog-forum] Interpreting OWL

 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 wrote: From: John F. Sowa 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 _________________________________________________________________ Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/  Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/  Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx Shared Files: http://ontolog.cim3.net/file/ Community Wiki: http://ontolog.cim3.net/wiki/ To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx

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 Current Thread [ontolog-forum] Interpreting OWL, sean barker Re: [ontolog-forum] Interpreting OWL, Matthew West Re: [ontolog-forum] Interpreting OWL, Ian Bailey Re: [ontolog-forum] Interpreting OWL, Ed Barkmeyer Re: [ontolog-forum] Interpreting OWL, John F. Sowa Re: [ontolog-forum] Interpreting OWL, Amanda Vizedom [ontolog-forum] Oooh, FOL is too hard to learn., Ian Bailey Re: [ontolog-forum] Interpreting OWL, John F. Sowa Re: [ontolog-forum] Interpreting OWL, Bill Andersen Re: [ontolog-forum] Interpreting OWL, Pavithra Re: [ontolog-forum] Interpreting OWL, Rich Cooper <= Re: [ontolog-forum] Interpreting OWL, Pavithra Re: [ontolog-forum] Interpreting OWL, Godfrey Rust Re: [ontolog-forum] Interpreting OWL, John F. Sowa Re: [ontolog-forum] Interpreting OWL, doug foxvog Re: [ontolog-forum] Interpreting OWL, Rich Cooper Re: [ontolog-forum] Interpreting OWL, John F. Sowa Re: [ontolog-forum] Interpreting OWL, Rich Cooper Re: [ontolog-forum] Interpreting OWL, doug foxvog Re: [ontolog-forum] Interpreting OWL, Rich Cooper Re: [ontolog-forum] Interpreting OWL, Pavithra