To: |
Alan Ruttenberg <alanruttenberg@xxxxxxxxx> |
---|---|

Cc: |
"[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx> |

From: |
Pat Hayes <phayes@xxxxxxx> |

Date: |
Tue, 4 Mar 2008 12:25:19 -0600 |

Message-id: |
<p06230909c3f33e538391@[10.100.0.20]> |

At 12:31 PM -0500 3/4/08, Alan Ruttenberg wrote:
On Mar 4, 2008, at 11:38 AM, Pat Hayes wrote:
My problem is much simpler than this. The original question used
the term 'orthogonal'. Your reply did not use the term. I had no idea
how your reply related to the original question.
I note that the word "orthogonal" is sometim Yes, I did note that. It seems to be quite widely used now,
without ever being defined. Sigh.
One group (that I am associated with) uses the term "orthogonal" in this way I am pretty sure that group introduced the term in this ontology
context, and must therefore bear the responsibiilty for saying what it
is intended to mean :-)
(http://www.obofoundry.org/crit.shtml)
- first defining the orthogonality of two terms in an ontology (=def don't denote the same set of things). OK, that's a definition, thanks. That sounds like simply the
denial of owl:sameAs, or in a logical language, denial of an equation:
'A' and 'B' are orthogonal when (not (= A B)) is true. That is, when
'A' and 'B' denote different things.
Is that right? And do you really mean true, or do you mean
'provable from the ontology'? I suspect that you might mean the
latter, in fact.
=> orthogonal(term,term) So 'A' is orthogonal to S when there is no _expression_ E over the
vocabulary of S with (= A E) true/provable.
- Implicitly defining orthogonal(term, ontology) as orthogonal(term, the set of terms in the ontology) OK.
- Defining orthogonality of ontologies ont1 and ont2 as (lambda(ont1,ont2) (apply 'and (mapcar (lambda(term) (orthogonal(term,ont2))) ont1)) => orthogonal(ontology,ontology). Well, no need to get into Lisp (a long time since I saw mapcar in
a definition :), I get the idea. But now, which ontology are we doing
the proving in?
-----
If I follow all this, it can be much more straightforwardly
described in terms of definability.
1. A term A is
definable in an ontology O is there is an
_expression_ DEF using the vocabulary of O such that (= A DEF) is
provable in O. The equation is called a definition of A
wrt O.(This is fairly standard; it needs to be modified to handle
recursive definitions, which is much more tricky, but can be done. It
can be extended to handle relational terms by allowing the
sentence
(forall (x1 ... xn)(iff (A x1 ... xn) DEF))
to be provable in O, where x1 ... xn are all free in DEF. Or
whatever is the appropriate translation into the ontology language:
I'm using ISO CLIF here.)
2. A term A is
orthogonal to O when it is not definable in
O.3. Two ontologies O and P are
orthogonal when every term
in O is orthogonal to P and every term in P is orthogonal to O.Note in 3 that each half of the condition uses different notions
of 'provable'.
?? Unless Im completely missing the point (quite possible) , this
seems to contradict orthogonality. So are you saying here that
orthogonality is harmless??
, provided that the system doing the query can infer, given such definitions, that the terms denote the same set of things. c) Many query systems do not accomplish b) because either the language one has available for expressions is not adequate to the task, or because the query system do not compute and use all valid inferences to solve the query Does that help you understand what I intended to convey? You be the judge, given my responses.
Pat
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