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At 12:31 PM -0500 3/4/08, Alan Ruttenberg wrote:
On Mar 4, 2008, at 11:38 AM, Pat Hayes
wrote:
That all sounds reasonable.
Thanks. I try to be.
What has it got to do with the topic of
the question?
The original poster asked: "When are ontologies
orthogonal?"
I use the word "term" below to mean a name that denotes some
set of things, understanding that terms can be defined to denote sets
of thing by expressions that relate the sets denoted by other terms.
An "Ontology", in the sense I am using it here, is, among
other things, a set of such terms and associated
expressions.
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)
I give here my understanding of how the term is used in that context,
by
- 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)
- then defining orthogonality of term with respect to another
set of terms (=def doesn't denote the same thing as some _expression_ in
terms of the other terms) => orthogonal(term,set of
terms)
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'.
In addition, I add commentary motivating the utility for defining
orthogonality - namely that it can be usefully used to describe a
situation that one might want to avoid - using together two ontologies
that are not orthogonal, or adding a term to an ontology that is not
orthogonal to the others.
Implicit: a) You can add the name as a synonym in such
situations, instead of defining a new terms b) It is harmless to add
terms that are defined as set of necessary and sufficient conditions
that are expressions in terms of the others
?? 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
If not, would you mind helping me further debug? Or suggest
alternative language for conveying what you considered reasonable in
my previous message.
foodly yours,
Alan
On Mar 4, 2008, at 11:38 AM, Pat Hayes wrote:
At 9:10 AM -0500 3/4/08, Alan Ruttenberg
wrote:
As used in the OBO Foundry, orthogonality
is better first understood
on a term by term basis. Adding a term that is trivially redundant
with another one, by denoting the same thing, is the first thing
to
avoid. Less trivially, if there is a way to logically define the
new
terms in terms of existing ones, then not doing so leads to a
situation where two users might denote the same thing in two
unconnected ways: Using the new term, or using the compound of
existing terms. This is also to be avoided, if possible.
That all sounds reasonable. What has it got to do with the topic of
the question?
The reason to avoid these situations is that one typically uses an
ontology to mediate queries and it is desirable to have any query
return all relevant answers. Having two ways to say the same thing
means that the user needs to know both ways to ask the question,
and
this puts a higher burden on learning and using the
ontology.
Quite. I repeat, what has this got to do with 'orthogonality'
(whatever that is supposed to mean)?
Generalizing to orthogonality between ontologies, we'd understand
two
ontologies as being orthogonal if no term in one is orthogonal to
the
other ontology, in the senses above.
You havn't GIVEN a 'sense above'.
Also, this reads oddly. Two ontologies are foodle if NO term in one is
foodle to the other? Are you sure that is what you meant to
say?
-Alan
(preparing to take cover ;-)
No, don't take cover. Just tell us what the hell you are talking
about.
Pat
On Mar 4, 2008, at 8:42 AM, Bill Andersen wrote:
It's a category error to apply the
notion of orthogonality to
ontologies since ontologies are not vectors.
More informally speaking, there may be some sort of
linguistic-based
heuristic notion you're after but you'd have to say what that
might be
and what you want to do with it.
Bill Andersen
Ontology Works, Inc.
3600 O'Donnell Street, Suite 600
Baltimore, MD 21224
+1.410.675.1204 (w)
+1.410.675.1201 (f)
+1.443.858.6444 (m)
On Mar 4, 2008, at 5:31 AM, "Alexander Garcia
Castro"
<alexgarciac@xxxxxxxxx
wrote:
Hopefully this is not so out of
focus. I am looking for a definition
for orthogonality. When are ontologies orthogonal? Any body who
can
recommend me some good papers about orthogonal ontologies? Is
there
a measure for orthogonality?
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