On Mar 4, 2008, at 11:38 AM, Pat Hayes wrote:
>
> That all sounds reasonable. (01)
Thanks. I try to be. (02)
> What has it got to do with the topic of the question? (03)
The original poster asked: "When are ontologies orthogonal?" (04)
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. (05)
I note that the word "orthogonal" is sometimes used, in current
language, in a sense that applies to ontologies (ref: google
"orthogonal ontology"). (06)
One group (that I am associated with) uses the term "orthogonal" in
this way (http://www.obofoundry.org/crit.shtml) (07)
I give here my understanding of how the term is used in that context, by (08)
- first defining the orthogonality of two terms in an ontology
(=def don't denote the same set of things). => orthogonal(term,term) (09)
- 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) (010)
- Implicitly defining orthogonal(term, ontology) as orthogonal(term,
the set of terms in the ontology) (011)
- Defining orthogonality of ontologies ont1 and ont2 as (lambda
(ont1,ont2) (apply 'and (mapcar (lambda(term) (orthogonal
(term,ont2))) ont1)) => orthogonal(ontology,ontology). (012)
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. (013)
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, 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 (014)
Does that help you understand what I intended to convey? (015)
If not, would you mind helping me further debug? Or suggest
alternative language for conveying what you considered reasonable in
my previous message. (016)
foodly yours,
Alan (017)
On Mar 4, 2008, at 11:38 AM, Pat Hayes wrote: (018)
> 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? (019)
>
>>
>> -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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