Hi Bill,
Thanks for the example – it can help
illuminate any discussions.
Suppose I take a set of facts F0. Then
I have two modelers provide two ontologies that explain those facts –
call them M0 and M1.
Then if I take the quality measure I
suggested below, and apply it to both ontologies M0 and M1, I can determine
whether M0 is more concise than M1, or vice versa. It is likely that a
more concise explanation MI of the exact same facts F0 using less resources
than the explanation of MJ of said F0 is a higher quality model than MJ as well.
My concern is that multiple ontologies of
the same fact base be fused properly. Another concern is equivalence of
entities – do the entities in MI designate the same entities in MJ or are
the MI entities distinct and indiscernible in MJ?
Given a set Q of such quality measurements
over a set of Ontologies M[k] each ontology explaining the same fact base F0, which
of those measures correlate with observations “Better(M[i],M[j])”
where Better implies more agents in the group agree with the model ontology.
For those that value high consistency, degrees
of consistency could be measured by some of the qualities in a subset
measurements.
-Rich
Sincerely,
Rich Cooper
EnglishLogicKernel.com
Rich AT EnglishLogicKernel DOT com
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From: Burkett, William [USA]
[mailto:burkett_william@xxxxxxx]
Sent: Friday, May 06, 2011 8:55 AM
To: Rich Cooper
Subject: RE: [ontolog-forum]
Quality Hunch for Ontology Metric
Hey, Rich –
thanks for the response. I only now have had time to read through it.
I’m not sure
that my point came across given your response, though maybe it did and I just
need to assimilate your response. My point was (keeping in mind that
I’m a data modeler) is that information can be represented (in a data
model) either as attribute or structure:
Vehicle(Type=Automobile,
Manufacturer=GM, Make=Chevrolet, Model=Camaro)
viz
Vehicle >
Automobile > GM > Chevrolet > Camaro
So, more relationships
(4 in the second example, none in the first) doesn’t necessarily
mean a low-quality model – nor does it mean a high-quality
model. It may mean
either, so I don’t think it’s a useful metric for evaluating the
quality of a model (or ontology).
Bill
From: Rich Cooper [mailto:rich@xxxxxxxxxxxxxxxxxxxxxx]
Sent: Thursday, May 05, 2011 11:21
AM
To: Burkett, William [USA]
Subject: RE: [ontolog-forum]
Quality Hunch for Ontology Metric
Hi Bill,
Thanks for your thoughts. For number
(2),
A
well-designed ontology that just happens to encode/represent more information
in structured relationships than in “primitive” concepts.
I agree that more structure implies more
analysis has probably been done, resulting in more succinct information at the
kernel of a concept’s definition. That is good for Q&A
interpretation purposes, but I am still uncertain how to measure that in
quality terms.
From a paper on formal concept analysis at
http://www.google.com/url?sa=t&source=web&cd=4&ved=0CE8QFjAD&url="">
I find this quote, with my emphasis added:
From a philosophical
point of view a concept is a unit of thoughts consisting of two parts, the
extension and the intension. The extension covers all objects belonging to this
concept and the intension comprises all
attributes valid for all those objects (WAGNER 73). Hence objects
and attributes play a prominent role together with several relations like e.g.
the hierarchical "subconcept-superconcept" relation between concepts,
the implication between attributes, and the incidence relation "an object
has an attribute".
I had been familiar with the idea that the
set of initial cases, through deductive closure, leads to the symbolic
_expression_ designating ALL members of the concept. But the definition
quoted above, only enumerates the attributes, and casts objects A, each with a
subset of attributes of object B, as a subordinate concept in lattice terms.
But it seems to me that the lattice above
has poor explanatory quality – the arcs leading from the top node down
one level are by no means an exhaustive list of predicates, and the FOL
equivalents would be
(Or
(IsA Thing ‘Mammal),
(IsA
Thing ‘Bird)
(Preys Thing)
(Flies Thing)
)
Which IMHO has very low quality for
Q&A purposes since the meaning of that conditional is so unlike any elegant
simple node expansion you see in FOL texts. This example is about formal
concept analysis, but the example is a poster instance for poor quality.
-Rich
Sincerely,
Rich Cooper
EnglishLogicKernel.com
Rich AT EnglishLogicKernel DOT com
9 4 9 \ 5 2 5 - 5 7 1 2
From: Burkett, William [USA]
[mailto:burkett_william@xxxxxxx]
Sent: Thursday, May 05, 2011 9:55
AM
To: Rich Cooper
Subject: RE: [ontolog-forum]
Quality Hunch for Ontology Metric
Rich:
FWIW, I think a lot
of relationships can be indicative of one of two things:
(1)
As
you/_X suggested, a poorly designed/thought out/selected set of concepts that
require a lot of relationships to make it make sense;
(2)
A
well-designed ontology that just happens to encode/represent more information
in structured relationships than in “primitive” concepts.
Bill
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Rich Cooper
Sent: Wednesday, May 04, 2011
11:45 AM
To: '[ontolog-forum] '
Subject: [ontolog-forum] Quality
Hunch for Ontology Metric
Ontologizers All,
I found this quote on a SEMWEB list:
“(_X) tells me that empirical evidence
suggests that using a larger number of relationships correlates to poorer
ontologies.”
Note that _X reportedly used the descriptive word
“relationship”, not the usual suspect “relation”, so
the total number of tuples/rows/records in each relation that involves the
ontology, summed over all such relations, would seem to capture the intuitive
meaning of that phrase.
Is quality really inversely proportional to the number of
relation-rows in sum total? That would be an expensive, but easily
implemented way to measure the “number of relationships” as
suggested by _X. Optimization could then drive the computing cost down to
just maintaining a count with each ontology, I suppose.
Also, do others consider this metric validly described as
“empirical evidence”? I’m sure there are examples
having many duplicated relationships which actually correspond to only a single
“essential” relationship.
But what is empirical to one ontologist seems to be the next
ontologist’s formal system, and the previous ontologist’s
intuitively obvious fact. We each see an ontology distorted through our
subjective, focused lenses. Same as we used to see just entities,
properties, relationships and domains.
-Rich
Sincerely,
Rich Cooper
EnglishLogicKernel.com
Rich AT EnglishLogicKernel DOT com
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