The issue of what to do with existential qualifiers is
important, and the answer, I think, will have to depend on how the ontology is
going to be used, and how big it is.
For my purposes I categorize existential qualifiers into four
categories:
(1)
Informative: the assertions are in the ontology only in effect
as documentation, for a human to read and to provide an unambiguous human-interpretable
definition of the intended meaning of the term, but the logical implications
are never used by the machine (never!)
(2)
Advisory: one is allowed to enter data for individuals without
entering data for the implied individuals, but at data entry time the machine provides
a warning that there is a missing implied individual, but does nothing. The
existential may or may not be used in reasoning.
(3)
Supplementary; if no individual that satisfies an existential
qualifier exists at data entry time, the system creates one, of the most
specific implied Type, and provides a warning.
(4)
Required: if no implied individual exists at data entry time,
the system refuses to accept the input data.
In case 2, the system may or may not create implied individuals at
query time. If the system is at all large, creating those individuals may
result in an avalanche of skolemized individuals generated, making the results
hard to interpret, and the time to completion very long. If the system is not
too large, this may be tolerable.
The Ontology Works IODE system provides the option to make an
existential (they consider them as “integrity constraints”) either
advisory (2), and not used at query time, or critical (4) , refusing to load if
the constraint is violated. This conforms to the Database practice of using
integrity constraints on data. I find the IODE system more effective than any
other (of a small list) that I have tried. Nice system – but, alas! expensive.
I think that OWL falls into the (2)(not used) category; they
don’t cause any problems in reasoning. But Protégé will put a red box around
any relation widgets having missing implied individuals – essentially,
just advisory, and that’s their warning mechanism. The OWL validator (“vowlidator”)
will also catch missing implied individuals and provide a warning.
I think there is a place for each of these existential
statement types, but managing them (other than (1), which I think can be very
useful) may be complex for full first-order systems. I would be interested in
the thoughts of others on the topic.
Pat
Patrick Cassidy
MICRA, Inc.
908-561-3416
cell: 908-565-4053
cassidy@xxxxxxxxx
From:
ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of jayanosy@xxxxxxxxxxxxxxxxxxx
Sent: Wednesday, December 12, 2007 5:01 PM
To: [ontolog-forum]
Cc: [ontolog-forum]; ontolog-forum-bounces@xxxxxxxxxxxxxxxx
Subject: Re: [ontolog-forum] brainwaves (WAS: to concept or not to
concept, is this a question?)
Back to
reasoning about knowledge using logic and semantic interpretations, ala, for
example using the OWL language.
I have
the question regarding the existential quantifier when applied as a restriction
to a property between individuals in two different classes. (There must be at
least one individual in the range class for the property associated with the
domain class for each member of the domain class.)
PROBLEM
It would seem
that in a situation where knowledge about individuals (in the ontology) is
gathered over time, there is some complex balance between the number and type
of property existential restrictions that must be satisfied for individual
membership in a class to ensure both appropriate classification and inference
across the model, and the need to capture knowledge while it is gathered.
QUESTION
My question is
"Does the use of an existance quantifier in an OWL ontology restrict the
entry of individuals for a class when there is insufficient knowledge of other
individuals that satisfy the existential restrictions on properties for that
class?
or restated
We have partial
knowledge about an individual, a, and have problem with capturing it in an
ontology with existential restrictions..
OPTIONS
If an OWL
ontology is used subsequently to develop a knowledge base of facts, and there
are multiple Existential restrictions on properties between classes, in the
case of partial knowledge about an individual in the domain of a property , I
have the following options:
- I
cannot enter an individual for a class in a knowledge base unless I have
knowledge about all individuals in the range classes that satisfy the
necessary existential restrictions on properties for the domain class
- I
add the individual for a class in a knowledge base even though there is
not sufficient knowledge of other individuals in other classes to satisfy
all necessary existential property restrictions
CONSEQUENCES OF
EACH OPTION
The PROS and
CONs appear to be
1 PRO -
the knowledge base is consistent and only has individuals that satisfy all
criteria of the ontology model, all individuals in the knowledge base are
correctly classified according to the model
1 CON - there
is lost knowledge since the partial knowledge about an individual was not
entered into the knowledge base
2. PRO -
partial knowledge about an individual is captured in a knowledge base
2. CON -
individuals are entered in the knowledge base that do not satisfy all model
criteria, these individual may be incorrectly classified with partial
knowledge, results of reasoning may be ambiguous?
ANOTHER THOUGHT
Is it possible
to define an ontology where individuals can be entered in more general classes
with fewer existential property restrictions, and as knowledge about other
individuals is discovered and are entered, we may have the case where the
original individuals entered in more general classes may now satisfy the
more existential property restrictions for specialized classes. Is there a way
for this membership in more specialized classes to be automatic inferred as
data is entered instead of having to create an additional entry?
If the answer
is yes than I can see a pragmatic way to define an ontology that will
automatically specialize the classification of individuals, from more general
classes, as more knowledge is added to the knowledge base.
Is this
reasoning correct?
Best Regards,
John A. Yanosy Jr.
Cell: 214-336-9875
PH: 972-705-1807
Email: JAYANOSY@xxxxxxxxxxxxxxxxxxx
|
Pat
Hayes <phayes@xxxxxxx>
Sent by:
ontolog-forum-bounces@xxxxxxxxxxxxxxxx
12/12/2007
12:58 PM
|
Please respond to
"[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
|
|
|
To
|
Duane
Nickull <dnickull@xxxxxxxxx>
|
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cc
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"[ontolog-forum]"
<ontolog-forum@xxxxxxxxxxxxxxxx>
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|
Subject
|
Re:
[ontolog-forum] brainwaves (WAS: to concept or not to concept, is this a
question?)
|
|
>On 12/10/07 8:35 AM, "Christopher
Menzel" <cmenzel@xxxxxxxx> wrote:
>
>> Well, I obviously can't deny that you *experience*
something, but
>> until you can come up with some reasonably hard data rather
than
>> feelings and anecdotes, I don't think you've got any real
>> justification for your belief that there's anything more
than
>> coincidence involved.
>
>Which leads us into ....
>
>Probability and statistics!
>
>I am surprised this group has never had a discussion on this topic or
had
>someone present on P&S (irony - there is a chance I might be
wrong). For
>some scientific axioms, tenets, etc. there seem to be a search for
proof by
>verifying that the one universal truth is not mere coincidence.
For
>example, if I state here are 10 random numbers and give you these:
>
>1,1,1,1,1,1,1,1,1,1
>
>You really don't know if they are truly random. Knowing how they
are
>generated helps ( for example - knowing how the Java.Math.Random class
works
>and the core algorithm is written and run on the metal) but other than
that,
>there is no verification that these are truly random. The
chance they are
>random is equal with every other possible 10 random numbers.
>
>So what does a scientist do? Observe until they are reasonably
satisfied
>there is a norm or baseline then look for statistical anomalies?
Isn't this
>somewhat flawed too since we can never really be 100% sure we have
truly
>tested everything? I got into an argument with a friend last
weekend over
>the existence of god. He stated that since there is no positive
evidence
>god exists, it proves there is no god. His inference takes a
quantum leap
>in logic obviously as what it really means is that god's existence
cannot be
>scientifically verified. God may exist or may not exist was my
position.
>
>So how does this conflict with the topic of the thread. The
experience that
>you think of someone and they call you? Statistically, unless it
had been
>studied (I am sure it has
indeed it has, extensively and rigorously. And
no, repeat, NO, claims of telekinesis or
telepathy have ever survived experimental test.
That is, the claimed phenomena are either
undetectable or are no more probable than chance.
So, as you say, back to the topic of this thread.
Chris did not say that there was any PROOF that
some humans are not superhuman in some way. What
he said, and he is absolutely correct, is that
there is no REAL JUSTIFICATION for such a belief.
One can believe anything, and protect that belief
with a suitable irrational explanation. (The
reason you can't see the little green men pushing
the protons around is that they hide before you
can shine a light on them. The reason there are
fossils is that God put them there to test our
faith. Etc.) The resulting system of beliefs is
probably impossible to refute, but that does not
make it any more rational to believe it, or
provide any justification for not rejecting it as
irrational.
>), there is a small but real probability than some
>human beings have capabilities beyond our perceptions.
And the reason they have never shown up is that
they are so rare that nobody has captured one yet
to put them into a laboratory? Or do their
capabilities mean that they can see the white
coats coming and avoid them?
> Just like my friend
>stating "it proves god does not exist", the correct statement
is probably
>more along the lines of "telekinesis has not been scientifically
resolved to
>a point where it can be satisfactorily quantified"
Er...no. The correct statement is that
telekinesis has never been reliably observed: as
far as anyone can tell, there is no such thing as
telekinesis.
>. It does not mean it
>does not exist or is not real.
It strongly suggests it is not real. On what
basis would anyone insist it was real, if there
is no evidence for it, and repeated attempts to
find such evidence have failed? At what point
will one conclude that this search seems to be a
waste of further time?
Pat
>
>Duane
>
>
>
>
>--
>**********************************************************************
>"Speaking only for myself"
>Blog - http://technoracle.blogspot.com
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http://technoracle.blogspot.com/2007/08/adobe-max-2008.html
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>
>
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