There is also the notion of descriptive complexity (under Finite Model
Theory), which tries to characterize the expressive complexity of
various logics, i.e., Immerman's chart:
http://www.cs.umass.edu/~immerman/descriptive_complexity.html (01)
It's closely related to Kolmogorov expressive complexity of logics,
i.e., the number of bits needed to express the given logical theory:
http://www-mgi.informatik.rwth-aachen.de/Publications/pub/jurek/iandc.p
s. In fact, this is a good formal intro to the whole area. (02)
It would be nice to factor in Semantic Web languages (and description
logics) to this. Ian Horrocks has some work in this area. And of
course, taxonomies, thesauri, and most conceptual models don't have a
formalization, so it's hard to place them within this framework.
Natural language is the most expressive, but it's not really
characterizable yet as far as I know (except perhaps under the Chomsky
hierarchy of formal languages, but no one as far as I know has put all
of this stuff together yet). Perhaps some folks here might think about
such a program? Chris, Mike? (03)
Thanks,
Leo (04)
_____________________________________________
Dr. Leo Obrst The MITRE Corporation, Information Semantics
lobrst@xxxxxxxxx Center for Innovative Computing & Informatics
Voice: 703-983-6770 7515 Colshire Drive, M/S H305
Fax: 703-983-1379 McLean, VA 22102-7508, USA (05)
-----Original Message-----
From: ontology-summit-bounces@xxxxxxxxxxxxxxxx
[mailto:ontology-summit-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Uschold,
Michael F
Sent: Friday, February 23, 2007 2:00 PM
To: Ontology Summit 2007 Forum; patrick@xxxxxxxxxxx
Subject: Re: [ontology-summit] ontology as logical theory? (06)
ChrisW said: (07)
The "degree of formalization" was the primary axis in all the continua
(?) I've seen. This can be related to the language you use. There is
not one "logic".
-- (08)
Probably so. It is important to note that it is not the only important
factor/dimension. Another key one that is fairly orthogonal is the
"amount of meaning specified" in an ontology. Some things called
ontologies (e.g. a thesaurus, or a taxonomy) don't have much facility
for expressing meaning. Also, you can take a simple informal ontology
with little meaning specified, and represent it in a formal logic, and
while it is in one sense unambiguous (from a formal model theory
perspective) it is highly ambiguous from the perspective of real world
meaning (i.e unintended models). The more meaning you have the fewer
unintended models you have. (09)
Conversely, natural language is highly expressive and capable of
capturing 'ontologies' that express a lot of meaning, even if the
language is informal. (010)
Mike (011)
==========================
Michael Uschold
M&CT, Phantom Works
425 373-2845
michael.f.uschold@xxxxxxxxxx
========================== (012)
----------------------------------------------------
COOL TIP: to skip the phone menu tree and get a human on the phone, go
to: http://gethuman.com/tips.html (013)
-----Original Message-----
From: Chris Welty [mailto:cawelty@xxxxxxxxx]
Sent: Friday, February 23, 2007 8:54 AM
To: patrick@xxxxxxxxxxx; Ontology Summit 2007 Forum
Subject: Re: [ontology-summit] ontology as logical theory? (014)
Patrick Durusau wrote:
> John F. Sowa wrote:
>> I agree that different people will have different perspectives that
>> may require different views, terminology, and notations.
>>
>> MFU> Before we come up with a definition, lets identify who it is
>> MFU> for,
>>> and what purpose the definition is intended to serve.
>> But I believe that we can have a general definition, based on (1)
>> logic,
>> (2) theoretical views of ontology, and (3) methodologies for
adapting (015)
>> logic and ontology (in the philosophical sense) to the kn.
>> engineering problems of developing *an* ontology for some particular (016)
>> domain and enabling multiple systems and users share it and reuse
it.
>
> I have no doubt that logic can be imposed on an ontology that was
> developed without the use of logic. But, then the ontology imposed
> upon is no long the ontology as it existed prior to the imposition of (017)
> the logical framework is it? It is now (post-imposition) an ontology
> that is interpreted through the lens of logic. (As Pat Hayes and
> others have argued in aside comments, that can prove to be very
useful (018)
> in terms of exposing hidden assumptions, etc. But the utility of the
> use of logic is not the question I mean to address.) (019)
Logic is just a language that you might use (and that has been
traditionally used over the centuries) to describe an ontology. The
description, in logic, is always an approximation of what you actually
intend. Even if you "impose" some weaker and more ambiguous language
like English or topic maps or whatever, you still have only an
approximation of what your ontology intends to convey. (020)
So the proposed definition can be generalized from "logic" to
"language"
and then specialized again into what people like me want, ontologies
that are described using formal, logical languages. I like "formal
ontology" as a label for that, though I realize it is not what Barry
and
others who originally coined the term meant at the time. (021)
> The imposition of logic may make the ontology more useful to those
who (022)
> wish to use logic or tools based on logic, but there has been no
> showing that logic is a prerequisite for the development of an
> ontology. Or that ontologies developed in the absence of the use of
> logic are in some way less useful to those who use them. (023)
One can always define "usefulness" to suit their own purposes. What is
established as fact, and can be proven with a few simple examples that
any of us who've done this a bazillion times before have experienced
repeatedly, is that using logic makes the description of
your ontology more precise and less ambiguous. This is what we mean
by "eliminating unintended models". (024)
> Actually I have been lead to understand that the goal of the forum is (025)
> not *a* definition of ontology but rather a discussion of the many
> meanings that may be given to the term "ontology" so that we can
> better communicate with each other. (026)
I would like *a* definition of ontology, but as I've said I can accept
something that is more general than the one I want as long as there is
a
well understood way to specialize it. (027)
> For example, assuming we gather up dozens of definitions of
> ontologies, one dimension for a continuum could be the use of formal
> logic. Some definitions are going to be closer to the formal logic
end (028)
> of the continuum than others. But, that is of interest only if a user (029)
> is interested in using the dimension of logic as a rule for choosing
> an ontology. (030)
The "degree of formalization" was the primary axis in all the continua
(?) I've seen. This can be related to the language you use. There is
not one "logic". (031)
> Or if we organized ontologies along a continuum of generality, so
that (032)
> upper ontologies are at one end and that local ontologies are nearer
> the other, that is of interest if you are concerned with the
> generality of an ontology as a basis for choosing an ontology.
>
> Or any other dimension that you would like to choose for establishing (033)
> a continuum of the various definitions of ontologies that are likely
> to result from this forum. (034)
I'd be happy with several dimensions, yes. (035)
-Chris (036)
>
> My point being that no definition of an ontology or a continuum for
> organizing such definitions is free from some interest that will be
> promoted by a particular definition or continuum. Drawing on my
> background in biblical studies, the ability to exclude is one
> significant purpose of a definition, cf. the first Council of Nicea.
> That was followed by a burning of all the books that did not qualify
> for inclusion in the Bible. (Only partially successful but did result (037)
> in the loss of a large number of items which leaves us with a
> distorted view of religious texts of that period.)
>
>> Different users in different domains may view the same logical
>> statements in different languages for different purposes. That is
>> the main reason why we developed Common Logic with an abstract
syntax (038)
>> and no privileged or preferred concrete syntax. That allows
>> different notations that support different subsets, such as RDF,
OWL, (039)
>> Datalog, SQL, SPARQL, CLIF, CGIF, XCL, and many others, including
>> dialects of controlled natural languages. But all those notations
>> can support *identical* semantics, although some versions may be
>> subsets or supersets of other versions.
>>
> All of which you could add are machine processable, if that is part
of (040)
> your definition of "ontology."
>
> Hope you are having a great day!
>
> Patrick
> (041)
--
Dr. Christopher A. Welty IBM Watson Research Center
+1.914.784.7055 19 Skyline Dr.
cawelty@xxxxxxxxx Hawthorne, NY 10532
http://www.research.ibm.com/people/w/welty (042)
_________________________________________________________________
Msg Archives: http://ontolog.cim3.net/forum/ontology-summit/
Subscribe/Config:
http://ontolog.cim3.net/mailman/listinfo/ontology-summit/
Unsubscribe: mailto:ontology-summit-leave@xxxxxxxxxxxxxxxx
Community Files: http://ontolog.cim3.net/file/work/OntologySummit2007/
Community Wiki:
http://ontolog.cim3.net/cgi-bin/wiki.pl?OntologySummit2007
Community Portal: http://ontolog.cim3.net/ (043)
_________________________________________________________________
Msg Archives: http://ontolog.cim3.net/forum/ontology-summit/
Subscribe/Config:
http://ontolog.cim3.net/mailman/listinfo/ontology-summit/
Unsubscribe: mailto:ontology-summit-leave@xxxxxxxxxxxxxxxx
Community Files: http://ontolog.cim3.net/file/work/OntologySummit2007/
Community Wiki:
http://ontolog.cim3.net/cgi-bin/wiki.pl?OntologySummit2007
Community Portal: http://ontolog.cim3.net/ (044)
_________________________________________________________________
Msg Archives: http://ontolog.cim3.net/forum/ontology-summit/
Subscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontology-summit/
Unsubscribe: mailto:ontology-summit-leave@xxxxxxxxxxxxxxxx
Community Files: http://ontolog.cim3.net/file/work/OntologySummit2007/
Community Wiki: http://ontolog.cim3.net/cgi-bin/wiki.pl?OntologySummit2007
Community Portal: http://ontolog.cim3.net/ (045)
|