Chuck, (01)
This message is a bit long, so be forewarned! I'll divide it into your
2 questions. (02)
1) Typically taxonomies are trees, i.e., one root, no multiple
inheritance ala graphs (cyclic/acyclic). But of course in conceptual
models and logical theories (ontologies) that (strong) subclass-based
taxonomic backbone can be a graph, though there are still strong
arguments that you need to minimize multiple parents: cf. the OntoClean
methodology of Guarino and Welty (multiple citations). Thesauri
"taxonomies" are typically trees too, with possibly multiple roots
(multiple broaderThan/narrowerThan subsumptive taxonomies) sometimes
called "facets". Which then support cross-references. (03)
2) Concerning reasoning over taxonomy/subsumption (subsumption just
means subset relationships, generalization at the top downward to
increased specialization) structures, and how those are interpreted
with respect to intension/extension: (04)
You can consider class nodes to be intensional, meaning, e.g., that the
class Person is considered to be a description (with properties such as
having a birthdate, a name, an address, etc.) that potentially many
instances could be covered under. Then the intensional Person could
have multiple extensions, meaning that the intension Person in one
context/world/database consists of the extension "John Smith, Harry
Jones, Mary White", in another context/world/database consists of the
extension "Joe Public, Sally Brown, Kathy Citizen". This is why a
relational database schema is called the intensional database, and the
actual rows of data are called the extensional database: you can use
the same schema and have different rows. Over time in a database, you
have different extensions. (05)
But you can also consider classe to be extensional, and this is
probably the usual meaning of class in philosophy, etc., i.e., close to
the notion in mathematical set theory of a member of a set, e.g., the
class person = {joe, mary, harry}. And the class mammal = {{joe, mary,
harry}, {tyger, leo}, {rover, spot, lassie}, {tabby, garfield}, ...},
i.e., the set of all subsets of mammal, each subset of which probably
identifies a particular extensional class: human, tiger, dog, cat, ... (06)
The usual distinction: intension talks about the property, extension
talks about the things that have that property in a particular context.
Example: consider the red property. You can say a lot about what the
red property means, e.g., it's typically a range of visible spectrum,
with particular wavelengths, frequencies, etc. And you can talk about
particular objects having the red property: this red ball, that red
rose, in fact all of the actual things in the universe that have the
red property. The former is the intension (the property), the latter is
the extension (things that have the property, i.e., members of the set
having that propertys). (07)
Now there are many fine points about intension/extension, but I won't
go into them here. Suffice it to say, different knowledge
representation (KR) languages do things differently. (08)
For example, description logics (of which OWL is one) typically have
intensional classes. Classes are "descriptions", meaning they are more
like "definite descriptions" in natural language semantics: the
description "the man with the hat in the corner", "the current
president of the USA", "the morning star", "the evening star", "the
property red". Rather than particular persons or planets that have
those descriptions (Bob, George Bush, Venus, etc.) (09)
But OWL has an "equivalentClass" which means that two classes (as
distinct intensions/descriptions) have the same extensions (cf.
http://www.w3.org/TR/owl-ref/#equivalentClass-def), but the two
intensional concepts are not the same (e.g., "president of the US" \=
"current primary resident of the White House"). (010)
The reasoning over either the intensional or the extensional form can
be as robust. We could get a bit more complicated and talk about FOL
vs. modal predicate logic (the former usually extensional, the latter
intensional), but we won't here. (011)
Hope this helps a bit. I know it's kind of confusing, but I hope this
clarified it at least a little. (012)
Thanks,
Leo (013)
________________________________________
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 (014)
-----Original Message-----
From: ontac-forum-bounces@xxxxxxxxxxxxxx
[mailto:ontac-forum-bounces@xxxxxxxxxxxxxx] On Behalf Of Charles D
Turnitsa
Sent: Wednesday, March 01, 2006 3:32 PM
To: ontac-forum@xxxxxxxxxxxxxx
Subject: Re:[ontac-forum] Future directions for ontologies and
terminologies (015)
Leo, (016)
In your descriptions of both strong and weak taxonomy models, do you
see
either as being supportable as a proper tree structure (i.e.- one
parent
per child node), or as a more general acyclic directed graph (multiple
parents possible per child node)? (017)
Also, considering the parent-child relationship, do you see limitations
on
the ability for a computational system to reason over such a model, if
the
parent-child relationships are intensional vs. extensional (in terms of
the
resulting children from the defined relationship)? (018)
Chuck Turnitsa (019)
Charles Turnitsa
Lab Manager/Project Scientist
Virginia Modeling, Analysis & Simulation Center
Old Dominion University Research Foundation
7000 College Drive
Suffolk, Virginia 23435
(757) 638-6315 (voice)
(757) 686-6214 (fax)
cturnits@xxxxxxx (020)
> Date: Wed, 1 Mar 2006 12:08:47 -0500
> From: "Obrst, Leo J." <lobrst@xxxxxxxxx>
> Subject: RE: Re:[ontac-forum] Future directions for ontologiesand
> terminologies (021)
> Denise,
>
> But WordNet does have hypernymy (parent or broader-than) and hyponymy
> (child or narrower-than) links between words (synsets), no? So it's
> very close to a thesaurus. You are right that you cannot use a
> thesaurus for concepts or describing meaning, since thesauri are
about
> term relationships. I think your rich domain thesaurus is probably a
> conceptual model.
>
> The usual range of semantic models I characterize as, from less to
more
> expressive semantics: taxonomy, thesaurus, conceptual model, logical
> theory, with the addendum that taxonomies are weak (arbitrary
> parent-child relation) or strong (narrowerThan or subClass
parent-child
> relations, the former for terms as in the taxonomic backbone of a
> thesaurus, the latter for concepts in a conceptual model or logical
> theory's taxonomic backbone). Conceptual models can be viewed as weak
> ontologies; logical theories as strong ontologies, with the primary
> distinction being that logical theories are expressed in a knowledge
> representation language that is logic-based, hence supports machine
> semantic interpretation, and conceptual models do not.
>
> You can review my recent Ontolog 2 part briefing (Jan. 12 & 19, 2006)
> on these distinctions (using the Ontology Spectrum) "What is an
> Ontology: The Range of Semantic Models" at:
> http://ontolog.cim3.net/cgi-bin/wiki.pl?ConferenceCall_2006_01_12,
> i.e.:
>
>
http://ontolog.cim3.net/file/resource/presentation/LeoObrst_20060112/On
> tologySpectrumSemanticModels--LeoObrst_20060112.ppt.
>
> Also an audio track of both talks are available at:
>
> Part 1, Jan. 12, 2006, 1 Hour 40 Minutes, Recording File Size: 23.4
MB
> (in mp3 format):
>
http://ontolog.cim3.net/file/resource/presentation/LeoObrst_20060112/On
>
tologySpectrumSemanticModels--LeoObrst_Recording-2473397-874999_2006011
> 2.mp3
>
> Part 2, Jan. 19, 2006, 1 Hour 42 Minutes, Recording File Size: 23.9
MB
> (in mp3 format):
>
http://ontolog.cim3.net/file/resource/presentation/LeoObrst_20060112/On
>
tologySpectrumSemanticModels--LeoObrst_Recording-2496706-401969_2006011
> 9.mp3
>
> Thanks,
> Leo
>
> _____________________________________________
> 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
> (022)
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