Michael Gruninger is correct that the COSMO should have a proper
axiomatization of the meaning of "Type" and its associated relations -
subtype (I prefer the verbal isaSubtypeOf)
instance-of (I prefer the verbal isanInstanceOf) (01)
... and I am now requesting that anyone with an interest in finding
agreement on that formalization please send me a note directly so that
we can conduct a discussion by direct e-mail and resolve that issue
quickly. (02)
There are some axioms in SUMO relevant to the interpretation of "Class"
(our Type), "subclass" and "instance", which are in the Structural
module and were not included in Chris Menzel's quote from SUMO, the
most relevant missing axiom being: (03)
--------------------------------------------
(instance subclass BinaryPredicate)
(instance subclass PartialOrderingRelation)
(domain subclass 1 SetOrClass)
(domain subclass 2 SetOrClass)
(documentation subclass "(&%subclass ?CLASS1 ?CLASS2) means that
?CLASS1 is
a subclass of ?CLASS2, i.e. every instance of ?CLASS1 is also an
instance of
?CLASS2. A class may have multiple superclasses and subclasses.") (04)
(<=>
(subclass ?SUBCLASS ?CLASS)
(and
(instance ?SUBCLASS SetOrClass)
(instance ?CLASS SetOrClass)
(forall (?INST)
(=>
(instance ?INST ?SUBCLASS)
(instance ?INST ?CLASS)))))
--------------------------------------------------- (05)
This expresses the basic characteristic behavior of Types (SUMO
"Classes") and instances, namely that the subtype ("subclass") relation
is transitive (a "PartialOrderingRelation" in SUMO) and every instance
of a type is also an instance of that type's parent types. (06)
The very modest experience I have had working with OpenCyc, SUMO,
Protege-OWL and Ontology Works' IODE makes it appear to me that the
Type-equivalents in all those all exhibit the same behavior with
respect to the axiom above. The "Class" of ISO15926 may be different,
but that was not included in my list of equivalents.
If anyone knows of some behavior of any of the ontologies that
actually is different from the above, please let us know about it.
As Chris's note pointed out, there are a lot of useful things one
might say about Types in addition to the above, and I strongly urge
that those interested send me a note so we can begin productive
discussion immediately within a focused working group. (07)
Pat (08)
Patrick Cassidy
MITRE Corporation
260 Industrial Way
Eatontown, NJ 07724
Mail Stop: MNJE
Phone: 732-578-6340
Cell: 908-565-4053
Fax: 732-578-6012
Email: pcassidy@xxxxxxxxx (09)
-----Original Message-----
From: ontac-forum-bounces@xxxxxxxxxxxxxx
[mailto:ontac-forum-bounces@xxxxxxxxxxxxxx] On Behalf Of Michael
Gruninger
Sent: Monday, January 23, 2006 2:41 PM
To: ONTAC-WG General Discussion
Subject: Re: [ontac-forum] Result of vote: Type (010)
Cassidy, Patrick J. wrote: (011)
>ONTACWG:
> Thanks to all those who participated in unexpectedly vigorous
>discussion of this particular term.
>
> The final tally of preferences expressed by ONTACWG members is:
> "Type" 11
> "Class" 7
> one vote was also cast for "Type or Class" (synonyms) and one for
>"Type and Class"
>
>
I am still a little dismayed by this strange methodology.
Math, logic, science, and engineering are not democracies;
we do not vote on the correctness of evolution :-) or adopt bylaws that (012)
ban the
use of irrational numbers. (013)
>Therefore in the official FOL version of the COSMO, "Type" will be
used
>to refer to those intensionally-defined groupings called:
>
> Class in Ontolingua and Protege
> Class in RDF and OWL
> Class in SUMO
> Collection in OpenCyc
> Universal in DOLCE
> Property in Ontology Works' IODE system
>
>
>
This still presumes that all of these concepts are equivalent,
which has not been shown. If they really are equivalent, then it's fine
to vote about which string of characters we will use to denote the
concept,
but if they are not equivalent, then the following claim is illusory: (014)
>One major purpose of the ONTACWG is to enable accurate and automatic
>translation among different terminologies,
> (015)
The question of the equivalence of a set of axioms is not a matter of
opinion
or personal taste. (016)
This seems to be a Working Group in which nobody wants to do any work. (017)
Thankfully, Chris Menzel provided the SUMO axiomatization, and
indicated
that a CL axiomatization of the RDF and OWL notions will be available
in the
near future.
We need to formally evaluate the relationship between these axioms and
the axioms for OpenCyc Collection and DOLCE Universal; it would be
nice for people familiar with these two ontologies to post the relevant (018)
axioms. (019)
We won't get very far if we continue to vote on personal preferences
... (020)
- michael (021)
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