''Class'' is clearly a favorite in the ontological race of basic terms,
however... (01)
The whole situation reminds me a political voting in my country, Great
Russia, where the aspiring power are divided into two taxa: a ruling CLASS
party of the incumbent president including all sorts of corrupted
politicians, officials, governors, and yet not-in-jail billioners and
various TYPES of small parties made up of so-called 'democrats', eternally
marked by badly abusing the credited power with the help of Clinton's folks.
As a result, the CLASS party doesn't tax itself with any political platform
and social programs stating that the people should vote for them only
because they are behind the president. While the different small TYPE
parties are uselessly noising their declarative aims and principles never to
be fulfiled.
What's the point of this allegory? (02)
Before voting or at least after voting, the significant matter of choosing a
top sitting ontological ruler clearly suggests the necessity of giving the
definition added with the basic axiomatic restrictions imposed on its power,
as Michael Gruninger is proposing. (03)
Curently all entities and things may be divided into a hierarchy of
groupings to be denominated either as categories or universals or genera or
kinds or classes in ontology; sets or classes or aggregates or collections
or categories in mathematics and logics; classes and types in programming
languages; classes or categories or taxa or kinds in biological
classification.
It is plain without any voting that the ''class'' comes as an intersection
category representing the common ground among the diverse domains and
theories.
But to avoid all this confused interpretations of Class made by current
upper ontologies and semantic web languages as RDF and OWL, it is necessary
to define the nature and essential properties (by axioms) of class in
general by specifying its essence (or identity), state (quality and
quantity), behavior, and possible interrelationships.
Then the identity of Class is to be determined by the principles of
intensionality (definition, abstraction, comprehension) and extensionality;
its state by the collection of lawfully related properties (attributes),
like the size of a class is measired by cardinality; its behavior is
specified by all possible operations generating such combinations as the
union class, the intersection class, the complement class, the disjoint
union class, or the complement union class; and its relationships as
part-whole and inclusion relations is described by the product class or
well-ordering class or the power set axiom or by n-ary mathematical
relations. (04)
Above all, we need a univocal definition, like '' a class is a collection
(number, group) of entities of one kind'' or ''a class is a number of things
showing differences in kind'' or '' a class is a single whole of things with
common properties''. For the definition must cover both the mass entities
(as substances, the whole class of things) and the countable entities (the
class of things as a whole, a collection of instances and individuals). (05)
We know that in the ontological classificatory system, there is the
all-comprehensive entity, which is the universal class, the basic unit
entity, which is a kind (a natural kind as a species), and the elementary
entity, which is the null class of which nothing is a member. We know that
the classes are symbolized by variables ranging both over classes and their
instances and individuals, etc.
But it is still to be discovered what is the nature and meaning and real
properties of the class as a basic ontological and semantic term [after
Being and Thing] both the richest and the emptiest of all the vocabulary of
human minds and possibly machine minds. (06)
Azamat Abdoullaev
http://www.eis.com.cy (07)
----- Original Message -----
From: "Michael Gruninger" <mudcat@xxxxxxxxxxxxxxx>
To: <ontac-forum@xxxxxxxxxxxxxx>
Sent: Saturday, January 21, 2006 10:58 PM
Subject: Re: [ontac-forum] Type vs. Class - last chance to vote. (08)
>
>> In order to resolve a terminological question, we are in the process of
>> voting whether to use the term "Type" or "Class" 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
>
> A vote like this only makes sense if these concepts
> really are equivalent, and I cannot make such a judgment
> without seeing the relevant axioms.
>
> First of all, the above list contains a mix of languages
> (RDF, OWL) and ontologies (OpenCyc, DOLCE).
> I'm not sure what to call Ontolingua, Protege, and IODE.
>
> Can people from the above named ontologies please provide
> the relevant axioms for their terms?
> Common Logic axioms are preferable, but at this point,
> anything is a place to start.
> Can someone please post the axiomatic definitions of
> RDF/OWL Class in Common Logic?
>
> - michael
>
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> (09)
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