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Michael
Very nice analysis.
Thank you!
Dick McCullough Ayn Rand do speak od mKR done; mKE do enhance od Real
Intelligence done; knowledge := man do identify od existent
done; knowledge haspart proposition list; http://mKRmKE.org/
----- Original Message -----
Sent: Monday, September 08, 2008 2:35
PM
Subject: Re: [ontolog-forum] Thing and
Class
Azamat said:
Sum up: If Thing goes as the universal
class, of which everything is a
member, it will equivalent to Class, as the
class of all classes. Other
interpretations will be inconsistent, asking
for many questions.
Whatever you choose to call these things, I
find the following distinctions helpful:
- X: the set of all things in the universe of discourse
- Y: the set of all things that have member individuals
- Z: the set of all things that do NOT have member individuals
- U: the set of all things whose members do not themselves have
members
(i.e. the set of all things whose members are members of the class Z)
- V: the set of all things whose members also have member
individuals
(i.e the set of all things whose members are all members of the
class, Y)
The names I find most useful for these things are
(substituting into the text above)
- THING: the set of all things in the universe of discourse
- CLASS: the set of all things that have member individuals
- INDIVIDUAL: the set of all things that do NOT have member individuals
- ORDINARYCLASS: the set of all things whose members do not themselves
have
members
(i.e. the set of all things whose members are members of the class
INDIVIDUAL)
- METACLASS: the set of all things whose members also have member
individuals
(i.e the set of all things whose members are all members of the
class, CLASS)
Here is the class hierarchy: THING (the most
general anything)
CLASS (the most general class)
INDIVIDUAL (the top of the ordinary class
hierarchy)
INDIVIDUAL and CLASS form a partition of
THING ORDINARYCLASS and METACLASS form a partition of CLASS THING
and CLASS have all of the five things below as members:
- THING
- CLASS
- ORDINARYCLASS
- METACLASS
- INDIVIDUAL
ORDINARYCLASS has members:
- INDIVIDUAL (any any of its subclasses)
METACLASS has
members:
- CLASS
- METACLASS
- ORDINARYCLASS
INDIVIDUAL has members that are inherited from any
of its subclasses (e.g. individual persons, or companies, or drugs, depending
on the domain).
Michael
On Thu, Aug 28, 2008 at 12:58 AM, Azamat <abdoul@xxxxxxxxxxxxxx>
wrote:
As a devil's advocate, seemingly unsanctioned with the
3WC, Richard is doing
a useful work raising sometimes justified
objections for SW candidates
looking for canonization
(standardization).
As for James's reading of Thing and Class, it looks
more as punning,
possibly intentionally.
The interrelations of
classes as well as classes and things are actually
more subtle and deep,
than generally presented in various specifications.
A member of a class
may itself be a class. For example, the class of humans
is a member of
the class of species of animals. An individual human, even
being a member
of its class, is not a member of the latter one, the class
of
species of animals. For a human is not a species of animal.
Whatever the
number of human beings, it will not affect the number of
species of
animals. This goes as a kind of ontological rule of all
taxonomies:
whatever the number of instances, objects, particulars, it will
not
change the number of classes of things. Again, this means
that
relationships of class inclusion (subsumption) and class membership
have
some principal differences. Namely, the class inclusion is a
transitive
relation, while the CLASS MEMBERSHIP IS NOT TRANSITIVE. This
fundamental
fact is missing in some large scale, common sense ontologies,
making the
whole hierarchy just as invalid for computing
applications.
Sum up: If Thing goes as the universal class, of which
everything is a
member, it will equivalent to Class, as the class of all
classes. Other
interpretations will be inconsistent, asking for many
questions.
Hope this will be of use,
Azamat
Abdoullaev
----- Original Message -----
From: "James Leigh"
<james-nospam@xxxxxxxxxxx>
To:
"Richard H. McCullough" <rhm@xxxxxxxxxxxxx>
Cc: "Semantic
Web at W3C" <semantic-web@xxxxxx>
Sent:
Thursday, August 28, 2008 4:30 AM
Subject: Re: Thing and
Class
>
> Hi Richard et al.
>
> Here is an
informal interpretation of some of the spec written in plain
>
English.
>
> Class stands for classification.
> We use
Class to classify things.
> Class is a set of Things.
> "I am a
Human" - I just classified myself as Human (I hope I'm right).
> "I am
a Thing" - that is true for everything.
> Human is a classification of
all people.
> Thing is a classification of all things.
> Every
Human is a Thing. Therefore Thing is a super set of Human.
> Is Human
a Thing? No! its a Class!
> Everything Thing is an individual.
>
Human is not an individual, it is a classification of individuals.
>
Thing is not an individual, it is a classification of individuals.
>
Can we classify Classes? Yes we can! Human is a classification - I
just
> classified Human as a classification.
> Human is a
Class.
> Thing is a Class.
> Are all Things Classes? No! I am a
Thing, but I am not a classification.
> Is Thing the same as Class?
No! Human is not a Thing, but Human is a
> Class.
>
> Hope
this helps,
>
James
>
>
>
>
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