Re: [ontolog-forum] Thing and Class

["Michael F Uschold" <uschold@xxxxxxxxx>]

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:

1. X: the set of all things in the universe of discourse
2. Y: the set of all things that have member individuals
3. Z: the set of all things that do NOT have member individuals
4. 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)
   
5. 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)

1. THING: the set of all things in the universe of discourse
2. CLASS: the set of all things that have member individuals
3. INDIVIDUAL: the set of all things that do NOT have member individuals
4. 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)
   
5. 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)

ORDINARYCLASS
METACLASS

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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