Re: [ontolog-forum] Thing and Class

[Matthew West <dr.matthew.west@xxxxxxxxx>]

Dear Colleagues,

 

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)

[MW] As it happens, Michael here describes almost exactly the structure of the upper levels of ISO 15926.

http://www.tc184-sc4.org/wg3ndocs/wg3n1328/lifecycle_integration_schema.html

The differences are:

What Michael calls ORDINARYCLASS we call class_of_individual.

What Michael calls METACLASS we call class_of_class.

 

We also allow relationships as abstract objects, and classes of relationship, which means these are objects that can themselves have relationships.

 

All the statements below hold (though not all are captured in the EXPRESS).

 

Regards

 

Matthew West

http://www.matthew-west.org.uk/

 

 

 

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

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