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Re: [ontolog-forum] Types of Formal (logical) Definitions in ontology

To: ontolog-forum@xxxxxxxxxxxxxxxx
From: John F Sowa <sowa@xxxxxxxxxxx>
Date: Mon, 23 Jun 2014 16:47:22 -0400
Message-id: <53A8925A.7040707@xxxxxxxxxxx>
Ed and Pat,    (01)

Pat raises an important point:    (02)

PJH
> If all classes are defined in terms of other classes, where does
> the whole process get started?    (03)

All three of those methods assume you have some classes to start:    (04)

EJB
> 1) identify a more general concept and the delimiting characteristics
>    of the subordinate concept being defined
>    This is exactly:  An A is a B that C.
> 2) identify a list of subordinate concepts that together cover the
>    more general concept being defined  the union of other defined classes:
>    An A is a B or a C or a D.
> 3) One can also define a Class as the intersection of two or more classes,
>    but that is just a special case of (1):  An A is a B that is also a C.    (05)

Those are all set forming operations.  Set theory has a starting method:
    {x | P(x)} -- the set of all x for which some property P is true.    (06)

That property P can also be specified by enumeration:
    {x | x=a or x=b or x=c}    (07)

What distinguishes a class from a set are the identity criteria:    (08)

  1. Two sets S1 and S2 are identical if they have the same elements.    (09)

  2. Two classes or concepts C1 and C2 are identical if they have the
     same or logically equivalent defining property or predicate P.    (010)

The set of all cows, for example, changes with every birth or death.
But the concept cow is determined by an unchanging predicate P.    (011)

John    (012)

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