[Top] [All Lists]

Re: [ontolog-forum] Universal and categories in BFO & DOLCE

To: ontolog-forum@xxxxxxxxxxxxxxxx
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Fri, 09 Sep 2011 07:28:46 -0400
Message-id: <4E69F86E.7000904@xxxxxxxxxxx>
Dear Matthew,    (01)

I agree with your point:    (02)

> 1. Stop thinking of inheritance and specialisation as being synonymous.
> Inheritance of properties can happen through other relationships as well.    (03)

> 2. Think in set theoretic terms. So each member of a subset is a member of
> the superset. If a method belongs to the superset, it is not "inherited" by
> the subset, but it applies to each member of the subset because it is also a
> member of the superset.    (04)

But please note that inheritance is not applicable to an arbitrary
set, but only to a set S that satisfies two conditions:    (05)

  1. There is some predicate P(x) that is true of every element x of S.    (06)

  2. Any method, property, or whatever that can be inherited by every
     element of S must be characterized by some predicate m(x) that is
     implied by P(x):    (07)

     For all x, if P(x), then m(x).    (08)

This predicate P(x) is not necessarily the defining predicate for S
because there might be some larger set {x | P(x)}, which includes
S as a proper subset.    (09)

The critical point is that there must exist some such predicate P(x)
that meets the two conditions above.    (010)

I would call that predicate P *intensional* information about the set S,
but you don't have to use the word 'intensional' if you don't like it.    (011)

John    (012)

Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/  
Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/  
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/ 
To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J    (013)

<Prev in Thread] Current Thread [Next in Thread>