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

To: "'[ontolog-forum] '" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Rich Cooper" <rich@xxxxxxxxxxxxxxxxxxxxxx>
Date: Fri, 9 Sep 2011 11:31:09 -0700
Message-id: <244E9D80D213479681F072C32D6FC659@Gateway>
Dear John,    (01)

Comments below,
-Rich    (02)

Rich Cooper
Rich AT EnglishLogicKernel DOT com
9 4 9 \ 5 2 5 - 5 7 1 2    (03)

-----Original Message-----
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On
Behalf Of John F. Sowa
Sent: Friday, September 09, 2011 4:29 AM
To: ontolog-forum@xxxxxxxxxxxxxxxx
Subject: Re: [ontolog-forum] Universal and
categories in BFO & DOLCE    (04)

Dear Matthew,    (05)

I agree with your point:    (06)

> 1. Stop thinking of inheritance and
specialisation as being synonymous.
> Inheritance of properties can happen through
other relationships as well.    (07)

> 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.    (08)

But please note that inheritance is not applicable
to an arbitrary set, but only to a set S that
satisfies two conditions:    (09)

  1. There is some predicate P(x) that is true of
every element x of S.    (010)

In this case, S is the set of all sentence
signatures.  So if signature x is a transitive and
y is intransitive, then x and y do not share the
transitive-intransitive property, but they do
share the signature property.      (011)

  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):    (012)

     For all x, if P(x), then m(x).    (013)

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.    (014)

So for all x, if Transitive(x) then method     (015)

        (PTrans(x) or MTrans(x))    (016)

is applicable, and those x can be directed along a
different specialization arc than YTrans(x) which
share the Intransitive(x) property?      (017)

I have to think about that one for a while to
understand its sentential signature implications,
but it sounds like a fruitful thing to think
about.      (018)

The critical point is that there must exist some
such predicate P(x) that meets the two conditions
above.    (019)

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.    (020)

John    (021)

I don't have to like it; if it works it works and
that is truth enough for functional purposes.  So
Transitive(x) and Intransitive(x) are
"intensional" informations about x.      (022)

How can I apply that to sentential signature
descriptions, i.e., how would one distinguish
"intensional" characteristics of signatures from a
linguistic categorization viewpoint?    (023)

Thanks; that seems worth spending some thought on.    (024)

-Rich    (025)

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