Dear John, (01)
Comments below,
Rich (02)
Sincerely,
Rich Cooper
EnglishLogicKernel.com
Rich AT EnglishLogicKernel DOT com
9 4 9 \ 5 2 5  5 7 1 2 (03)
Original Message
From: ontologforumbounces@xxxxxxxxxxxxxxxx
[mailto:ontologforumbounces@xxxxxxxxxxxxxxxx] On
Behalf Of John F. Sowa
Sent: Friday, September 09, 2011 4:29 AM
To: ontologforum@xxxxxxxxxxxxxxxx
Subject: Re: [ontologforum] 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
transitiveintransitive 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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