By the same logic, a concept can be the product of
'subordinate components', or more linguistically
aimed, 'a product of properties and behaviors'.
The choice of alternative interpretations, or the
choice of a component list, is the distinction
between Mereology and other forms of logical
representation. (01)
So unions of alternatives and products of
component parts seem to be equivalent castings. (02)
-Rich (03)
Sincerely,
Rich Cooper
EnglishLogicKernel.com
Rich AT EnglishLogicKernel DOT com
9 4 9 \ 5 2 5 - 5 7 1 2 (04)
-----Original Message-----
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On
Behalf Of Barkmeyer, Edward J
Sent: Monday, June 23, 2014 2:17 PM
To: [ontolog-forum]
Subject: Re: [ontolog-forum] Types of Formal
(logical) Definitions in ontology (05)
John makes an important addition to my list. In
addition to defining a concept as the union of a
set of 'subordinate' concepts', it is also
possible to define a 'class' or a 'term' (less
clearly a 'concept') as a specific set of named
things. This latter is also referred to as an
"extensional definition". One can define 'primary
color' as "one of red, orange, yellow, green,
blue, indigo, violet," without being at all clear
about what the distinguishing properties are. (06)
(I tend to think that a 'concept' should have a
definition that involves specifying properties,
but then "being the color red" and "being John
Malkovich" can be considered properties.) (07)
-Ed (08)
> -----Original Message-----
> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-
> bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F
Sowa
> Sent: Monday, June 23, 2014 4:47 PM
> To: ontolog-forum@xxxxxxxxxxxxxxxx
> Subject: Re: [ontolog-forum] Types of Formal
(logical) Definitions in ontology
>
> Ed and Pat,
>
> Pat raises an important point:
>
> PJH
> > If all classes are defined in terms of other
classes, where does the
> > whole process get started?
>
> All three of those methods assume you have some
classes to start:
>
> 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.
>
> 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.
>
> That property P can also be specified by
enumeration:
> {x | x=a or x=b or x=c}
>
> What distinguishes a class from a set are the
identity criteria:
>
> 1. Two sets S1 and S2 are identical if they
have the same elements.
>
> 2. Two classes or concepts C1 and C2 are
identical if they have the
> same or logically equivalent defining
property or predicate P.
>
> The set of all cows, for example, changes with
every birth or death.
> But the concept cow is determined by an
unchanging predicate P.
>
> John
>
>
__________________________________________________
________
> _______
> Message Archives:
http://ontolog.cim3.net/forum/ontolog-forum/
> Config Subscr:
http://ontolog.cim3.net/mailman/listinfo/ontolog-f
orum/
> 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
> (09)
__________________________________________________
_______________
Message Archives:
http://ontolog.cim3.net/forum/ontolog-forum/
Config Subscr:
http://ontolog.cim3.net/mailman/listinfo/ontolog-f
orum/
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?WikiHomePa
ge#nid1J (010)
_________________________________________________________________
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 (011)
|