Pat, (01)
Now that you put it that way, I suppose there are two other approaches: (02)
(3) There is the mathematical approach: axiomatic definition. You specify a
set of axioms involving Xs and every thing t that satisfies all of those axioms
is an X. The concept is exactly: "things that obey this set of axioms,
regardless of what other properties they may have." This is also called the
"if it walks like a duck" approach. But the predicates that are used in the
axioms other than is-a-X must also have been previously defined. (In
mathematics, the best known examples of pure axiomatic definition are
'equivalence relation' and 'ordering relation'.) (03)
(4) There is the special case of (3) that is "co-definition". The set of
axioms that defines X uses the undefined symbol Y, but what is happening is the
simultaneous definitions of two kinds of things (X and Y) by their
interrelationships. (The familiar example in mathematics is 'group' and
'operator'.) (04)
To start the process, there must somewhere be 'primitive concepts' -- things
you can't formally "define". In ISO 1087 terms, such things have
'descriptions', by which a human might be able to figure out what you are
talking about, as opposed to 'definitions', which are clear as to how to make
the determination. In an ontology, the primitive predicates/concepts are the
ones you elect not to define explicitly (via iff) or axiomatically, whether you
could have or not. When I construct ontologies, I try to at least be aware of
the 'primitive concepts' that it introduces. Note also that a theory may
intentionally leave some fundamental concepts undefined, so as to enable the
theory to be applied to a variety of things; each application then assumes that
some class of things is a subclass of the fundamental theoretical concept. (05)
Dictionaries ultimately avoid 'turtles all the way down', either by ultimately
becoming descriptive rather than definitive, or by ultimately becoming circular. (06)
-Ed (07)
> -----Original Message-----
> From: Pat Hayes [mailto:phayes@xxxxxxx]
> Sent: Monday, June 23, 2014 1:26 PM
> To: [ontolog-forum]; Barkmeyer, Edward J
> Subject: Re: [ontolog-forum] Types of Formal (logical) Definitions in ontology
>
>
> On Jun 23, 2014, at 10:19 AM, Barkmeyer, Edward J
> <edward.barkmeyer@xxxxxxxx> wrote:
>
> > Robert,
> >
> > ISO 1087-1 and ISO 704, which are standards for creating vocabularies and
> definitions (and did not arise from a formal logic community), specify two
> mechanisms for defining a 'concept' or 'class':
> > 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.
>
> This reminds me of the Gaia hypothesis to explain the origin of life: it came
> from somewhere else. If all classes are defined in terms of other classes,
> where does the whole process get started?
>
> Pat
>
>
> >
> > 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.
> >
> > I'm not aware of any others.
> >
> > -Ed
> >
> > From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
> > [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of
> > rrovetto@xxxxxxxxxxx
> > Sent: Saturday, June 21, 2014 9:32 PM
> > To: [ontolog-forum]
> > Subject: [ontolog-forum] Types of Formal (logical) Definitions in
> > ontology
> >
> > All,
> >
> > 1) How many types of formal (logical) definitions of terms/classes do you
> know of?
> >
> > For example, a term can be defined in a genus-species form: An A is a B
> that C.
> >
> > What others do you know of?
> >
> > 2) For ontologies, are there non-FOL definitions?
> > Are there definitions not based on syllogistic logic?
> >
> > 3) And what are the pro's and con's of each?
> >
> > Thank you.
> >
> > Robert
> >
> >
> __________________________________________________________
> _______
> > 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
>
> ------------------------------------------------------------
> IHMC (850)434 8903 home
> 40 South Alcaniz St. (850)202 4416 office
> Pensacola (850)202 4440 fax
> FL 32502 (850)291 0667 mobile (preferred)
> phayes@xxxxxxx http://www.ihmc.us/users/phayes
>
>
>
>
> (08)
_________________________________________________________________
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 (09)
|