Re: SUO: Classification Ontology
All,
A KIF classification has an alternate functional representation that is
often more useful. Here the instance set, the type set and the incidence
predicates are written as KIF functions.
(UnaryRelation Classification)
(UnaryFunction inst)
(forall (?c ?p)
(=> (= (inst ?c) ?p)
(and (Classification ?c) (UnaryRelation ?p))))
(UnaryFunction typ)
(forall (?c ?t)
(=> (= (typ ?c) ?p)
(and (Classification ?c) (UnaryRelation ?p))))
(UnaryFunction |=)
(forall (?c ?p)
(=> (= (|= ?c) ?p)
(and (Classification ?c) (BinaryRelation ?p))))
(forall (?c ?i ?t)
(=> ((|= ?c) ?i ?t)
(and ((inst ?c) ?i) ((typ ?c) ?t))))
__________
KIF definitions and declarations are changed accordingly.
For example, the intent and extent functions are defined as follows.
Define a binary KIF function 'int' that denotes the intent of an instance
'i' in a classification 'c' defined by
int(i) = {t in typ(c) | i |= t}.
(BinaryFunction int)
(forall (?c ?i ?p)
(=> (= (int ?c ?i) ?p)
(and (Classification ?c) ((inst ?c) ?i) (UnaryRelation ?p))))
(forall (?c ?i ?t)
(=> (and (Classification ?c) (Instance ?i) (Type ?t))
(<=> (int ?c ?i) ?t) ((|= ?c) ?i ?t))))
Dually, define a binary KIF function 'ext' that denotes the extent of a type
't' in a classification 'c' defined by
ext(t) = {i in inst(c) | i |= t}.
(BinaryFunction ext)
(forall (?c ?i ?p)
(=> (= (ext ?c ?t) ?p)
(and (Classification ?c) ((typ ?c) ?t) (UnaryRelation ?p))))
(forall (?c ?i ?t)
(=> (and (Classification ?c) (Instance ?i) (Type ?t))
(<=> (ext ?c ?t) ?i) ((|= ?c) ?i ?t))))
Robert E. Kent
rekent@ontologos.org
----- Original Message -----
From: "Robert E. Kent" <rekent@ontologos.org>
To: "Michael Uschold" <mfu@redwood.rt.cs.boeing.com>
Cc: "SUO" <standard-upper-ontology@ieee.org>
Sent: Friday, January 19, 2001 4:09 PM
Subject: Re: SUO: Classification Ontology
> Hi Mike,
>
> I agree. I have ongoing work on the Information Flow Framework (IFF). What
I
> sent was an extraction from the appendix of an unpublished paper of mine
on
> a "Classification Metatheory." I will try to send a more completely
> annotated document later. As a stopgap let me send the basic part of this
> appendix -- the part without the colimit representation. Although this
also
> is a bit terse, perhaps it will suffice in the meantime.
>
> Robert E. Kent
> rekent@ontologos.org
>
>
> ----- Original Message -----
> From: "Michael Uschold" <mfu@redwood.rt.cs.boeing.com>
> To: <rekent@ontologos.org>; <standard-upper-ontology@ieee.org>
> Sent: Thursday, January 18, 2001 5:24 PM
> Subject: Re: SUO: Classification Ontology
>
>
> >
> > Robert,
> >
> > It would be helpful to augment Kif-ese with English documentation
> > indicating what is going on. In my opinion, this is more important
> > than the KIF - in communicating.
> >
> > Mike
>