Re: Semantics for SUO-KIF

[David Whitten <whitten@lynx.eaze.net>]

> 
> 
> All,
> 
> OK. I think I understand my problem. I was assuming that the universe of
> discourse was everything used in the first argument of instance-of, which in
> the example is represented by Entity, the universal class of individuals.
> However, it seems that Entity is the same thing that I have been calling
> Individual. In short, Entity does not denote everything -- there are
> type-like things in the domain of discourse. Hence, if there was a Class
> term, which there currently is not, the domain of discourse would be the
> disjoint union
>     SUO[*] = SUO[Entity] + SUO[Class]
> However, as I mentioned in my comments on the Heraclitus distinction
> [http://ltsc.ieee.org/logs/suo/msg02424.html], in order to have classes,
> such as Triangle, as instances of other classes, I would like to extend
> instance-of to include classes in its first argument.
> 
> Robert E. Kent
> rekent@ontologos.org

Ironically, I think this is a content message, (and hence should be on
the main list) instead of a KIF question.

The only way it could be a KIF question is if KIF were sorted,
which only an extension to KIF is sorted. SUO-KIF is unsorted.

I certainly think that you should be able to state that any member of
the class of the entire class of things in the domain of discourse should
be treated as the instance of a subclass of the entire class of things
in the domain of discourse. Type-like things should not be excluded from
being classified.

In the document at http://ltsc.ieee.org/logs/suo/msg02301.html
the unary predicate Class is used instead of the Class named Class.

I agree with your desire to have instance-of including classes in
its first argument, and from my reading of John Sowa's KR book,
I believe Entity includes classes.

David

> 
> ----- Original Message -----
> From: "Robert E. Kent" <rekent@ontologos.org>
> To: <suo-kif@ieee.org>
> Sent: Friday, December 01, 2000 12:57 PM
> Subject: Semantics for SUO-KIF
> 
> 
> >
> > All,
> >
> > I believe that it is very important that we specify a semantics for all of
> > our work with SUO-KIF. However, when studying the example
> > [http://ltsc.ieee.org/logs/suo/msg02301.html], which is expressed in the
> > unsorted (one-sorted) version of SUO-KIF, I am having difficulty in
> defining
> > a semantics.
> >
> > A model for SUO-KIF should have a domain or universe of discourse, suppose
> > it is called SUO[*], and an interpretation (evaluation) for all predicate
> > symbols p and constants c, say they are called SUO[p] and SUO[c]. The
> > interpretations should satisfy the constraints: SUO[c] \member SUO[*] and
> > SUO[p] \subset SUO[*]^n for all predicate symbols p with valence n.
> >
> > In the above example the category terms "Entity", "Absurdity",
> > "Independent", ... are regarded as constants. So an interpretation should
> > map them to single elements of SUO[*], whereas the meaning is that these
> > terms be subsets of SUO[*]; in particular, since we want "Entity" to
> denote
> > the universal class of individuals, the interpretation should be
> SUO[Entity]
> > = SUO[*]. A sorted version of SUO-KIF would not present difficulties of
> this
> > kind, since then the category terms "Entity", "Absurdity", "Independent",
> > ... would be regarded as sorts.
> >
> > Robert E. Kent
> > rekent@ontologos.org
> >
>