Re: Cyclic Classes/Properties

On May 11, Sigfrid Lundberg, Lub NetLab writes:
> I think that the problem here boils down to the wish to be able to
> say things, and the wish to be able to infer things. I want to be
> able to say that a sub-title is a subclassof title, and that there
> should be no doubt whatsoever that all titles are not
> sub-titles. Just some titles are.
> 
> Some time ago, I was convinced by you (and other kind people on this
> list) that we do need a not-strict-sub-class-of. The cost of making
> certain inferences be would far too high if we didn't. So I accept
> this... But I'm not comfortable with it; aren't we trading
> inferability against expressiveness? Aren't we enhancing the former
> at the price of the latter.  To put this in another way: Could the
> ability to say (i.e., in rdf/daml) that sub-titles "<" titles rather
> than just that sub-titles "<=" titles make a more solid ground for
> inference. I mean, some statements could actually be more
> precise... I'd reckon that we need both.

If you have a propositionally closed representation language, then
having a not-strict-sub-class-of allows you to have the
strict-sub-class-of as well. So there is NO trading inferability
against expressiveness. This is how you could represent your example:

Introduce first a freshly new primitive class "non-sub-title".
Add the following axioms:

sub-title is-a-not-strict-sub-class-of title.
title is-a-not-strict-sub-class-of (sub-title or non-sub-title).
non-sub-title is-a-not-strict-sub-class-of ((not sub-title) and title).

This implies:
sub-title is-a-strict-sub-class-of title

cheers
-- e.

Enrico Franconi                     - franconi@cs.man.ac.uk
University of Manchester            - http://www.cs.man.ac.uk/~franconi/
Department of Computer Science      - Phone: +44 (161) 275 6170
Manchester M13 9PL, UK              - Fax:   +44 (161) 275 6204

Received on Friday, 11 May 2001 08:10:35 UTC