# Re: Cardinality Restriction Axioms too Weak

From: Richard Waldinger <waldinger@AI.SRI.COM>
Date: Thu, 09 Aug 2001 19:05:10 -0700
Message-ID: <3B734156.5532976E@ai.sri.com>
To: pat hayes <phayes@ai.uwf.edu>
CC: www-rdf-logic@w3.org, Paul Kogut <paul.a.kogut@lmco.com>, Jeff Smith <composablelogic@mediaone.net>, Ken Baclawski <kenb@ccs.neu.edu>, Mitch Kokar <kokar@coe.neu.edu>, "'Stephen Fitzpatrick'" <sfitzp@kestrel.kestrel.edu>, "andy.gurd" <andy.gurd@telelogic.com>, Jerzy Letkowski <jletkows@wnec.edu>, Cordell Green <green@kestrel.edu>, "Holmes III, William S" <william.s.holmes.iii@lmco.com>, "John J. Anton" <anton@kestrel.edu>, "Douglas E. Smith" <smith@kestrel.edu>, Mark Stickel <stickel@AI.SRI.COM>
```pat hayes wrote:
>
> Richard: your point seems to depend on the claim that all lists are
> finite. Where do you derive that claim from? If we allow infinite
> lists into the universe then the cardinality axioms stated in terms
> of lists being of length one would seem to work (?). (Provided of
> course that we have the concept of 'one' available.)
>

Right, the KIF/DAML axioms are ambiguous about whether lists must be
finite or can be infinite.  But what is missing is a kind of list
constructor axiom, which says that, for any property, the list of all
items that satisfy that property exists.  Adding that axiom (and
rephasing the cardinality restriction axioms accordingly) enables us to
prove the expected properties of cardinality restrictions.   But, unless
the entire domain is finite, adding the axiom also commits us to
infinite list.  I'm working on another message that introduces these
modifications to the theory and explores the consequence.---rw

.......

> So either way, the cardinality
> restrictions seem to work.

No, without some changes in the axioms, there is no way to prove that a
person can't have two fathers.
```
Received on Thursday, 9 August 2001 22:14:19 GMT

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