W3C home > Mailing lists > Public > www-rdf-logic@w3.org > April 2001

Infinite cardinalities

From: Ken Baclawski <kenb@ccs.neu.edu>
Date: Sun, 1 Apr 2001 17:34:48 -0400 (EDT)
To: www-rdf-logic@w3.org
Message-ID: <Pine.LNX.3.96.1010401165836.28086U-100000@steam>
Recently, Peter Patel-Schneider mentioned that DAML+OIL allows infinite
models.

On Fri, 30 Mar 2001, Peter F. Patel-Schneider wrote:

> ...
> DAML+OIL does not have a finite model restriction.  It is entirely possible
> to have DAML+OIL models with an infinite number of objects that are not
> datatype values.
> ...

Furthermore, the preface to the DAML+OIL axioms makes this statement which
seems to allow for models that have infinite cardinalities:

"This axiomatization is designed to place minimal constraints on the
interpretation of the non-logical symbols in the resulting logical theory. 
In particular, the axioms do not require use of a set theory, that classes
be considered to be sets or to be unary relations, nor do they require
that properties be considered to be mappings or binary relations." 

However, the axioms make frequent use of finite lists, which are much more
restrictive than sets.  Because of this there are implicit finiteness
assumptions in the axioms.  Consider for example Axiom 105: 

Ax105.(=> (and (PropertyValue onProperty ?r ?p)
                     (PropertyValue minCardinality ?r ?n))
                (forall (?i) 
                        (<=> (Type ?i ?r) 
                             (exists (?vl) 
                                     (and (no-repeats-list ?vl) 
                                          (forall (?v) 
                                                  (=> (PropertyValue 
                                                        item ?vl ?v) 
                                                      (PropertyValue
                                                        ?p ?i ?v))) 
                                          (>= (length ?vl) ?n))))))[9]

It follows from this axiom that restricting a property to have
minCardinality of 0 has the side-effect of restricting the cardinality to
be finite.  Is this what was intended?  Does DAML+OIL really support
infinite cardinalities?

Ken Baclawski
College of Computer Science
Northeastern University
kenb@ccs.neu.edu
Received on Sunday, 1 April 2001 17:34:55 GMT

This archive was generated by hypermail 2.2.0+W3C-0.50 : Monday, 7 December 2009 10:52:38 GMT