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Re: Infinite cardinalities

From: Peter F. Patel-Schneider <pfps@research.bell-labs.com>
Date: Mon, 02 Apr 2001 09:27:08 -0400
To: kenb@ccs.neu.edu
Cc: www-rdf-logic@w3.org
Message-Id: <20010402092708A.pfps@research.bell-labs.com>
From: Ken Baclawski <kenb@ccs.neu.edu>
Subject: Re: Infinite cardinalities
Date: Mon, 2 Apr 2001 09:01:45 -0400 (EDT)

> I did not mean to suggest that this was more than a local condition.  And,
> in fact, axiom 105 is okay.  It only assumes that the list is a subset of
> the set of values.  However, lists are used in a few other places as well. 
> They are used to define containers (Axiom 13), to define unionOf,
> disjointUnionOf, intersectionOf, etc.  There is still the question of
> whether DAML+OIL should support (local) infinite cardinalities.
> The use of list for Axiom 13 is particularly noteworthy.  Axiom 66 states
> that lists are sequences, Axiom 14 implies that sequences are containers
> and Axiom 13 states that containers are lists.  It appears to be a cycle.
> It is not an actual cycle because Axiom 13 is using the built-in
> KIF list, not the DAML list, but it isn't clear that it is entirely
> consistent either.
> Ken Baclawski
> College of Computer Science
> Northeastern University

The ...Of lists are part of the syntax of the language, which is indeed
finite, and finite by design, so this is OK.   The other concerns above
should be investigated by the authors of the axiomatization.

Received on Monday, 2 April 2001 09:28:03 UTC

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