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Re: Infinite cardinalities

From: pat hayes <phayes@ai.uwf.edu>
Date: Mon, 2 Apr 2001 14:20:53 -0700
Message-Id: <v0421010db6ee9c5eea28@[]>
To: "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>, kenb@ccs.neu.edu
Cc: www-rdf-logic@w3.org
>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.

Yes, but there is a narrow line here. It is one thing to claim that 
certain structures are part of the syntax and therefore finite by 
decree (which is OK, I agree), but another to then go on and argue 
that since these structures are described in the langauge, that they 
denote things in the interpretation, and since we have agreed that 
they are finite, the things they denote must also be finite. That is 
*not* OK; in fact it is a fallacy; but it is perilously easy to slip 
over into this region if we don't have a clear distinction between 
datastructures and syntax. KIF 3.0 made this mistake, for example.

In fact this is a very neat illustration of the need to keep 
implementation structure and syntactic structure as two distinct 

Pat Hayes

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Received on Monday, 2 April 2001 17:18:56 UTC

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