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Re: FAQ: stratified class hierarchies vs. RDFS

From: pat hayes <phayes@mail.coginst.uwf.edu>
Date: Mon, 24 Jun 2002 16:32:07 -0500
Message-Id: <p05111b08b93d3d3ec250@[65.217.30.113]>
To: "R.V.Guha" <guha@guha.com>
Cc: www-rdf-comments@w3.org, Dan Connolly <connolly@w3.org>, Tim Berners-Lee <timbl@w3.org>

>Dan,
>
>  There is a rather fundamental difference in the intended meaning of 
>rdfs:Class vs Sets. One comes from cognitive science and the other 
>from Math.  rdfs:Class is intended to capture the concept of 
>"category" or "kind" as that term is used in cog-sci and not the 
>concept of Set.

Be careful. I know what you mean, but as a matter of fact simple 
languages (like RDF and FOL) have no ability to make this kind of 
distinction. You need at least a modal logic to do it,and even then 
its controversial whether a formalized modal logic is capable of 
capturing it. (I think not, myself.)  Quine is talking about the 
distinction in human language.

>In Cyc, for example, we had different nodes corresponding to Class 
>and Set. (Quine wrote a very nice essay on this topic [1]).

>Here are some examples that illustrate the difference. (V is the 
>union operator).
>a) Both perspectives would include the concepts of Person and Table. 
>The rdfs:Class perspective would not  include (Person V  Table). The 
>Set perspective would.

Not all formal set theories need to have this. Set theories designed 
for foundations of mathematics would, but so would for example 
description logics which claim to be 'natural kind'-ish, such as DAML.

>b) DanC is an instanceOf Person. In the set perspective, he would 
>also be an instanceof (Person V SquareTriangle) and (Person V 
>SuperNovasOnEarth) ...

Hey, if you allow those things to exist, then indeed he would be in 
them. (If you want to have a theory (whatever you call it) which 
allows there to be such things but wants to say that Dan wouldn't be 
in them, then you need to explain what that 'V' is really supposed to 
mean.)

>
>Saying that rdfs:Class is the rdfs:Class of all rdfs:Classes does 
>not cause problems because we do not and cannot have a theory of 
>rdfs:Classes such as ZF set theory.

That won't do, because we DO have a theory of rdfs:Classes, and 
moreover it is expressed in set-theoretic terms.

>
>Both these concepts are very useful and we need them both. But it is 
>important not to mix up the two.

I don't accept that there are two notions here. rdfs:Class extension 
are sets; not all sets are rdfs:Class extensions, but that doesn't 
mean that this is a category distinction of some kind. That position 
would be very hard to maintain while also giving a model theory.

>Both approaches are relatively common, with the rdfs:Class approach 
>being more commonly used in large scruffy implementations and the 
>set oriented approach being more common in formalizations such as 
>DLs.
>
>The important question is, which one do we use to describe concepts 
>like "Person"? My personal preference is for the cog-sci approach. 
>It is more pliable and fairly immune to logical nastinesses like 
>paradoxes.

There is no such approach that is immune from logical nastiness. Come 
on, Guha, you are the one suggesting that we USE logic to give the 
semantics for all this. How can you simultaneously be saying that it 
is cognitive-sciency and therefore un-logical?

>I would also argue that this robustness also makes it a better 
>choice for the SW.

What robustness? What choice?

Pat
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Received on Monday, 24 June 2002 17:32:13 GMT

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