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Re: FAQ: stratified class hierarchies vs. RDFS

From: pat hayes <phayes@mail.coginst.uwf.edu>
Date: Mon, 24 Jun 2002 18:06:16 -0500
Message-Id: <p05111b00b93d5229a989@[]>
To: "R.V.Guha" <guha@guha.com>
Cc: www-rdf-comments@w3.org, Dan Connolly <connolly@w3.org>, Tim Berners-Lee <timbl@w3.org>

>I don't think I was clear enough. The current RDF MT models 
>rdfs:Class as denoting a set. I am taking the position that we 
>should consider modeling rdf:type is just another relation, i.e., as 
>not having anything special in the model theory.

Right, its just a relation. It does have a special relationship to 
the class extensions, but that's because the classes are defined that 
way. That is, the class extensions are *defined* to be the sets of 
things that bear the rdf:type relation to the class. And the class 
itself - not its extension, but the thing itself - is just another 
'thing' in the universe.

My point was only to point out that the class/set distinction 
shouldn't be thought of as a distinction of kind, more one of scope.

>It is only when one says that rdfs:Class = set of all sets,

Right, never say that.  Please nobody ever say that.

>that one gets into the "set of all sets that don't contain 
>themselves" paradox.

Oh, I see. Right, we aren't anywhere near *that* paradox in RDF. Even 
allowing sets to be members of themselves doesn't get one into the 
Russell-paradox territory, but it does violate what has become a 
widely-accepted intuition in set theory, that sets are well-founded: 
that if you take any set and look at its members, if any of those are 
sets then you look at their members, and so on, that you will 
eventually bottom out with things that don't have members. Its a bit 
like the intuition that any set can be written as an expression of 
the form {... {...} ...} where the brackets only get finitely deep. 
If we allow 'loops' then this idea breaks down which some people find 
unsettling. But its not in the least paradoxical or even dangerous, 
in fact, and set theory people have known this for about 2 decades 
now, but the news hasn't leaked out yet.

>If you regard rdf:type as just another relation (like dc:title or 
>dc:author), we don't have this issue.
>I am also further arguing that from a modelling perspective (i.e., 
>independent of logical paradox issues) "rdfs:Class = set of all 
>sets" does not capture the right intuition about rdfs:Class

Absolutely right. The key point is that "all sets" , though, right? 
That is, those class extensions are of course sets (what else would 
they be?) but they aren't ALL the sets. Anyone who claims to be 
saying things about ALL sets is taking on a very large expressive 
burden indeed, far more than anyone except a few mathematicians would 
even be interested in having.


>pat hayes wrote:
>>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?

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Received on Monday, 24 June 2002 19:06:33 UTC

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