Re: Dark triples are not inherently nonmonotonic

Jonathan,

 We were imprecise in our language. Sorry.

 We should have said that dark triples introduce non-mon into the rest 
of any language whose
semantics interprets them. DTs themselves are monotonic.

 As to your example, the issue is that the semantics of some language 
(in this case OWL),
would need to incorporate a check for formulae involving the color of 
terms in the formulae
wherein the color itself was expressed using other formulae. This is 
what causes the non-mon.

 My intuition is that the formulae stating darkness are coming near the 
realm of (but not close
enough to cause paradoxes) stating things about the semantics of the 
language that we are seeing
non-mon. Any closer or any more powerful constructs and we will be there.

guha



Jonathan Borden wrote:

>Pat, did you reall write:
>http://lists.w3.org/Archives/Public/www-webont-wg/2002May/att-0302/00-part ?
>
>Now I agree that the mechanism you proposed to indicate darkness e.g.
>
>owl:List a owl:Dark
>
>is problematic from a monoticity perspective, but to suggest that 
>
>[[
> but the exact details do not matter to the point being made here.
>]]
>
>and that _dark triples themselves are inherently nonmonotonic_ is going a
>bit to far, eh?
>
>For example than triples, are rather than dark, let's consider: colored
>triples, and so a triple becomes a quad:
>
>subject predicate object color .
>
>where color is a URIref just like the others.
>
>Now assume that for all current RDF documents, the parser generates a color
>rdf:White, which corresponds to an asserted triple in the MT.
>
>Now suppose that the color of the triples (really quads but go with this),
>is a function of some attribute on the <rdf:RDF> root element of any RDF
>document e.g.
>
><rdf:RDF color="red">
>    <rdf:Description rdf:ID="foo">
>        <ex:shape rdf:resource="#square">
>    </rdf:Description>
></rdf:RDF>
>
>which generates the following N-Quad:
>
><#foo> ex:shape <#square> rdf:red .
>
>of course the color doesn't need to be rdf:red, but could be any URI, but
>that really doesn't matter.
>
>So what could possibly be nonmonotonic about that?
>
>Now assume that dark triples are triples with the color rdf:black.
>
>Are you really suggesting that triples are monotonic, but quads are
>_inherently nonmonotonic_ ? Surely not.
>
>So, as with everything, the exact details do matter to the point being made
>here, and to suggest that dark triples are inherently nonmonotonic can only
>be true if your specific definition of what a dark triple is and how it is
>created causes the nonmonotonicity.
>
>Jonathan
>
>  
>

Received on Thursday, 30 May 2002 20:26:46 UTC