W3C home > Mailing lists > Public > w3c-rdfcore-wg@w3.org > February 2002

Re: Monotonicity

From: Sergey Melnik <melnik@db.stanford.edu>
Date: Mon, 04 Feb 2002 14:22:38 -0800
Message-ID: <3C5F09AE.90465924@db.stanford.edu>
To: Jeremy Carroll <jjc@hplb.hpl.hp.com>
CC: w3c-rdfcore-wg@w3.org
Jeremy Carroll wrote:
> 
> >    2B:
> >
> >    Monotonicity and the open world assumption on type information.
> >    S (idiom B and P) is non-monotonic with respect to type information,
> >    or at least forces the RDF application to behave as if the
> >    underlying theory were non-monotonic.
> > [Sorry this is rather obscure, I will ask for a clarification about S-P,
> > which will illustrate my concerns]
> 
> In S-P as I understand it rdf:value is understood in relation to the known
> datatypes:
> 
> [[[[
> 
> In other words, rdf:value "extracts" the lexical representation from a given
> pair:
> 
> EXT(I(rdf:value)) := {<<x,y>, y> | <x,y> is an element of a datatype
> mapping}
> 
> (Notice that for the above definition to be well-formed, we need to be able
> to enumerate all datatype mappings. This can be done using special
> vocabulary e.g., xsd:date.map rdfs:subClassOf rdfdt:DatatypeMapping).
> 
> ]]]]
> 
> So for example, in a  minimal RDF implementation in which we only have
> strings rdf:value is a 1-1 mapping. Thus in that sort of implementation we
> would have:
> 
> _:a <foo> _:b .
> _:b <rdf:value> "string" .
> _:c <bar> _:d .
> _:d <rdf:value> "string" .
> 
> implies
> 
> _:a <foo> _:b .
> _:c <bar> _:b .
> 
> (in the premise both _:b and _:d are < "string", "string" > )
> 
> If a second RDF implementation has a greater range of datatypes then it may
> be the case that "string" can map to something else. In this case the
> implication above does not hold.
> 
> e.g. if we support xsd:string and xsd:integer then we have the following:
> 
> _:a <foo> _:b .
> _:b <rdf:value> "1000" .
> _:c <bar> _:d .
> _:d <rdf:value> "1000" .
> 
> does not imply
> 
> _:a <foo> _:b .
> _:c <bar> _:b .
> 
> I believe the semantic web will be built on the systematic application of
> the open world assumption.
> 
> S-P requires a closed world assumption on datatypes, that results in
> defeasible implication, and hence non-interoperability. This is a
> significant concern.

I thought monotonicity was a feature, not a bug. As far as I remember
what logics etc. was about, if we drop monotonicity things become really
hairy and computationally impractical even for small data/knowledge
bases. Please correct me if I'm wrong...

Does TDL require non-monotonic reasoning?

Sergey
Received on Monday, 4 February 2002 17:05:41 EST

This archive was generated by hypermail pre-2.1.9 : Wednesday, 3 September 2003 09:45:04 EDT