- From: Sergey Melnik <melnik@db.stanford.edu>
- Date: Mon, 04 Feb 2002 14:22:38 -0800
- 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 UTC