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RE: Schema Algebra

Joe English wrote:
> A few comments on Jonathan Borden's "Schema Algebra" framework,
> <URL: http://www.rddl.org/SchemaAlgebra >:
> Definition [4] "schema equivalence" is a particularly elegant
> formulation.  However, to make it truly useful you'll probably want
> to place some sort of restriction on the kinds of transformations
> allowed.  Under the current definition almost any pair of
> schemas can be shown to be equivalent, for example:
[correct example snipped]
> One possibility is to restrict <t,t'> to "data-preserving"
> transformations,
> where a transformation T is "data-preserving" iff for all documents D
> Data(D) = Data(T(D)) and 'Data' is the function from XML documents
> to sets of strings defined (in terms of the XPath data model [**]) as:
>     Data(D) = { s : s is the value of a text or attribute node in D }

cool. i've been looking for something like this.

> Definition [10] ("Two URIs are equivalent when they map to the
> same set of entities") is problematic.  There are plenty of URIs
> which do not map to any entity at all (uuid: URNs, un-RDDLed
> XML namespace names, etc.); under this definition all of them
> are equivalent.

ok how about requiring the set cardinality > 0

I think the only workable definition of
> URI equivalence is the one used by RDF: "two URIs are equivalent
> iff they are textually identical".  Any attempt to compare
> URIs by examining the things they identify leads to trouble.

true, but that's part of the purpose of this, to develop a language by which
we can compare URIs and resources

> I don't quite understand the formula for Definition [12]:
>     schema(URI<sub>S</>) := exists schema S such that
>     	Entities(URI<sub>S</> <= Instances(S)

who knows what I was thinking... i've commented it out for the moment
(perhaps something will come to me :-)
thanks for your comments and suggestions,