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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: Take the list of all finite sequences of Unicode characters, and filter out those which are not well-formed XML documents conforming to the XHTML DTD; this gives you a bijection between Instances(XHTML) and the natural numbers. Do the same for DocBook. Now define t : XHTML -> DocBook as the function which takes the Nth XHTML document to the Nth DocBook document, and define t' : DocBook -> XHTML similarly. <t,t'> exhibits an equivalence between DocBook and XHTML. [*] 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 } I think this restriction should rule out pathological cases like [*], while still allowing transformations that reorder content, change elements to attributes, et cetera. ([**] or in terms of the Infoset as "... s is a maximal contiguous sequence of Character information items", or something like that). 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. 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. 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) Is the subscript 'S' in 'URI<sub>S</>' the same as the 'S' bound by the existential quantifier? Is 'schema' supposed to be a predicate defined on URIs, a predicate on Schema-subscripted-URIs, a function from URIs to schemas, or something else? The prose description speaks of "the" schema whose instances include all entities corresponding to the URI, but any entity is valid with respect to an infinite number of schemas; which one is distinguished? --Joe English jenglish@f...
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