Subtag
Subsumption Semantics for XML Tags*


Version: Apr 12, 2000

First Version Prepared for:
Dagstuhl Seminar 00121, Semantics for the Web
March 19-24, 2000

Harold Boley
DFKI GmbH







* "Practice what you preach": XML source of these slides at subtag.xml (subtag.xml.txt);
transformed to HTML via Michael Sintek's SliML stylesheet at slides.xsl
The Ontological XML Imperative Problem of Semantics for the Web:

One, Standardized Semantics

Would Boost the Web Further Than

Many, Non-Standardized Semantics



Proposed Solution Step:

Incorporate Subsumption Semantics

Right Into the Web's XML x.0 Tags (x>1):

Build Taxonomy Into DTDs, Leave Axioms To Schemas!

(Ontology = Taxonomy + Axioms)
Attacking a Problem with XML Main building blocks of XML DTDs are chaining (whole-part; inversely, part-of) relations between a parent element and an (ordered) sequence of child elements XML DTDs cannot specify subsumption (inversely, isa or kind-of) relations between a tag and an (unordered) set of subtags, as needed for the taxonomy backbone of ontologies Subsumption of element tags is thus handled ad hoc or in non-DTD schema languages RDF Schema: subClassOf specifies subsumption (not specific for tags) XML Schema (Part 1): derivedBy="extension" right-appends children (no subsumption specification) Various non-DTD tag-subsumption and -inheritance semantics thus lead to diverging XML uses An XML Sample

Consider this DTD for a sales database table:

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Also, one element for a corresponding tuple:

Onoffbook XML4You 12417 ]]> Differentiating Parent Subtags: From Copying to Subsumption

Now, for the E-commerce era, let us differentiate online-sales from offline-sales tags, which should both `inherit' their children from the neutral sales element:

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Instead of such copied child declarations or corresponding ENTITY declarations, we propose a new XML version (NEXML) with a true tag-inheritance construct SUBSUMES for DTDs, shortening the first three lines to:

]]> How NEXML Uses SUBSUMES: Child Inheritance

Element instances with online-sales and offline-sales tags thus obtain children with sales-declared company, item, and quantity tags (note the 329 `unclassified-rest' copies while Onoffbook is heading towards its offline/online break-even point for the book "XML4You"):

]]> Onoffbook XML4You 329 Onoffbook XML4You 12417 Onoffbook XML4You 15182 ]]> Element Attributes vs. Element Children (NE)XML elements, with attributes and children, correspond to frame/OOP instances; their DTDs correspond to frame/OOP classes Children are ordered, with inheritance for DTD declarations only Attributes are unordered, hence (inspired by frame/OOP) inheritance in DTDs: performed for declarations in processors: permitted for values "#REQUIRED" in NEXML, by attribute inheritance, means "required for all descendant leaf elements" How NEXML Uses SUBSUMES: Attribute Inheritance

Element instances with online-sales and offline-sales tags also obtain sales-declared attributes such as year and price (the DTD inherits both attribute declarations; an element processor should inherit the year attribute's 2000 value):

]]> ... | | v ... ... ]]> Differentiating Child Subtags: From Copying to Subsumption

Let us now differentiate household-item from business-item tags, which should both `inherit' their child context (siblings) from the neutral item element:

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Instead of such copied sibling declarations we can use the XML choice (|) construct, shortening the first three lines to:

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However, to express the subsumption semantics hidden within this choice, we again use our tag-inheritance construct SUBSUMES for NEXML DTDs, obtaining:

]]> Combining Parent and Child Subtags: "Multiplying Out" Subsumption

We can also combine the parent differentiation online-sales/offline-sales with a child differentiation such as household-item/business-item, obtaining (#PCDATA declarations omitted):

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As in the child-differentiation example, this can be regarded as the result of "multiplying out" choices from a shorter DTD:

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As in the parent- and child-differentiation examples, it can also be regarded as the XML result of "multiplying out" SUBSUMES from a more semantic NEXML DTD:

]]> Left and Right Child Extensions in NEXML DTDs Child chaining and tag subsumption can alternate arbitrarily Since children are ordered, a subtag can extend inherited child content to the left and/or right This is indicated in NEXML DTDs by using ELEMENT declarations with two (possibly empty) parenthesized child sequences for subtags: the left and right extensions We do not employ multiple supertag inheritance simply because a specification corresponding to item 3. would become much harder when multiple child sequences have to be merged A Refined NEXML DTD Example

This is the full DTD of the original NEXML sample refined by online-sales subtags and item children, one of which rooting a product-taxonomy top-level (sales' subtags online-sales and offline-sales are extended by children to both sides; the online-sales subtag web-sales is extended only to the left; email-sales, only to the right):

]]> A Tree-Like Diagram Form of NEXML DTDs Chained (ordered) children branch horizontally, in green; subsumed (unordered) tags branch vertically, in red Left and right child extensions are shown via geometric branch positions Attributes are written (in italics) next below their elements' tags For repeated tag occurrences, the tree-like structure needs repeated tag nodes, which could be expanded/contracted via "+"/"-"-buttons or FlexDAGs Further EBNF-like DTD syntax can be accommodated by labels (*, +, ?) on branches and a new kind of branch (|) The Refined NEXML DTD Diagram Implementation Approaches Two approaches for implementing NEXML in validators, browsers, stylesheet processors, and other tools: DTD preprocessor: Reduce NEXML DTDs to XML 1.0 DTDs by "multiplying out" the SUBSUMES hierarchy as shown in the examples XML successor: Develop a version of NEXML that directly supports the SUBSUMES hierarchy into a new XML x.0 for W3C standardization Approach 1. can explode the size of generated DTDs, which in certain cases can be avoided by XML choices (|) and ENTITY declarations Still, approach 2. should be attempted, utilizing efficient subsumption algorithms, e.g. from description logics The remaining XML 1.0 features (ENTITY, NOTATION, etc. ) can be taken over to XML x.0, making XML 1.0 DTDs upward compatible Conclusions NEXML augments XML 1.0 by SUBSUMES declarations and enhanced ELEMENT declarations for subsumption DTDs A corresponding XML x.0 version would be immediately useful by enabling a standardized subsumption semantics for the information on the Web Further refinements could, e.g., comprise overlapping vs. disjoint subsumptions (special integrity constraints) Subsumption DTDs constitute a taxonomy that can also be accessed by axioms (e.g., general ICs) in schemas, giving us the full power of ontologies By moving expressivity from RDF Schema and XML Schema into XML x.0, these separate standards could be reconciled (cf. The Cambridge Communique)