Appendix: Mechanical Rules (GRDDL)

Appendix: Mechanical Rules (Informative)

The GRDDL specification uses formal definitions such as...

Normative Statement

Mechanical Rule
(Informative)

If F and G are GRDDL results of IR, then the merge [RDF-MT] of F and G is also a GRDDL result of IR.

?IR grddl:result ?F, ?G.
(?F ?G) log:conjunction ?H.

?IR grddl:result ?H.

The premises and conclusions of the mechanical rules are written as SPARQL graph patterns[SPARQL].

The term grddl:result is introduced and specified in these rules. The RDF Semantics[RDF-MT] document doesn't define an RDF property for the merge of two RDF documents, but some research work, Semantic Web Tutorial Using N3 does define semantic extension of RDF where log:conjunction relates a list/set of RDF graphs to their merge, so we use that.

Other terms from various namespaces are used as follows:

fn - fn:doc, fn:normalize-space, fn:base-uri, fn:string, fn:namespace-uri are used as RDF properties specified in the XQuery standard namespace, http://www.w3.org/2006/xpath-functions#
owl - owl:FunctionalProperty, owl:someValuesFrom etc. are used from the OWL standard namespace http://www.w3.org/2002/07/owl#
rdf - rdf:subject is used per the RDF standard namespace, http://www.w3.org/1999/02/22-rdf-syntax-ns#. In particular, an RDF graph literal with one triple is used as an rdf:Statement.
grddl - grddl:transformation, grddl:result, etc. are specified by these rules in the GRDDL namespace, http://www.w3.org/2003/g/data-view#. Note that it this namespace includes grddl:RootNode, imported from [XPATH], and grddl:InformationResource from [WEBARCH].
gspec - various auxiliary terms introduced for the purpose of this specification are collected in the namespace http://www.w3.org/2004/01/rdxh/spec_rules#
Some from RDF/XML:
- gspec:rdfParse Whenever the RDF/XML spec says that an RDF/XML document with root node ROOT represents a graph G, we have ?ROOT gspec:rdfParse ?G.
Some from XPath and XSLT:
- gspec:resultTree - whenever the XSLT specification says that the result of TX given IN is OUT, we have (?TX ?IN) gspec:resultTree ?OUT.
- gspec:xpath - whenever the XPath specification says that EXPR evaluated at N1 includes N2, we have (?N1 ?EXPR) gspec:xpath ?N2.
Some terms are derived for reasoning about hypertext links in HTML and HTTP:
- gspec:htmlBase to relate an XPath node from an XHTML document to the the document's base URI or the URI given in the base element.
- gspec:profileName to relate a node or link or HTTP message to a profile name (URI)
- gspec:bodyXML to relate an HTTP message bearing XML content to an XPath root node for that content
- gspec:requestURI to relate an HTTP response to the request URI that it corresponds to
- gspec:httpLink to relate an HTTP response each link
- gspec:httpRef to relate a link from an HTTP response to the URI-Reference in the link
- gspec:httpRel to relate a link from an HTTP response to the value of the rel link-param of the link
list list:member relates a list to any of its members, e.g. its rdf:first; it comes from the research namespace http://www.w3.org/2000/10/swap/list#.
log in addition to log:conclusion discussed above, log:uri is taken from http://www.w3.org/2000/10/swap/log#. Whenever [WEBARCH] says that a resource X is identified by a URI I, have ?X log:uri ?I

In the first example in the specification, <http://www.w3.org/2001/sw/grddl-wg/td/titleauthor.html> has two GRDDL results. The following is a derivation of one of them from the following sources:

grddl-rules3.n3 - an N3 rules file derived from the rules in the specification using txrulesn3.xsl to wrap the SPARQL query patterns a la { ...premise... } => { ...conclusion... }
grddl-rule-tests.n3 some test data
data-view.rdf, the RDF/XML representation of the GRDDL namespace document @@which should be captured in a test and hence ratified by the WG
owlAx.n3 some rules to capture a little bit of the semantics of RDFS (especially rdfs:range) and OWL (especially owl:someValuesFrom)

See Makefile for details.

1: <http://www.w3.org/2001/sw/grddl-wg/td/titleauthor.html> :uri "http://www.w3.org/2001/sw/grddl-wg/td/titleauthor.html" . [by built-in Axiom log:uri] 2: """glean_title.xsl http://www.w3.org/2001/sw/grddl-wg/td/getAuthor.xsl""" :normalize-space "glean_title.xsl http://www.w3.org/2001/sw/grddl-wg/td/getAuthor.xsl" . [by built-in Axiom fn:normalize-space] 3: ( "glean_title.xsl http://www.w3.org/2001/sw/grddl-wg/td/getAuthor.xsl" "[ \t\r\n]+" ) :tokenize ( "glean_title.xsl" "http://www.w3.org/2001/sw/grddl-wg/td/getAuthor.xsl" ) . [by built-in Axiom fn:tokenize] 4: ( "glean_title.xsl" "http://www.w3.org/2001/sw/grddl-wg/td/getAuthor.xsl" ) :member "glean_title.xsl" . [by built-in Axiom list:member] 5: ( "glean_title.xsl" "http://www.w3.org/2001/sw/grddl-wg/td/titleauthor.html" ) :resolve-uri "http://www.w3.org/2001/sw/grddl-wg/td/glean_title.xsl" . [by built-in Axiom fn:resolve-uri] 6: <http://www.w3.org/2001/sw/grddl-wg/td/glean_title.xsl> :uri "http://www.w3.org/2001/sw/grddl-wg/td/glean_title.xsl" . [by built-in Axiom log:uri] 7: ... [by parsing <grddl-rule-tests.n3>] 8: @forSome :_g28, :_g29, g:_g6 . ( g:_g6 "/*" ) gspec:xpath :_g28 . ( g:_g6 """/*/@*[local-name()="transformation" and namespace-uri()= "http://www.w3.org/2003/g/data-view#"]""" ) gspec:xpath :_g29 . :_g28 fn:base-uri "http://www.w3.org/2001/sw/grddl-wg/td/titleauthor.html" . :_g29 fn:string """glean_title.xsl http://www.w3.org/2001/sw/grddl-wg/td/getAuthor.xsl""" . [by erasure from step 7] 9: ... [by parsing <grddl-rules3.n3>] 10: @forAll :BASE, :E, :N, :REF, :TX, :TXURI, :V, :Vnorm . { @forSome run:_g30, run:_g31 . ( :N "/*" ) gspec:xpath :E . ( :N """/*/@*[local-name()="transformation" and namespace-uri()= "http://www.w3.org/2003/g/data-view#"]""" ) gspec:xpath run:_g30 . ( :REF :BASE ) fn:resolve-uri :TXURI . ( :Vnorm "[ \t\r\n]+" ) fn:tokenize run:_g31 . run:_g30 fn:string :V . run:_g31 list:member :REF . :E fn:base-uri :BASE . :TX log:uri :TXURI . :V fn:normalize-space :Vnorm . } log:implies {:N grddl:transformation :TX . } . [by erasure from step 9] 11: ... [by rule from step 10 applied to steps [2, 3, 4, 5, 6, 8] with bindings {'E': '[...]', 'TX': '<http://www.w3.org/2001/sw/grddl-wg/td/glean_title.xsl>', '_g_L14C16': '[...]', 'TXURI': '"http....xsl"', 'N': '<grddl-rule-tests.n3#_g6>', 'Vnorm': '"glea....xsl"', 'BASE': '"http...html"', 'V': '"glea....xsl"', '_g_L16C35': '?', 'REF': '"glea....xsl"'}] 12: @forSome :_g6 . :_g6 grddl:transformation <http://www.w3.org/2001/sw/grddl-wg/td/glean_title.xsl> . [by erasure from step 11] 13: ... [by parsing <data-view.rdf>] 14: :Transformation owl:onProperty :transformationProperty; owl:someValuesFrom :TransformationProperty . [by erasure from step 13] 15: :transformation s:range :Transformation . [by erasure from step 13] 16: @forSome :_g6 . :_g6 grddl:transformation <http://www.w3.org/2001/sw/grddl-wg/td/glean_title.xsl> . [by erasure from step 11] 17: ... [by parsing <owlAx.n3>] 18: @forAll :C, :O . { @forSome run:_g32, run:_g33 . run:_g32 run:_g33 :O . run:_g33 s:range :C . } log:implies {:O a :C . } . [by erasure from step 17] 19: ... [by rule from step 18 applied to steps [15, 16] with bindings {'C': '<http://www.w3.org/2003/g/data-view#Transformation>', '_g_L2C6': '<http://www.w3.org/2003/g/data-view#transformation>', '_g_L2C3': '<grddl-rule-tests.n3#_g6>', 'O': '<http://www.w3.org/2001/sw/grddl-wg/td/glean_title.xsl>'}] 20: <http://www.w3.org/2001/sw/grddl-wg/td/glean_title.xsl> a :Transformation . [by erasure from step 19] 21: @forAll :C, :P, :S . { @forSome run:_g34 . run:_g34 owl:onProperty :P; owl:someValuesFrom :C . :S a run:_g34 . } log:implies { @forSome run:_g35 . run:_g35 a :C . :S :P run:_g35 . } . [by erasure from step 17] 22: ... [by rule from step 21 applied to steps [14, 20] with bindings {'P': '<http://www.w3.org/2003/g/data-view#transformationProperty>', 'C': '<http://www.w3.org/2003/g/data-view#TransformationProperty>', '_g_L3C8': '<http://www.w3.org/2003/g/data-view#Transformation>', 'S': '<http://www.w3.org/2001/sw/grddl-wg/td/glean_title.xsl>'}] 23: @forSome :_g24 . <http://www.w3.org/2001/sw/grddl-wg/td/glean_title.xsl> grddl:transformationProperty :_g24 . [by erasure from step 22] 24: @forSome :_g6 . "http://www.w3.org/2001/sw/grddl-wg/td/titleauthor.html" fn:doc :_g6 . [by erasure from step 7] 25: <http://www.w3.org/2001/sw/grddl-wg/td/glean_title.xsl> :uri "http://www.w3.org/2001/sw/grddl-wg/td/glean_title.xsl" . [by built-in Axiom log:uri] 26: @forSome :_g24 . <http://www.w3.org/2001/sw/grddl-wg/td/glean_title.xsl> grddl:transformationProperty :_g24 . [by erasure from step 22] 27: @forSome :_g1, :_g6 . "http://www.w3.org/2001/sw/grddl-wg/td/glean_title.xsl" fn:doc :_g1 . ( :_g1 :_g6 ) gspec:resultTree [ gspec:rdfParse {<http://musicbrainz.org/mm-2.1/album/6b050dcf-7ab1-456d-9e1b-c3c41c18eed2> <http://purl.org/dc/elements/1.1/title> "Are You Experienced?" . } ] . [by erasure from step 7] 28: @forAll :G, :R, :RDFXML, :TP, :TXDOC, :TXNODE . { @forSome run:_g25 . ( :TXNODE :R ) gspec:resultTree :RDFXML . run:_g25 fn:doc :TXNODE . :RDFXML gspec:rdfParse :G . :TXDOC log:uri run:_g25; grddl:transformationProperty :TP . } log:implies {:R :TP :G . } . [by erasure from step 9] 29: ... [by rule from step 28 applied to steps [25, 26, 27] with bindings {'TXDOC': '<http://www.w3.org/2001/sw/grddl-wg/td/glean_title.xsl>', '_g_L111C11': '"http....xsl"', 'G': '{6b050dcf-7ab1-456d-9e1b-c3c41c18eed2 dc:title "Are ...ced?"}', 'TP': '[...]', 'R': '<grddl-rule-tests.n3#_g6>', 'RDFXML': '[...]', 'TXNODE': '<grddl-rule-tests.n3#_g1>'}] 30: @forSome :_g24, g:_g6 . g:_g6 :_g24 {<http://musicbrainz.org/mm-2.1/album/6b050dcf-7ab1-456d-9e1b-c3c41c18eed2> <http://purl.org/dc/elements/1.1/title> "Are You Experienced?" . } . [by erasure from step 29] 31: @forAll :G, :IR, :R, :TP . { @forSome run:_g26, run:_g27 . run:_g26 fn:doc :R . run:_g27 grddl:transformationProperty :TP . :IR log:uri run:_g26 . :R grddl:transformation run:_g27; :TP :G . } log:implies {:IR grddl:result :G . } . [by erasure from step 9] 32: ... [by rule from step 31 applied to steps [1, 12, 23, 24, 30] with bindings {'_g_L24C13': '"http...html"', '_g_L25C25': '<http://www.w3.org/2001/sw/grddl-wg/td/glean_title.xsl>', 'G': '{6b050dcf-7ab1-456d-9e1b-c3c41c18eed2 dc:title "Are ...ced?"}', 'IR': '<http://www.w3.org/2001/sw/grddl-wg/td/titleauthor.html>', 'TP': '[...]', 'R': '<grddl-rule-tests.n3#_g6>'}] 33: <http://www.w3.org/2001/sw/grddl-wg/td/titleauthor.html> :result {<http://musicbrainz.org/mm-2.1/album/6b050dcf-7ab1-456d-9e1b-c3c41c18eed2> <http://purl.org/dc/elements/1.1/title> "Are You Experienced?" . } . [by erasure from step 32]

Changes

$Log: spec_rules.html,v $
Revision 1.11  2007/04/26 15:07:32  connolly
introduce htmlBase

Revision 1.10  2007/03/01 17:45:09  connolly
fix httpLink id

Revision 1.9  2007/03/01 17:44:32  connolly
add doctype for pubrules-happiness

Revision 1.8  2007/02/20 18:24:45  connolly
simplify HTML linking constructs while mixing in HTTP stuff

Revision 1.7  2007/02/20 01:38:07  connolly
elaborated rules appendix; rationalized namespaces

Revision 1.6  2007/02/15 18:34:39  connolly
2 more steps to get to the relevant result

Revision 1.5  2007/02/15 06:58:48  connolly
replace nicely marked-up proof with one that's
un-retouched (other than truncation after the first
interesting result at step 24 of 149)

Revision 1.4  2007/02/15 06:54:22  connolly
add x:xpath in 2007/ont/xml namespace
add webarch namespace (not sure it's needed)

Revision 1.3  2007/02/07 08:21:50  connolly
move mechanical rule explanation to this separate file