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a dark triples solution for OWL

From: Peter F. Patel-Schneider <pfps@research.bell-labs.com>
Date: Thu, 22 Aug 2002 17:42:05 -0400
To: www-webont-wg@w3.org
Message-Id: <20020822174205A.pfps@research.bell-labs.com>

Hi:

I put together a quick draft of how a dark triples solution for OWL might
work.  Unfortunately, there are artifacts.

There is no mention of ``dark triples'' below, but they would be the ones
removed when going to the RDF portion of an RDF/OWL KB.

peter


This is the outline of a treatment of OWL as an extension of RDF where the
OWL domain of discourse is the same as the RDF domain of discourse.
It does not handle, so far, datatypes.  Also, it doesn't work - the reasons
for various failures are indicated below.


An OWL knowledge base is as in the OWL Web Ontology Language 1.0 Abstract
Syntax document.  

A OWL knowledge base with separated names is an OWL knowledge base where 
1/ no name is used as more than one of <datatypeID>, <classID>,
   <individualID>, <datavaluedPropertyID>, and
   <individualValuedPropertyID>; and
2/ no name from the rdf: or rdfs: namespaces is used as a <datatypeID>,
   <classID>, <individualID>, <datavaluedPropertyID>, or
   <individualValuedPropertyID>;
[[NOTE:  The separation of names is required to prevent the conflation of
	 classes, properties, and individuals in RDF from showing up in
	 OWL.]] 

An RDF/OWL knowledge base is the result of mapping an OWL knowledge base
with separated names using the mapping to RDF triples in the OWL Web
Ontology Language 1.0 Abstract Syntax document, with the following changes:
1/ Individual(<ID> type=<type1> ... type=<typen> 
			 (<ID1> <value1>) (<IDm> <valuem>>))
   is mapped to
   <ID> rdf:type T(<type1>) .  ... <ID> rdf:type T(<typen>) .
   <ID> <ID1> T(value1>) . ... <ID> <IDm> T(valuem>) .
[[NOTE: This is done so as to remove an unneeded owl:sameIndividualAs
	from <ID> to a bnode used in the other triples.]]
2/ <X> owl:sameClassAs <Y> .
   is replaced by
   <X> rdfs:subClassOf <Y> .
   <Y> rdfs:subClassOf <X> .
3/ <X> owl:samePropertyAs <Y> .
   is replaced by
   <X> rdfs:subPropertyOf <Y> .
   <Y> rdfs:subPropertyOf <X> .


The RDF portion of an RDF/OWL knowledge base consists of those triples in
the RDF/OWL knowledge base that 
1/ do *not* have a property from the owl:, rdf:, or rdfs: namespaces, 
   except for rdf:type, rdfs:subClassOf, and rdfs:subPropertyOf.
[[WARNING:  The treatment of rdfs:subClassOf and rdfs:subPropertyOf is more
	    shaky than the rest of this effort.]]
2/ do not mention rdf:List, owl:Class, owl:DatatypeProperty,
   owl:ObjectProperty, owl:SymmetricProperty, 
   owl:FunctionalProperty, owl:InverseFunctionalProperty, 
   owl:TransitiveProperty, or owl:Restriction.


Let KB be an OWL knowledge base with separated names.
Let KBRO be the RDF/OWL knowledge base version of KB.
Let KBR be the RDF portion of KBRO. 


An RDF/OWL interpretation, I', of an RDF knowledge base with separated
names and vocabulary V', KB, is an RDFS interpretation of KBR, 
I = < R, EXT, S > with vocabulary V, plus  
	EC : V' -> 2^R u 2^LV
	ER : V' -> 2^(RxR) u 2^(RxLV)
	S' : V' -> R
such that <R, EXT, S, EC, ER> is an OWL interpretation of I'
as defined in Section 2 of the Model-Theoretic Semantics for OWL (trading
the datatype stuff for a single string domain whose value space is LV).

[[NOTE:  V contains the rdf: and rdfs: vocabulary, but V' does not.]]

As well, for any d,e in R, v' in V', and l in LV,

  S(v') = S'(v')

  <d,e> in ER(v')  iff  <d,e> in EXT(S'(v'))
  <d,l> in ER(v')  iff  <d,l> in EXT(S'(v'))
	
[[FAILURE: This requires the presence of elements of IR corresponding to
	    each extensionally-different property.  Although these elements
	    can be overlaid on top of the individuals and cannot be
	    referenced directly, they may increase the size of IR, with
	    noticeable effects.]] 

  d in EC(v')  iff  <d,S'(v')> in EXT(S(rdf:type))

[[FAILURE: This requires the presence of IR corresponding to each
	    extensionally-different class and for rdf:type.  Although these
	    elements can be overlaid on top of the individuals and cannot
	    be referenced directly, they may increase the size of IR, with
	    noticeable effects.]] 

[[FAILURE: There must be elements of IR that are the image of rdf:Property,
	   rdf:Statement, ..., rdf:Seq, ..., rdf:_1, ..., rdfs:domain,
	   ... rdfs:subClassOf, rdfs:subPropertyOf under S.  I believe that
	   many of these can be mapped into a single element of R whose
	   class extension would be R and whose extension would be
	   Rx(RuLV), but they increase the size of IR, with noticeable
	   effects.]]


RDF/OWL entailment is defined on RDF knowledge bases using RDF/OWL
interpretations in the obvious way.


Conjecture:  Given two OWL knowledge bases with separated names, K and Q, 
	     K OWL entails Q  iff  K RDF/OWL entails Q.
Received on Thursday, 22 August 2002 17:42:13 GMT

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