Mapping to RDF Graphs

W3C Editor's Draft 26 November 2008

This version:

http://www.w3.org/2007/OWL/draft/ED-owl2-mapping-to-rdf-20081126/

Latest editor's draft:

http://www.w3.org/2007/OWL/draft/owl2-mapping-to-rdf/

Previous version:

http://www.w3.org/2007/OWL/draft/ED-owl2-mapping-to-rdf-20081121/ (color-coded diff)

Editors:

Peter F. Patel-Schneider, Bell Labs Research, Alcatel-Lucent

Boris Motik, Oxford University

Contributors:

Bernardo Cuenca Grau, Oxford University

Ian Horrocks, Oxford University

Bijan Parsia, The University of Manchester

Note: The complete list of contributors is being compiled and will be included in the next draft.

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Copyright © 2008 W3C^® (MIT, ERCIM, Keio), All Rights Reserved. W3C liability, trademark and document use rules apply.

Abstract

Status of this Document

May Be Superseded

This section describes the status of this document at the time of its publication. Other documents may supersede this document. A list of current W3C publications and the latest revision of this technical report can be found in the W3C technical reports index at http://www.w3.org/TR/.

Set of Documents

This document is being published as one of a set of 11 documents:

1. Structural Specification and Functional-Style Syntax
2. Direct Semantics
3. RDF-Based Semantics
4. Conformance and Test Cases
5. Mapping to RDF Graphs (this document)
6. XML Serialization
7. Profiles
8. Quick Reference Guide
9. New Features and Rationale
10. Manchester Syntax
11. rdf:text: A Datatype for Internationalized Text

Please Comment By 2008-11-28

The OWL Working Group seeks public feedback on these Working Drafts. Please send your comments to public-owl-comments@w3.org (public archive). If possible, please offer specific changes to the text that would address your concern. You may also wish to check the Wiki Version of this document for internal-review comments and changes being drafted which may address your concerns.

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This document defines mappings by means of which every OWL 2 ontology [OWL 2 Specification] can be mapped into an RDF graph and back. These transformations do not incur any change in the formal meaning of the ontology. More precisely, let O be any OWL 2 ontology, let T(O) be the RDF graph obtained by transforming O as specified in Section 2, and let O' be the OWL 2 ontology obtained by applying the reverse transformation from Section 3 to T(O); then, O and O' are logically equivalent — that is, they have exactly the same set of models.

The mappings presented in this document are backwards-compatible with that of OWL DL: every OWL DL ontology encoded as an RDF graph can be mapped into a valid OWL 2 ontology using the reverse-transformation from Section 3 such that the resulting OWL 2 ontology has exactly the same set of models as the original OWL DL ontology.

The syntax for triples used in this document is the one used in the RDF Semantics [RDF Semantics]. Full URIs are abbreviated using the namespaces from the OWL 2 Specification [OWL 2 Specification]. OWL 2 ontologies mentioned in this document should be understood as instances of the structural specification of OWL 2 [OWL 2 Specification]; when required, these are written in this document using the functional-style syntax.

The following notation is used throughout this document for referring to parts of RDF graphs:

• *:x denotes a URI reference;
• _:x denotes a blank node;
• x denotes a blank node or a URI reference; and
• lt denotes a literal.

The italicized keywords MUST, MUST NOT, SHOULD, SHOULD NOT, and MAY specify certain aspects of the normative behavior of OWL 2 tools, and are interpreted as specified in RFC 2119 [RFC 2119].

This section defines a mapping of an OWL 2 ontology O into an RDF graph T(O). The mapping is presented in three parts. Section 2.1 shows how to translate axioms that do not contain annotations, Section 2.2 shows how to translate annotations, and Section 2.3 shows how to translate axioms containing annotations.

The definition of the operator T uses the operator TANN in order to translate annotations. The operator TANN is defined in Section 2.2. It takes an annotation and an URI reference or a blank node and produces the triples that attach the annotation to the supplied object.

In the mapping, each generated blank node (i.e., each blank node that does not correspond to an anonymous individual) is fresh in each application of a mapping rule. Furthermore, the following conventions are used in this section to denote different parts of OWL 2 ontologies:

• OP denotes an object property;
• OPE denotes an object property expression;
• DP denotes a data property;
• DPE denotes a data property expression;
• PE denotes an object or a data property expression;
• AP denotes an annotation property;
• C denotes a class;
• CE denotes a class expression;
• DT denotes a datatype;
• DR denotes a data range;
• U denotes a URI;
• F denotes a constraining facet;
• a denotes an individual (named or anonymous);
• *:a denotes a named individual;
• lt denotes a literal;
• as denotes an annotation source; and
• av denotes an annotation value.

In this section, T(SEQ y₁ ... y_n) denotes the translation of a sequence of objects from the structural specification into an RDF list, as shown in Table 1.

An RDF syntax ontology document is a sequence of octets accessible from some URI by means of the standard protocols that can be parsed into an RDF graph G, which can then be transformed into an OWL 2 ontology according to the canonical RDF parsing process defined in this section. This parsing process is specified as an instance of canonical parsing, defined in Section 3.6 of the OWL 2 Specification [OWL 2 Specification]. It is important to understand that canonical RDF parsing merely defines the result of the transformation. An OWL 2 implementation MAY implement whatever algorithm it chooses; however, the result MUST be structurally equivalent to the result of canonical RDF parsing.

Canonical RDF parsing maintains the following functions that map a URI reference or a blank node x occurring in G into an object of the structural specification. In particular,

• CE(x) maps x into a class expression,
• DR(x) maps x into a data range,
• OPE(x) maps x into an object property expression,
• DPE(x) maps x into a data property expression, and
• AP(x) maps x into an annotation property.

Initially, these functions are undefined for all URIs and blank nodes occurring in G; this is written as CE(x) = ε, DR(x) = ε, OPE(x) = ε, DPE(x) = ε, and AP(x) = ε. The functions are updated as parsing progresses. All of the following conditions MUST be satisfied at any given point in time during parsing.

• For each x, at most one of OPE(x), DPE(x), and AP(x) is defined.
• For each x, at most one of CE(x) and DR(x) is defined.

Furthermore, the value of any of these functions for any x MUST NOT be redefined during parsing (i.e., if a function is not undefined for x, no attempt should be made to change the function's value for x).

The function OPEorDPE is defined as follows:

• OPEorDPE(x) = OPE(x) if OPE(x) ≠ ε;
• OPEorDPE(x) = DPE(x) if DPE(x) ≠ ε; and
• OPEorDPE(x) = ε otherwise.

The following sections contain rules in which triple patterns are matched to G. The notation NN_INT(n) can be matched to any literal whose value n is a nonnegative integer.

Additional conditions on the pattern are enclosed in curly braces { }. Some patterns use optional parts, which are enclosed in square brackets '[ ]'. If a pattern contains a variable number of triples, the maximal possible subset of G MUST be matched.

The abbreviation T(SEQ y₁ ... y_n) denotes the pattern corresponding to RDF lists, as shown in Table 3. This is similar to the mapping for lists presented in Table 1, but here the abbreviation is used to recognize lists instead of mapping them into RDF.

• The ontology document accessible from the URI *:y is retrieved as specified in Section 3.2.2 of the OWL 2 Specification [OWL 2 Specification].
• The document is parsed into an RDF graph G' using an appropriate RDF syntax.
• If the parsing succeeds and the graph G' does not contain a triple of the form
  z rdf:type owl:Ontology
  then G' is merged (as in RDF Semantics [RDF Semantics]) into G and the triple
  x owl:imports *:y
  is removed from G.

Next, the set of declarations Decl(G) is extracted from G according to Table 7. The matched triples are not removed from G — the triples from Table 7 can contain annotations so, in order to correctly parse the annotations, they will be matched again in the step described in Section 3.6.

Finally, the set RIND of anonymous individuals used in reification is identified. This is done by initially setting RIND = ∅ and then applying the patterns shown in Table 8. The matched triples are not deleted from G.

Next, for each ontology URI U imported into G, the document of the ontology identified by U is accessed as specified in Section 3.2.2 of the OWL 2 Specification [OWL 2 Specification]. The ontology header and the declarations of that document are determined according to the rules of the syntax in which the document was written, and the process is repeated recursively until the header and the declarations of all ontologies in the import closure of G are determined.

The set AllDecl(G) of all declarations is computed by taking the union of the set Decl(G), the sets Decl(D') for each ontology document D' imported (directly or indirectly) into G, and the declarations for built-in entities from Table 9 of the OWL 2 Specification [OWL 2 Specification]. The set AllDecl(G) MUST satisfy the typing constraints from Section 5.8.1 of the OWL 2 Specification [OWL 2 Specification].

Next, the functions CE, DR, OPE, DPE, and AP are initialized as shown in Table 9.

An instance O of the Ontology class from the structural specification is created with the header as determined in Section 3.2. Let x be the node that was matched in G to *:x or _:x according to the patterns from Table 4; then, ANN(x) determines the set of ontology annotations of O.

Next, functions OPE, DR, and CE are extended as shown in Tables 11, 12, and 13, as well as in Tables 14 and 15. The patterns in the latter two tables are not generated by the mapping from Section 2, but they can be present in RDF graphs that encode OWL DL ontologies. Each time a pattern is matched, the matched triples are removed from G. Pattern matching is repeated until no triple pattern can be matched to G.

Next, O is populated with axioms. For clarity, the axiom patterns are split into two tables.

• Table 16 presents the patterns for axioms without annotations.
• Annotated axioms are parsed as follows:
  • In case of the patterns for owl:AllDisjointClasses, owl:AllDisjointProperties, owl:AllDifferent, and owl:NegativePropertyAssertion, axiom annotations are defined by ANN(_:x).
  • For all other axioms, axiom annotations are obtained by additionally matching patterns from Table 17 in G during axiom matching.

The axioms in G are parsed as follows:

• All annotated axioms are parsed first.
• Only when no pattern for annotated axioms can be matched in G, then the patterns for axioms without annotations are matched.

In either case, each time a triple pattern is matched, the matched triples are removed from G.

Next, for each blank node or URI reference x such that x ∉ RIND, and for each annotation Annotation( annotation₁ ... annotation_n AP y ) ∈ ANN(x) with n possibly being equal to zero, the following annotation assertion is added to O:

Finally, the patterns from Table 18 are matched in G, the resulting axioms are added to O. These patterns are not generated by the mapping from Section 2, but they can be present in RDF graphs that encode OWL DL ontologies. (Note that the patterns from the table do not contain triples of the form *:x rdf:type owl:Class because such triples are removed while parsing the entity declarations, as specified in Section 3.2.) Each time a triple pattern is matched, the matched triples are removed from G.

At the end of this process, the graph G MUST be empty.

The structure of O is checked, and O MUST be an OWL 2 ontology — that is, it must satisfy all the restrictions listed in Section 3 of the OWL 2 Specification [OWL 2 Specification].

[OWL 2 Specification]

Structural Specification and Functional-Style Syntax Boris Motik, Peter F. Patel-Schneider, Bijan Parsia, eds. W3C Editor's Draft, 26 November 2008, http://www.w3.org/2007/OWL/draft/ED-owl2-syntax-20081126/. Latest version available at http://www.w3.org/2007/OWL/draft/owl2-syntax/.

[RDF Semantics]

RDF Semantics. Patrick Hayes, Editor, W3C Recommendation, 10 February 2004

[RFC 2119]

RFC 2119: Key words for use in RFCs to Indicate Requirement Levels. Network Working Group, S. Bradner. Internet Best Current Practice, March 1997