RIF RDF and OWL Compatibility

W3C Editor's Draft 22 February10 April 2008

This version:

http://www.w3.org/2005/rules/wg/draft/ED-rif-rdf-owl-20080222/http://www.w3.org/2005/rules/wg/draft/ED-rif-rdf-owl-20080410/

Latest editor's draft:

http://www.w3.org/2005/rules/wg/draft/rif-rdf-owl/

Previous version:

http://www.w3.org/2005/rules/wg/draft/ED-rif-rdf-owl-20080219/http://www.w3.org/2005/rules/wg/draft/ED-rif-rdf-owl-20080222/ (color-coded diff)

Editors:

Jos de Bruijn, Free University of Bozen/Bolzano

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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May Be Superseded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 53 documents:

1. RIF Basic Logic Dialect
2. RIF Framework for Logic Dialects
3. RIF Data Types and Built-Ins RIF Use Cases and Requirements RIFRDF and OWL Compatibility (this document)

Note for Working Group

This draft is ready for Working Group Review. A publication decision is scheduled for 15 April.

Please Comment By 19 February 20082008-04-14

The Rule Interchange Format (RIF) Working Group seeks public feedback on these Working Drafts. Please send your comments to public-rif-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.

No Endorsement

Publication as a Working Draft does not imply endorsement by the W3C Membership. This is a draft document and may be updated, replaced or obsoleted by other documents at any time. It is inappropriate to cite this document as other than work in progress.

Patents

This document was produced by a group operating under the 5 February 2004 W3C Patent Policy. W3C maintains a public list of any patent disclosures made in connection with the deliverables of the group; that page also includes instructions for disclosing a patent. An individual who has actual knowledge of a patent which the individual believes contains Essential Claim(s) must disclose the information in accordance with section 6 of the W3C Patent Policy.

The Rule Interchange Format (RIF), specifically the Basic Logic Dialect (BLD) [(RIF-BLD ], defines), is a meansformat for the interchange of (logical)interchanging logical rules over the Web. Rules whichthat are exchanged using RIF may refer to external data sources and may be based on certaindata models whichthat are represented using a language different from RIF. The Resource Description Framework RDF [(RDF-Concepts ]) is a Web-based language for the representation and exchange of data; RDF Schema (RDFS) [(RDF-Schema ]) and the Web Ontology Language OWL [(OWL-Reference ]) are Web-based languages for the representationrepresenting and exchange ofexchanging ontologies (i.e., data models). This document specifies how combinations of RIF BLD Rule setsRulesets and RDF data and RDFS and OWL ontologies must be interpreted.interpreted; i.e., it specifies how RIF interoperates with RDF/OWL.

The RIF working group plans to develop further dialects besides BLD, most notably a dialect based on Production Rules [(RIF-PRD ];); these dialects are not necessarily extensions of BLD. Future versions of this document willmay address compatibility of these dialects with RDF and OWL as well. In the remainder of the document, when mentioning RIF, we meanRIF is understood to refer to RIF BLD [(RIF-BLD ].).

RDF data and RDFS and OWL ontologies are represented using RDF graphs. Several syntaxes have been proposed for the exchange of RDF graphs, the normative syntax being RDF/XML [(RDF-Syntax ], which is an XML-based format.). RIF does not provide a format for exchanging RDF;RDF graphs, since this would be a duplication. Instead, it is assumed that RDF graphs are exchanged using RDF/XML, or any other syntax that can be used for representing or exchanging RDF graphs.

This document does not, as yet, define whether or how RDF documents/graphs should be referred to from RIF rule sets. The specification of combinations in this document does not depend on (the existence of) this mechanism: it applies in case an RIF rule sets explicity points to (one or more) RDF documents, but also in case the references to the RDF document(s) are not interchanged using RIF, but using some other (out of bounds) mechanism.A typical scenario for the use of RIF with RDF/OWL includesis the exchange of rules whichthat either use RDF data or an RDFS or OWL ontology. In terms of rule interchange the scenario is the following:ontology: an interchange partner A has a rules language whichthat is RDF/OWL-aware, i.e., it allows tosupports the use of RDF data, it uses an RDFS or OWL ontology, or it extends RDF(S)/OWL. A sends its rules (using RIF),using RIF, possibly with a referencereferences to the appropriate RDF graph(s), to partner B. B can now translatereceives the RIFrules into its own rules language, retrieveand retrieves the referenced RDF graph(s) (which is published most likely using RDF/XML), and process(published as, e.g., RDF/XML (RDF-SYNTAX)). The rules in its ownare translated to the internal rules language of B and are processed, together with the RDF graphs, using the RDF/OWL-aware rule engine, which is also RDF/OWL-aware.engine of B. The use case Vocabulary Mapping for Data Integration [(RIF-UCR ]) is an example of the interchange of RIF rules whichthat use RDF graphs.data and RDFS ontologies.

A specialization of this use casescenario is the publication of RIF rules whichthat refer to RDF graphs (notice thatgraphs: publication is a specificspecial kind of interchange). In such a scenario,interchange. A rule publisher A publishes its rules on the Web. There may be several consumers whothat retrieve the RIF rules and RDF graphs from the Web, andtranslate the RIF rules to their own rules languages.languages, and process them together with the RDF graphs in their own rules engine. The use case Publishing Rules for Interlinked Metadata [(RIF-UCR ] is an example of) illustrates the publication of RIF rules related to RDF graphs.scenario.

Another specialization of this use casethe exchange scenario is the interchange of rule extensions to OWL [(RIF-UCR ].). The intention of the rule publisher in this scenario is to extend an OWL ontology with rules: interchange partner A has a rules language that extends OWL. A splits its ontology+rules description into a separate OWL ontology and ana RIF rule set,ruleset, publishes the OWL ontology, and sends (or publishes) the RIF rule set,ruleset, which includes a reference to the OWL ontology. The consumersA consumer of the rules retrieves the OWL ontology,ontology and translates the ontology and the rule setruleset into a combined ontology+rules description in its own rules language which also extendsrule extension of OWL.

AnA RIF rule set whichruleset that refers to RDF graphs,graphs and/or RDFS/OWL ontologies, or any use of ana RIF rule setruleset with RDF graphs, is viewed as a combination of an RIF rule seta ruleset and a number of RDF graphs.graphs and ontologies. This document specifies how, in such a combination, the rule set interacts withruleset and the RDF graphs. With "interaction" we meangraphs and ontologies interoperate in a technical sense, i.e., the conditions under which the combination is satisfiable,satisfiable (i.e., consistent), as well as the entailments defined for(i.e., logical consequences) of the combination. The interaction between RIF and RDF and OWLRDF/OWL is realized by connecting the model theory of RIF (specified in [(RIF-BLD ]))) with the model theories of RDF (specified in [(RDF-Semantics ]))) and OWL (specified in [(OWL-Semantics ]),)), respectively.

The RDF semantics specification [ RDF-Semantics ] defines 4 notions of entailment for RDF graphs. AtThroughout this stage it has not yet been decided which of these notions are of interest in RIF. Therefore, we specifydocument the interaction betweenfollowing conventions are used when writing RIF and RDF for all 4 notions. EDITOR'S NOTE: Currently, this document only defines how combinations of RIF rule setsstatements in examples and definitions.

• RIF constants in the symbol space rif:iri, i.e., constants that are absolute IRIs, are abbreviated. Specifically, constants of the form "absolute-IRI"^^rif:iri are written as compact IRIs (CURIE), i.e., as prefix:localname, where prefix is understood to refer to an IRI namespace-IRI, and prefix:localname stands for the IRI (absolute-IRI) obtained by concatenating namespace-IRI and localname.
• RDF triples are written using the Turtle syntax (Turtle): for the purposes of this document, triples are written as s p o, where s, p, o are IRIs delimited with '<' and '>', compact IRIs prefix:localname, or typed literals "literal"^^datatype-IRI.
• The following namespace prefixes are used throughout this document: ex refers to the example namespace http://example.org/example#, xsd refers to the XML schema namespace http://www.w3.org/2001/XMLSchema#, rdf refers to the RDF namespace http://www.w3.org/1999/02/22-rdf-syntax-ns#, rdfs refers to the RDFS namespace http://www.w3.org/2000/01/rdf-schema#, owl refers to the OWL namespace http://www.w3.org/2002/07/owl#, and rif refers to the RIF namespace http://www.w3.org/2007/rif#.

The RDF semantics specification (RDF-Semantics) defines four notions of entailment for RDF graphs. At this stage it has not been decided which of these notions are of interest in RIF. The OWL semantics specification (OWL-Semantics) defines two notions of entailment for OWL ontologies, namely OWL Lite/DL and OWL Full; both notions are of interest in RIF. This document specifies the interaction between RIF and RDF/OWL for all six notions.

EDITOR'S NOTE: Currently, this document only defines how combinations of RIF rulesets and RDF/OWL should be interpreted; it does not suggest how references to RDF graphs and OWL ontologies are specified in RIF, nor does it specify which of the RDFRDF/OWL entailment regimes (simple, RDF, RDFS, or D)D, OWL DL, OWL Full) should be used. Finally, there are two notions of interoperation with OWL DL: one that does not consider annotation properties, and one that does it is an open issue whether this distinction should be reflected in the syntax. Possible ways to refer to RDF graphs and RDFS/OWL ontologies include annotations in RIF rule setsrulesets and extensions of the syntax of RIF. Note that no agreement has yet been reached on this issue, and that especially the issue of the specification of entailment regimes is controversial (see http://lists.w3.org/Archives/Public/public-rif-wg/2007Jul/0030.html and the ensuing thread). See the Annotations page for a proposal for extending RIF with annotations.

The #Appendix: Embedding RDF CombinationsEmbeddings (Informative) describes how reasoning with combinations of RIF rules with RDF and a subset of OWL DL can be reduced to reasoning with RIF rule sets,rulesets, which can be seen as a guide to describing how ana RIF processor could be turned into an RDF-awareRDF/OWL-aware RIF processor. This reduction can be seen as a guide for interchange partners whichthat do not have RDF-aware rule systems, but stillwant to be able to process RIF rules whichthat refer to RDF graphs. In terms of the scenario above:aforementioned scenario: if the interchange partner B does not have an RDF-awareRDF/OWL-aware rule system, but B can process RIF rules, then the appendix explains how theB's rule system could be used for processing combinations. EDITOR'S NOTE: The future status of the appendix with the embedding is uncertain . The appendix is not about interchange, but rather about possible implementation, so it can be argued that it should not be included in this document. On the other hand, many think the appendix is useful. If we decide not to include it in this document, we might consider publishing it as a separate note (not recommendation-track document).RIF-RDF.

 john brotherOf jack . jack parentOf maryex:john ex:brotherOf ex:jack . 
ex:jack ex:parentOf ex:mary . 

Forall ?x, ?y, ?z  (?x["uncleOf"^^rif:iri ->(?x[ex:uncleOf -> ?z] :- 
      And( ?x["brotherOf"^^rif:iri ->And(?x[ex:brotherOf -> ?y]  ?y["parentOf"^^rif:iri ->?y[ex:parentOf -> ?z]))

Typed literals in RDF may be ill-typed, which means that the literal string is not part of the lexical space of the datatype under consideration. Examples of such ill-typed literals are "abc"^^xsd:integer"abc"^^xsd:integer, "2"^^xsd:boolean"2"^^xsd:boolean, and "<non-valid-XML"^^rdf:XMLLiteral"<non-valid-XML"^^rdf:XMLLiteral. Ill-typed literals are not expected to be used very often. However, as the RDF recommendation (RDF-Concepts) allows creating RDF graphs with ill-typed literals, their occurrence cannot be completely ruled out.

Rules whichthat include ill-typed symbols are not well-formedlegal RIF rules, so there are no RIF symbols whichthat correspond to ill-typed literals. However,As with blank nodes, variables may quantifydo range over objects denoted by such literals. The following example illustrates the interaction between RDF and RIF in the face of ill-typed literals and blank nodes.

Consider a combination of an RDF graph whichthat contains the triple

_:x  hasName "a"^^xsd:integerex:hasName "a"^^xsd:integer . 

saying that there is some blank node whichthat has a name, which is an ill-typed literal, and ana RIF rule set whichruleset that contains the rules

Forall ?x, ?y ( ?x[rdf:type  -> "nameBearer"^^rif:iri]-> ex:nameBearer] :-  ?x["hasName"^^rif:iri ->?x[ex:hasName -> ?y] )
Forall ?x, ?y (  " http://a "^^rif:iri[" http://p "^^rif:iri ->"http://a"^^rif:iri["http://p"^^rif:iri -> ?y] :-  ?x["hasName"^^rif:iri ->?x[ex:hasName -> ?y] )

which say that whenever there is a some x whichthat has some name y, then x is of type nameBearerex:nameBearer and http://a has a property http://p with value y.

From this combination we can derivethe following RIF condition formulasformula can be derived:

Exists ?z ( And( ?z[rdf:type  -> "nameBearer"^^rif:iri] ) Exists ?z ( " http://a "^^rif:iri[" http://p "^^rif:iri ->-> ex:nameBearer]  "http://a"^^rif:iri["http://p"^^rif:iri -> ?z]  ) as well))

as can the following RDF triplestriples:

_:y rdf:type  nameBearerex:nameBearer .
 < http://a > < http://p > "a"^^xsd:integer<http://a> <http://p> "a"^^xsd:integer . 

However, " http://a "^^rif:iri[" http://p "^^rif:iri -> "a"^^xsd:integer]"http://a"^^rif:iri["http://p"^^rif:iri -> "a"^^xsd:integer] cannot be derived, because it is not a well-formed RIF formula, due to the fact that "a""a" is not an integer; it is not in the lexical space of the datatype xsd:integer.

This remainder of this section formally defines combinations of RIF rules with RDF graphs and the semantics of such combinations. Combinations are pairsA combination consists of a RIF rule setsruleset and setsa set of RDF graphs. The semantics of combinations is defined in terms of combined models, which are pairs of RIF and RDF interpretations. The interaction between the two interpretations is defined through a number of conditions. Entailment is defined as model inclusion, as usual.

An RDF vocabulary V consists of the following sets of names:

• absolute IRIs V_U, (correspond(corresponds to the Concepts and Abstract Syntax term ""RDF URI references ";"; see the [(End note on RDF URI references ])))

• plain literals V_PL (i.e., character strings with an optional language tag), and

• typed literals V_TL (i.e., pairs of character strings and datatype IRIs).

The syntax of the names in these sets is defined in RDF Concepts and Abstract Syntax [(RDF-Concepts ].). Besides these names, there is an infinite set of blank nodes, which is disjoint from the sets of literals and IRIs.

DEFINITION: Given an RDF vocabulary V, a generalized RDF graphtriple of V is a setstatement of generalized RDF triplesthe form s p o ., where s, p and o are names in V or blank nodes.

DEFINITION: Given an RDF vocabulary V, a generalized RDF graph is a set of generalized RDF triples of V.

(See the [(End note on generalized RDF graphs ])))

Even though RDF allows the use of arbitrary datatype IRIs in typed literals, not all such datatype IRIs are recognized in the semantics. In fact, simple entailment does not recognize any datatype and RDF and RDFS entailment recognize only the datatype rdf:XMLLiteral. Furthermore, RDF allows expressing typed literals for which the literal string is not in the lexical space of the datatype; such literals are called ill-typed literals. RIF, in contrast, does not allow ill-typed literals in the syntax. To facilitate discussing datatypes, and specifically datatypes supported in specific contexts (required for D-entailment), we usethe notion of datatype maps [(RDF-Semantics ].) is used.

A datatype map is a partial mapping from IRIs to datatypes.datatypes.

RDFS, specifically D-entailment, allows the use of arbitrary datatype maps, as long as the rdf:XMLLiteral datatype is considered.included in the map. RIF BLD additionally requires the following datatypes to be considered: xsd:long ,included: xsd:string, xsd:integer ,xsd:decimal, xsd:time, xsd:date, xsd:dateTime, and rif:text; we callthese datatypes are the RIF-required datatypes. We define the notion ofA conforming datatype map asis a datatype map whichthat recognizes at least the RIF-required datatypes.

DEFINITION: A datatype map D is a conforming datatype map if it satisfies the following conditions 1.conditions:

1. No RIF-supported symbol space whichthat is not an RIF-requireda datatype (these are rif:local and rif:iri in RIF BLD) is in the domain of D.
2. 2.The IRIs identifying all RIF-required datatypes are in the domain of D.
3. 3.D maps IRIs identifying XML schema datatypes to the respective data types [(XML-SCHEMA2 ],), rdf:XMLLiteral to the rdf:XMLLiteral datatype [(RDF-Concepts ],), and rif:text to the rif:text primitive datatype [(RIF-BLD ]. We now define).

The notions of well- and ill-typed literals, whichliterals loosely correspond to the notions of well-formedlegal and ill-formedillegal symbols in RIF.RIF:

DEFINITION: Given a conforming datatype map D, a typed literal (s, d) is a well-typed literal if

1. 1.d is in the domain of D and s is in the lexical space of D(d),
2. 2.d is the IRI of a symbol space supported by RIF BLD and s is in the lexical space of the symbol space, or
3. 3.d is not in the domain of D and does not identify a symbol space supported by RIF.

Otherwise (s, d) is an ill-typed literal.

DEFINITION: A RIF-RDF-combination is a pair < R,S >,>, where R is a Rule setRIF ruleset and S is a set of generalized RDF graphs of a vocabulary V.

When clear from the context, RIF-RDF combinationsRIF-RDF-combinations are referred to simply as combinations.

The RDF Semantics document [(RDF-Semantics ]) defines 4 (normative)four normative kinds of interpretations, as well as corresponding notions of satisfiability and entailment:

• simple interpretations, which do not poseimpose any conditions on the RDF and RDFS vocabularies,
• RDF interpretations, which impose additional conditions on the RDF vocabulary,
• RDFS interpretations, which impose additional conditions on the RDFS vocabulary, and
• D-interpretations, which impose additional conditions on the treatment of datatypes, relative to a datatype map D.

This distinction isThose four types of interpretations are reflected in the definitions of satisfaction and entailment in this section.

The correspondence between RIF semantic structures (interpretations) and RDF interpretations is defined through a number of conditions whichthat ensure the correspondence in the interpretation of names (i.e., IRIs and literals) and formulas, i.e., the correspondence between RDF triples of the form s p o .and RIF frames of the form s'[p' ->-> o'], where s', p', and o' are RIF symbols corresponding to the RDF symbols s, p, and o, respectively. We first reviewrespectively (cf. Table 1).

As defined in [(RDF-Semantics ],), a simple interpretation of a vocabulary V is a tuple I=< IR, IP, IEXT, IS, IL, LV >,>, where

• IR is a non-empty set of resources (the domain),
• IP is a set of properties,
• IEXT is an extension function, which is a mapping from IP into the power set of IR × IR,
• IS is a mapping from IRIs in V into (IR union IP),
• IL is a mapping from typed literals in V into IR, and
• LV is the set of literal values, which is a subset of IR, and includes all plain literals in V.

Rdf-, rdfs-, and D-interpretations are simple interpretations whichthat satisfy certain conditions:

• A simple interpretation I of a vocabulary V is an rdf-interpretation if V includes the RDF vocabulary and I satisfies the rdf axiomatic triples and the rdf semantic conditions.
• An rdf-interpretation I of a vocabulary V is an rdfs-interpretation if V includes the RDFS vocabulary and I satisfies the rdfs axiomatic triples and the rdfs semantic conditions.
• Given a datatype map D, an rdfs-interpretation I of a vocabulary V is a D-interpretation if V includes the IRIs in the domain of D and I satisfies the general semantic conditions for datatypes for every pair <d, D(d)>D(d)> such that d is in the domain of D.

As defined in [(RIF-BLD ],), a semantic structure is a tuple of the form I = <TV, DTS, D, D_ind, D_func, I_C, I_V, I_F, I_frame, I_SF, I_sub, I_isa, I₌, I_external, I_truth >. We restrict our attention here to>. The specification of RIF-RDF compatibility is only concerned with DTS, D, I_C, I_V, I_frame, I_sub, I_isa, and I _slottruth. The other mappings whichthat are parts of a semantic structure are not used in the definition of combinations.

• DTS is the set of datatypes, which have associated datatype identifiers,
• D is a non-emptyset (the domain),
• D_ind is a non-empty subset of D,
• I_C is a mapping from individual identifiers in Const to D_ind and from function symbols in Const to D,
• I_V is a mapping from Var to D_ind,
• andI_frame is (in BLD)a mapping from D_ind to truth-valuedfunctions of the form SetOfFiniteBags(D_ind × D_ind) → TV . 2.2.1.2 Common Interpretations DEFINITION: A common interpretation isD,
• I_sub is a mapping from D_ind × D_ind to D,
• I_isa is a mapping from D_ind × D_ind to D, and
• I_truth is a mapping from D to TV.

DEFINITION: A common-rif-rdf-interpretation is a pair (I, I), where I = <TV, DTS, D, D_ind, D_func, I_C, I_V, I_F, I_frame, I_SF, I_sub, I_isa, I₌, I_external, I_truth >> is ana RIF semantic structure and I=<IR, IP, IEXT, IS, IL, LV>LV> is an RDF interpretation of a vocabulary V, such that the following conditions hold 1. IR is a subset ofhold:

1. (IR union IP) = D_ind;
2. 2.IP is a superset of the set of all k in D_ind such that there exist some a, b in D_ind and I _{frame ( k )( a , b )=t (i.e. thetruth} value of(I_frame(k)(a,b ) is true ); 3. (IR union IP) = D))=t;
3. 4.LV is a subset of IR and asuperset of (D_ind intersection (union of allthe value spaces DSof all datatypes in DTS));
4. 5. IEXT(k)IEXT(k) = the set of all pairs (a, b), with a, b, and k in D_ind, such that I _slottruth(I_frame(k)(a,b )=))=t , for every k in D;
5. 6.IS(i) = I_C( "i"^^rif:iri"i"^^rif:iri) for every absolute IRI i in V_U;
6. 7.IL((s, d)) = I_C( "s"^^d"s"^^d) for every well-typed literal (s, d) in V_TL;
7. 8.IEXT(IS(rdf:type)) is equal to the set of all pairs <a,b><a,b> in D_ind × D_ind such that I_truth(I_isa(< a,b >)=t;>))=t; and
8. 9.IEXT(IS(rdfs:subClassOf)) is a superset of the set of all pairs <a,b><a,b> in D_ind × D_ind such that I_truth(I_sub(< a,b >)=t.>))=t.

Condition 1 ensures that all resources in an RDF interpretation correspond to elements in the RIF domain. Condition 2 ensures that the set of properties at least includes all elements which are used as properties in the RIF domain. Condition 3 ensures thatthe combination of resources and properties corresponds exactly to the RIF domain; note that if I is an rdf-, rdfs-, or D-interpretation, IP is a subset of IR, and thus IR=D. Condition 42 ensures that the set of RDF properties at least includes all elements that are used as properties in frames in the RIF domain. Condition 3 ensures that all concrete values in D are included in LV. Condition 54 ensures that RDF triples are interpreted in the same way as frame formulas. Condition 65 ensures that IRIs are interpreted in the same way. Finally,Condition 76 ensures that typed literals are interpreted in the same way. Note that no correspondences are defined for the mapping of names in RDF whichthat are not symbols of RIF, e.g., ill-typed literals and RDF URI references whichthat are not absolute IRIs. Condition 8 the7 ensures that typing in RDF and typing in RIF correspond, i.e.i.e., a rdf:type b is true iff a # b is true. Finally, condition 9 the8 ensures that whenever ana RIF subclass statement holds, the corresponding RDF subclass statement holds as well, i.e., a rdfs:subClassOf b is true if a ## b is true.

One consequence of conditions 65 and 76 is that IRIs of the form http://iri and typed literals of the form " http://iri "^^rif:iri which"http://iri"^^rif:iri that occur in an RDF graph are treated the same in RIF-RDF combinations,RIF-RDF-combinations, even if the RIF componentRuleset is empty. For example, consider an RIF-RDFthe combination withof an empty rule setruleset and an RDF graph whichthat contains the triple

 < http://a > < http://p > " http://b "^^rif:iri<http://a> <http://p> "http://b"^^rif:iri .
 

This combination allows to derive,the derivation of, among other things, the following triples: < http://a > < http://p > < http://b > . < http://a > " http://p "^^rif:iri " http://b "^^rif:iri . " http://a "^^rif:iri < http://p > " http://b "^^rif:iritriple:

<http://a> <http://p> <http://b> .

as well as the following frame formula:

 " http://a "^^rif:iri [" http://p "^^rif:iri -> " http://b "^^rif:iri]"http://a"^^rif:iri ["http://p"^^rif:iri -> "http://b"^^rif:iri]

DEFINITION: A common interpretationcommon-rif-rdf-interpretation (I, I) simple-satisfies an RIF-RDF combinationsatisfies a RIF-RDF-combination C=< R, S >> if I satisfiesis a model of R and I satisfies every RDF graph S in S; in this case (I, I) is called a simple model, or model, of C, and C is satisfiable. (I, I) satisfies a generalized RDF graph S if I satisfies S. (I, I) satisfies a closed RIFRIF-BLD condition formulaφ if TVal_I truth (φ)=((φ)=t.

Notice that not every combination is satisfiable. In fact, not every RIF rule setruleset has a model. For example, the rule setruleset consisting of the rule

Forall  ("1"^^xsd:integer="2"^^xsd:integer)("1"^^xsd:integer="2"^^xsd:integer)

does not have a model, since the symbols "1"^^xsd:integer"1"^^xsd:integer and "2"^^xsd:integer"2"^^xsd:integer are mapped to the (distinct) numbers 1 and 2, respectively, in every semantic structure.

Rdf-, rdfs-, and D-satisfiability are defined through additional restrictions on I:

DEFINITION: A model (I, I) of a combination C rdf-satisfiesis an rdf-model of C if I is an rdf-interpretation; in this case ( I , I) is called an rdf-model of C, andC is rdf-satisfiable.

DEFINITION: A model (I, I) of a combination C rdfs-satisfiesis an rdfs-model of C if I is an rdfs-interpretation; in this case ( I , I) is called an rdfs-model of C, andC is rdfs-satisfiable.

DEFINITION: Given a conforming datatype map D, a model (I, I) of a combination C D-satisfiesis a D-model of C if I is a D-interpretation; in this case ( I , I) is called a D-model of C, andC is D-satisfiable.

DEFINITION: Given a conforming datatype map D, an RIF-RDF combinationa RIF-RDF-combination C D-entails a generalized RDF graph S if every D-model of C satisfies S. Likewise, C D-entails a closed RIFRIF-BLD condition formulaφ if every D-model of C satisfies φ.

The other notions of entailment are defined analogously:

DEFINITION: A combination C simple-entails S (resp., φ) if every simple model of C satisfies S (resp., φ).

DEFINITION: A combination C rdf-entails S (resp., φ) if every rdf-model of C satisfies S (resp., φ).

DEFINITION: A combination C rdfs-entails S (resp., φ) if every rdfs-model of C satisfies S (resp., φ).

OWL [(OWL-Reference ]) specifies three increasingly expressive species, namely Lite, DL, and Full. OWL Lite is a syntactic subset of OWL DL, but the semantics is the same [(OWL-Semantics ].). Since every OWL Lite ontology is an OWL DL ontology, the Lite species is not explicitlyconsidered separately in the remainder.this document.

Syntactically speaking, OWL DL is a subset of OWL Full ., but the semantics of the DL and Full species are different, though [different (OWL-Semantics ].). While OWL DL has an abstract syntax with a direct model-theoretic semantics, the semantics of OWL Full is an extension of the semantics of RDFS, and is defined on the RDF syntax of OWL. Consequently, the OWL Full semantics does not extend the OWL DL semantics; however, everyall derivations sanctioned by the OWL DL entailment is ansemantics are sanctioned by the OWL Full entailmentsemantics.

Finally, the OWL DL RDF syntax, which is based on the OWL abstract syntax, does not extend the RDF syntax, but rather restricts it: every OWL DL ontology is an RDF graph, but not every RDF graph is an OWL DL ontology. OWL Full and RDF have the same syntax: every RDF graph is an OWL Full ontology and vice versa. Note thatThis syntactical difference is reflected in the abstract syntax form of OWL DL allows so-called punning (this is not allowed in the RDF syntax), i.e., the same IRI may be used in an individual position, a property position, and a class position; the interpretationdefinition of the IRI depends on its context. SinceRIF-OWL compatibility: combinations of RIF andwith OWL DL are based on the OWL abstract syntax of OWL DL, punning may also be used in these combinations. This paves the way towards combination with OWL 1.1, which is envisioned to allow punning in all its syntaxes. 3.2 Syntax of RIF-OWLwhereas combinations Sincewith OWL Full are based on the RDF graphs andsyntax.

Since the OWL Full ontologies cannot be distinguished, we usesyntax is the notion of RIF-RDF combinations forsame as the RDF syntax of combinations of RIF rule sets withand the OWL Full ontologies. For the combinationsemantics is an extension of RIF rule sets with OWL DL ontologies we definethe notionRDF semantics, the definition of RIF-OWL Full compatibility is a straightforward extension of RIF-RDF compatibility. Defining RIF-OWL DL combinations based oncompatibility in the abstract syntaxsame way would entail losing certain semantic properties of OWL DL. We need to furthermore impose certain restrictions on the syntaxOne of the rules. Specifically, we can only allow constant symbolsmain reasons for this is the difference in classthe way classes and property positions. DEFINITION: An RIF rule set R is a DL Rule set if for every frame formula a [ b -> c ]properties are interpreted in every ruleOWL Full and OWL DL. In the Full species, classes and properties are both interpreted as objects in the domain of interpretation, which are then associated with subsets of R it holds that b is a constantand if b =binary relations over the domain of interpretation using rdf:type , then c is a constant. DEFINITION: An RIF-OWL DL combination is a pair < R , O >, where R is a DL Rule setand O is a set of OWL DL ontologiesthe extension function IEXT, as in RDF. In abstract syntax form of a vocabulary V . When clear fromthe context, RIF-OWLDL combinationsspecies, classes and properties are referred to simplydirectly interpreted as combinations . 3.3 Semanticssubsets of RIF-OWL Combinationsand binary relations over the semantics of RIF-OWL Full combinationsdomain. The latter is a straightforward extension of the #Semanticskey property of RIF-RDF Combinations . TheDescription Logic semantics that enables the use of Description Logic reasoning techniques for processing OWL DL descriptions. Defining RIF-OWL DL combinations cannot straightforwardly extends the semanticscompatibility as an extension of RIF RDF combinations, becauseRIF-RDF compatibility would define a correspondence between OWL DL does not extendstatements and RIF frame formulas. Since RIF frame formulas are interpreted using an extension function, the RDF semantics.same way as in order to keep the syntax ofRDF, defining the rules uniformcorrespondence between RIF-Fullthem and RIF-OWLOWL DL combinations,statements would change the semantics of OWL statements, even if the RIF frame formulasruleset is slightly altered in RIF-OWL DL combinations. 3.3.1empty. Consider, for example, an OWL FullDL ontology with a class membership statement

a rdf:type C .

This statement says that the semantics of RIF-OWL Full combinationsset denoted by C contains at least one element that is denoted by a straightforward extension of. The semantics of RIF-RDF combinations. Itcorresponding RIF frame formula is

 based ona[rdf:type -> C]

The same notion of common interpretationsterms a, rdf:type, but defines additional notions of satisfiabilityand entailment. DEFINITION: Given a conforming datatype map D, a common interpretation ( I , I) OWL Full satisfies an RIF-RDF combination C=< R , S > if I satisfies R , I is an OWL Full interpretation , and I satisfies every RDF graph S in S ;C are all interpreted as elements in this case ( I , I) is called an OWL Full modelthe individual domain, and the pair of C,elements denoted by a and C is OWL Full satisfiablein the extension of the element denoted by rdf:type.

DEFINITION: Given a conforming datatype map D,This semantic discrepancy has practical implications in terms of entailments. Consider, for example, an RIF-RDF combination COWL Full entailsDL ontology with two class membership statements

a  generalized RDF graph S if every OWL Full model ofrdf:type C  satisfies S.
 Likewise, C OWL Full entailsD rdf:type owl:Class .

and a closedRIF condition formula φ ifruleset

Forall ?x ?y ?x=?y 

which says that every OWL Full model of C satisfies φ. 3.3.2 OWL DL The semantics of RIF-OWL DL combinationselement is similar in spirit tothe semantics of RIF-RDF combinations. We define a notion of common interpretations, which are pairs of RIF andsame as every other element (note that such statements can also be written in OWL DL interpretations,using owl:Thing and define a numberowl:hasValue). From the naïve combination of conditions which relate these interpretations. In contrast to RIF-RDF combinations,the conditions below definetwo one can derive C=D, and indeed

a  correspondence betweenrdf:type D .

This derivation is not sanctioned by the interpretation ofOWL DL classes and properties and RIF unary and binary predicates. Itsemantics, because even if every element is nowthe case that elementarysame as every other element, the class and property statements in OWL DL ofD might be interpreted as the formsempty set.

A and P correspondRIF-OWL combination that is faithful to the OWL DL semantics requires interpreting classes and properties as sets and binary relations, respectively, suggesting that correspondence could be defined with unary and binary predicates expressions inpredicates. It is, however, also desirable that there be uniform syntax for the RIF component of the forms A(?x) and P(?x,?y) , whereas elementary statements inboth OWL Full,DL and RDF/OWL Full combinations, because one may not know at time of writing the rules which are triples, correspond to frame formulas in RIF, e.g., a class membershiptype of inference will be used. Consider, for example, an RDF graph S with the following statement

 xa rdf:type C .

and a correspondsRIF ruleset with the rule

Forall ?x ?x[rdf:type -> D] :- ?x[rdf:type -> C]

The combination of the two, according to x[rdf:type -> A]the specification of [#RDF_Compatibility], allows deriving

a rdf:type D .

Therefore, rules which essentially expressNow, the same thing will look quite different, depending on whether they are used inRDF graph S is also an OWL DL and OWL Full ontologies. For example, in anontology. Therefore, one would expect the triple to be derived by RIF-OWL DL combination,combinations as well.

To ensure that the uncle rule looks something like: hasUncle(?x,?y) :- And(hasParent(?x,?y) hasBrother(?y,?z)) whereas, in anRIF-OWL Full combination, the rule will look something like: ?x[hasUncle -> ?y] :- And(?x[hasParent -> ?y] ?y[hasBrother -> ?z])DL combination is faithful to overcome this problem we define a slightly modifiedthe OWL DL semantics for RIF rulesand to enable using the use ofsame, or similar, rules with both OWL DL and RDF/OWL Full, the latter kindinterpretation of rulesframe formulas s[p -> o] in the RIF-OWL DL combinations.combinations is slightly different from their interpretation in RIF BLD and syntactical restrictions are imposed on the modified semantics essentially corresponds to a rewriting of atomic formulasuse of variables and function terms and frame formulas.

Note that the abstract syntax form x[rdf:type -> y] to y(x)of OWL DL allows so-called punning (this is not allowed in the RDF syntax), i.e., the same IRI may be used in an individual position, a property position, and x[p -> y] to p(x, y) . 3.3.2.1 Modified Semantics for RIF Frame Formulas We definea new truth valuation function forclass position; the interpretation of the IRI depends on its context. Since combinations of RIF formulas,and OWL DL are based on the abstract syntax of OWL DL, punning may also be used in these combinations. This paves the way towards combination with OWL 1.1, which is envisioned to allow punning in all its syntaxes.

EDITOR'S NOTE: The semantics of RIF-OWL DL combinations is similar in spirit to the Semantic Web Rule Language proposal. However, a reference to SWRL from the above text does not seem appropriate.

Since RDF graphs and OWL Full ontologies cannot be distinguished, the syntax of RIF-OWL Full combinations is the same as the truth valuation function definedsyntax of RIF-RDF-combinations.

The syntax of OWL ontologies in RIF-BLD , withRIF-OWL DL combinations is specified by the exceptionabstract syntax of OWL DL. Certain restrictions are imposed on the syntax of the RIF rules in combinations with OWL DL. Specifically, the only terms allowed in class and property positions in frame formulas.formulas are constant symbols.

DEFINITION: Given anA RIF-BLD condition φ is a RIF semantic structure IDL-condition if for every frame formula a[b -> c] in φ it holds that b is a constant and if b = < TV , DTS , Drdf:type, Ithen c , I V , I F , I frame , I SF , I sub , I isa , I = , I Truth >, the truth valuation function I T-DLis obtained by modifying the truth valuation ofa constant.

DEFINITION: A RIF-BLD ruleset R is a DL-Ruleset if for every frame formulas in I Truthformula a[b -> c] in the following way: I T-DL ( t [ rdf:type -> A ] ) = Ievery rule of R (it holds that b is a )( t )constant and I T-DL ( t 1 [ P -> t 2 ] )if b = I R ( P )( t 1rdf:type, t 2 ).then c is a constant.

DEFINITION: We say that I DL satisfiesA rule Q then  :- ifRIF-OWL-DL-combination is a pair < R,O>, where QR is a quantification prefix for allDL-Ruleset and O is a set of OWL DL ontologies in abstract syntax form of a vocabulary V.

When clear from the variablescontext, RIF-OWL-DL-combinations are referred to simply as combinations.

In the rule, if I * T-DL (then) ≥ I * T-DL (if) for every I * that agrees with I everywhere except possiblyliterature, several restrictions on somethe use of variables mentionedin Q . I is a DL modelcombinations of rules and Description Logics have been identified (Motik05, Rosati06) for the purpose of decidable reasoning. These restrictions are specified for RIF-OWL-DL combinations.

Given a ruleset R if it DL satisfies every rule in the set. 3.3.2.2 Semanticsof RIF-OWLOWL DL Combinations DEFINITION: Givenontologies in abstract syntax form O, a conforming datatype map D,variable ?x in a common DL interpretationRIF rule Q then :- if is a pair ( IDL-safe if it occurs in an atomic formula in if that is not of the form s[P -> o] or s[rdf:type -> A], I),where I = < TV , DTS , D , I C , I V , I F , I frame , I SF , I sub , I isaP or A, I =respectively, occurs in one of the ontologies in O. A RIF rule Q then :- if is DL-safe, I Truth >given O if every variable that occurs in then :- if is anDL-safe. A RIF semantic structurerule Q then :- if is weakly DL-safe, given O if every variable that occurs in then is DL-safe and I=<R, EC, ER, L, S, LV>every variable in if that is an abstract OWL interpretation with respect to Dnot DL-safe occurs only in atomic formulas in if that are of the form s[P -> o] or s[rdf:type -> A], where P or A vocabulary V, such thatrespectively, occurs in one of the following conditions hold 1. R= D ; 2. LVontologies in O.

EDITOR'S NOTE: it is not strictly necessary to disallow disjunctions in the definition, but it would make the definition a subsetlot more complex. It would require defining the disjunctive normal form of Ra condition formula and containsdefine safeness with respect to each disjunct. Given that the value spaces of all data types in D; 3. EC( u ) = set of all objects k in R suchsafeness restriction is meant for implementation purposes, and that Iconverting rules to disjunctive normal form is extremely expensive, it is probably a reasonable restriction to disallow disjunction.

DEFINITION: A RIF-OWL-DL-combination < R ( "u"^^rif:iri )( k ) = t (true), for,O> is DL-safe if every IRI urule in V ; 4. ER( u ) = set of all tuples ( k , l ) such that IR ( "u"^^rif:iri )( kis DL-safe, given O. A RIF-OWL-DL-combination < R, l ) = t (true), forO> is weakly DL-safe if every data valued and individual valued property identifier u in V ; 5. L(( s , d )) = I C ( "s"^^d ) for every well-typed literal ( s , d ) in V ; 6. S( i ) = I C ( "i"^^rif:iri ) for every IRI irule in VR is weakly DL-safe, given O.

Condition 1 ensuresEDITOR'S NOTE: Do we want additional safeness restrictions to ensure that variables do not cross the domainsabstract-concrete domain boundary?

The same. Condition 2 ensures thatsemantics of RIF-OWL Full combinations is a straightforward extension of the set#Semantics of literal values includesRIF-RDF Combinations.

The value spacessemantics of all considered datatypes. Condition 3 ensures thatRIF-OWL-DL-combinations cannot straightforwardly extend the interpretation (extension)semantics of anRIF RDF combinations, because OWL DL class u correspondsdoes not extend the RDF semantics. In order to keep the interpretationsyntax of the unary predicate with the same name in RIF. Condition 4 ensures thatrules uniform between RIF-OWL Full and RIF-OWL-DL-combinations, the interpretation (extension)semantics of RIF frame formulas is slightly altered in RIF-OWL-DL-combinations.

A D-interpretation I is an OWL DL object or datatype property u corresponds to theFull interpretation ofif it interprets the binary predicates withOWL vocabulary and it satisfies the same nameconditions in RIF. Condition 5 ensures that typed literals ofthe form ( s , d )sections 5.2 and 5.3 in (OWL DL are interpreted inSemantics).

The same way as constantssemantics of RIF-OWL Full combinations is a straightforward extension of the form "s"^^d in RIF. Finally, condition 6 ensures that individual identifiers in the OWL ontologies and the RIF rule sets are interpreted insemantics of RIF-RDF-combinations. It is based on the same way. Using the definitionnotion of common interpretation, satisfaction, models,common-interpretations, but defines additional notions of satisfiability and entailment are defined in the usual way:entailment.

DEFINITION: Given a conforming datatype map D, a common DL interpretationcommon-rif-rdf-interpretation (I, I) OWL DL satisfiesis an RIF-OWL DL combinationOWL-Full-model of a RIF-RDF-combination C=< R, O >S > if I DL satisfiesis a model of R, I is an OWL Full interpretation, and I satisfies every OWL DL ontology in abstract syntax form ORDF graph S in OS; in this case ( I , I) is called an OWL DL model of C, andC is OWL DL satisfiable . ( I , I) satisfies an OWL DL ontology in abstract syntax form O if I satisfies O . ( I , I) satisfies a closed RIF condition formula φ if I T-DL (φ)= tOWL-Full-satisfiable.

DEFINITION: Given a conforming datatype map D, an RIF-OWL DL combinationa RIF-RDF-combination C OWL DL entails an OWL DL ontology in abstract syntax form OOWL-Full-entails a generalized RDF graph S if every OWL DL modelOWL-Full-model of C satisfies S. Likewise, C OWL DL entailsOWL-Full-entails a closed RIFRIF-BLD condition formulaφ if every OWL DL modelOWL-Full-model of C satisfies φ.

The modification of the semantics of RIF rules. This limitationframe formulas is overcome inachieved by modifying the following definition. It is envisioned that the user will choose whether annotationmapping function for frame formulas (I_frame), and ontology propertiesleaving the RIF BLD semantics (RIF-BLD) otherwise unchanged.

Namely, frame formulas of the form s[rdf:type -> o] are to be considered. It is noted that itinterpreted as membership of s in the set denoted by o and frame formulas of the form s[p -> o], where p is envisioned that OWL 1.1 willnot define a semantics for annotation and ontology properties; therefore,rdf:type, as membership of the below definition cannot be extended topair (s, o) in the case of OWL 1.1.binary relation denoted by p.

DEFINITION: GivenA conforming datatype map D,RIF DL-semantic structure is a common DL interpretation (tuple I = <TV, I)DTS, D, D_ind, D_func, I_C, I_V, I_F, I_frame', I_SF, I_sub, I_isa, I₌, I_external, I_truth>, where I_frame' is a common DL annotation interpretation if the following condition holds 7. ER( u ) = setmapping from D_ind to total functions of all tuplesthe form SetOfFiniteFrame'Bags( k , lD × D) → D, such that I Rfor each pair ( "u"^^rif:iri )( k , la, b) = t (true), for every IRI uin V . Condition 7 ensuresSetOfFiniteFrame'Bags(D × D) holds that the interpretation of all properties (also annotation and ontology properties)if a≠I_C(rdf:type), then b in D_ind; all other elements of the OWL DL ontologies corresponds with their interpretationstructure are defined as in theRIF rules. DEFINITION: Given a conforming datatype map D,semantic structures.

We define I(o[a₁->v₁ ... a _{common DL annotation interpretationk}->v_k]) = I_frame(I , I) OWL DL annotation satisfies an RIF-OWL DL combination C=< R ,(o > if))({<I satisfies R and(a₁),I satisfies every OWL DL ontology in abstract syntax form O in O ; in this case(v₁)>, ..., <I(a_n),I(v_n)>}). The truth valuation function TVal_I , I) is called an OWL DL annotation model of C, and Cis OWL DL annotation satisfiablethen defined as in RIF BLD.

DEFINITION: GivenA conforming datatype map D, an RIF-RDF combination C OWL DL annotation entails an OWL DL ontology and abstract syntax form O if every OWL DL annotationRIF DL-semantic structure I is a model of C satisfies O . Likewise, C OWL DL annotation entailsa closed RIF condition formula φDL-Ruleset R if every OWL DL annotation model of C satisfies φ. We illustrate the difference between the two kindsTVal_I(R)=t.

As defined in abstract syntax form Ontology (ex:myOntology Annotation(dc:title "Example ontology")) which defines(OWL-Semantics), an ontologyabstract OWL interpretation with respect to a single annotation (title). Consider alsodatatype map D, with vocabulary V is a ruletuple I=< R, EC, ER, L, S, LV >, where

• R is a non-empty set which consistsof the following rule: Forall ?x, ?y ( ?x[ex:hasTitle -> ?y] :- ?x[dc:title -> ?y]) which says that whenever something hasresources (the domain); O is a dc:title , it has the same ex:hasTitle . The combinationnon-empty subset of the ontologyR, disjoint from LV,
• EC is a mapping from class and datatype identifiers to subsets of O and LV, respectively,
• ER is a mapping from property identifiers to subsets of R × R,
• L is a mapping from typed literals in V into LV,
• S is a mapping from IRIs in V into R, and
• LV is the ruleset of literal values, which is a subset of R, and includes all plain literals in V.

The OWL DL annotation entailssemantics imposes a number of further restrictions on the RIF condition formula ex:myOntology[ex:hasTitle -> "Example ontology"^^xsd:string] ;mapping functions as well as the combination does not OWL DL entailset of resources R, to achieve a separation of the formula. 4 References 4.1 Normative References [OWL-Semantics] OWL Webinterpretation of class, datatype, ontology Language Semanticsproperty, datatype property, annotation property, and Abstract Syntaxontology property identifiers.

DEFINITION: Given a conforming datatype map D, a common-rif-dl-interpretation is a pair (I, P. F. Patel-Schneider, P. Hayes, I. Horrocks, Editors, W3C Recommendation, 10 February 2004, http://www.w3.org/TR/2004/REC-owl-semantics-20040210/ . Latest version available at http://www.w3.org/TR/owl-semantics/ . [RDF-CONCEPTS] Resource Description Framework (RDF): Concepts and Abstract SyntaxI), where I = <TV, G. Klyne, J. Carroll (Editors), W3C Recommendation, 10 February 2004, http://www.w3.org/TR/2004/REC-rdf-concepts-20040210/ . Latest version available at http://www.w3.org/TR/rdf-concepts/ . [RDF-SEMANTICS] RDF SemanticsDTS, P. Hayes, Editor, W3C Recommendation, 10 February 2004, http://www.w3.org/TR/2004/REC-rdf-mt-20040210/ . Latest version available at http://www.w3.org/TR/rdf-mt/ . [RIF-BLD] RIF Basic Logic DialectD, H. Boley, M. Kifer (Editors), W3C Editor's Draft, http://www.w3.org/2005/rules/wg/wiki/BLD . Accessed on 2008-02-13T17:00 UTC. [XML-SCHEMA2] XML Schema Part 2: DatatypesI_C, W3C Recommendation, World Wide Web Consortium, 2 May 2001. This version is http://www.w3.org/TR/2001/REC-xmlschema-2-20010502/ . Latest version available at http://www.w3.org/TR/xmlschema-2/ . 4.2 Informational References [RDF-Schema] RDF Vocabulary Description Language 1.0: RDF SchemaI_V, D. Brickley, R.V. Guha, Editors, W3C Recommendation, 10 February 2004, http://www.w3.org/TR/2004/REC-rdf-schema-20040210/ . Latest version available at http://www.w3.org/TR/rdf-schema/ . [RDF-SYNTAX] RDF/XML Syntax Specification (Revised)I_F, D. Beckett, Editor, W3C Recommendation, 10 February 2004, http://www.w3.org/TR/2004/REC-rdf-syntax-grammar-20040210/ . Latest version available at http://www.w3.org/TR/rdf-syntax-grammar/ . [RFC-3066] RFC 3066 - Tags for the Identification of LanguagesI_frame', H. Alvestrand, IETF, January 2001. This document is http://www.isi.edu/in-notes/rfc3066.txt . [RIF-PRD] RIF Production Rule dialectI_SF, C. de Sainte Marie (Editors), Editor's Draft. Latest version available at http://www.w3.org/2005/rules/wg/wiki/PRdialect . [RIF-UCR] RIF Use Cases and RequirementsI_sub, A. Ginsberg, D. Hirtle, F. !McCabe, P.-L. Patranjan (Editors), W3C Working Draft, 10 July 2006, http://www.w3.org/TR/2006/WD-rif-ucr-20060710/ . Latest version available at http://www.w3.org/TR/rif-ucr . [OWL-Reference] OWL Web Ontology Language ReferenceI_isa, M. Dean, G. Schreiber, Editors, W3C Recommendation, 10 February 2004, http://www.w3.org/TR/2004/REC-owl-ref-20040210/ . Latest version available at http://www.w3.org/TR/owl-ref/ . 5 Appendix: Embeddings RIF-RDF combinations can be embedded into RIF Rule sets inI₌, I_Truth> is a fairly straightforward way, thereby demonstrating how an RIF-compliant translator without native support for RDF can process RIF-RDF combinations. For the embedding we use the concrete syntax ofRIF DL-semantic structure and the N-Triples syntax for RDF. Throughout this section the function trI=<R, EC, ER, L, S, LV> is defined, which maps symbols, triples, and RDF graphsan abstract OWL interpretation with respect to RIF symbols, statements, and rule sets. 5.1 Embedding Symbols Given a combination C=< R , S >, the function tr maps RDF symbolsD of a vocabulary V and a set of blank nodes B to RIF symbols, as defined in, such that the following table. RDF Symbol RIF Symbol Mapping IRI i in Vconditions hold

1. (O union LV)=D_ind;
2. EC(u Constant with symbol space rif:iri tr( i) = "i"^^rif:iri Blank node x<em>set of all objects k in <em>B<em></td> Variable symbols ? <em>x tr( x )O such that I_truth(I_frame'(I_C(rdf:type))(k,I_C("u"^^rif:iri))) = ? x Plain literal without a language tag xxxt, for every class identifier u in V PL Constant with the datatype xsd:string tr( "xxx";
3. ER(u) = "xxx"^^xsd:string Plain literal with a language tagset of all pairs ( xxxk, langl) in O × (O union LV) such that I_truth(I_frame'(I_C("u"^^rif:iri))( k, l ))) = t (true), for every data valued and individual valued property identifier u in V PL Constant with the datatype rif:text tr( "xxx"@lang );
4. L((s, d)) = "xxx@lang"^^rif:textI_C("s"^^d) for every well-typed literal (s, ud) in V TL Constant with;
5. S(i) = I_C("i"^^rif:iri) for every individual identifier i in V.

Condition 1 ensures that the symbol spacerelevant parts of the domains of interpretation are the same. Condition 2 ensures that the interpretation (extension) of an OWL DL class u tr( "s"^^ucorresponds to the interpretation of frames of the form ?x[rdf:type -> "u"^^rif:iri]. Condition 3 ensures that the interpretation (extension) of an OWL DL object or datatype property u corresponds to to the interpretation of frames of the form ?x["u"^^rif:iri -> ?y]. Condition 4 ensures that typed literals of the form (s, d) in OWL DL are interpreted in the same way as constants of the form "s"^^d in RIF. Finally, condition 5 ensures that individual identifiers in the OWL ontologies and the RIF rulesets are interpreted in the same way.