RDF/RuleML Interoperability

1 Introduction

Keeping positional Horn logic as one of its sublanguages, and even adding FOL, RuleML has been developed increasingly closer towards RDF, with an eye also on F-logic and Desription logic. This is already reflected by RuleML/RDF tools and a RuleML/N3 alignment. The newest RuleML release as described here will further simplify RDF interoperability regarding webizing, typing, and blank nodes. It also integrates two negations, as required for the Semantic Web. On this basis, F-logic/TRIPLE rules and SWRL rules are being introduced.

2 RDFizing RuleML

At the RDF Interest Group face to face meeting in Feb 2001 the Rule Markup Initiative was presented with a focus on RDF Relationships and DTD Modularization. This section shows the RDFizing of RuleML, using the new RuleML XML syntax.

2.1 RDF Triples and Rules as RuleML Sublanguages

Before Object-Oriented (OO) RuleML became available, the family of sublanguages of RuleML had to use (subject,predicate,object) triples for representing RDF as ground (variablefree) binary atoms predicate(subject,object), where predicate and subject needed to be webized and object was optionally webized. RDF rules could then be represented by allowing variables inside binary atoms.

As will be illustrated in section 2.2, the slots of OO RuleML have permitted to express 'subject-centered' RDF descriptions without duplicating a subject for every triple it participates in. These descriptions are anchored in the Web through URIs. To integrate RDF more deeply with other aspects of RuleML, and to reduce the number of sublanguages, the binary atoms are no longer distinguished in the newest RuleML.

2.2 RDF-Like Webizing of RuleML

RuleML allows an individual constant (Ind) to contain web labels and web references, leading to the following RDF correspondence:

The subject of an RDF triple or the about attribute in an rdf:Description becomes a RuleML role tag called oid (object identifier) containing an Ind with a wlab (web label) attribute.
An RDF predicate or property becomes the first child of a RuleML slot, which is an Ind with a wref (web reference) attribute.
An RDF object becomes the second child of a RuleML slot, which for an RDF literal is a RuleML Data element and for an RDF resource again is a wref-attributed Ind.

Illustrating the general correspondence (omitting namespace declarations):

<rdf:Description about="http://www.w3.org">
  <dc:title>World Wide Web Consortium</dc:title>
  <eg:director rdf:resource="http://www.w3.org/People/Berners-Lee"/>
</rdf:Description>

<Atom>
  <oid><Ind wlab="http://www.w3.org"/></oid>
  <slot><Ind wref="dc:title"/><Data>World Wide Web Consortium</Data></slot> 
  <slot><Ind wref="eg:director"/><Ind wref="http://www.w3.org/People/Berners-Lee"/></slot>
</Atom>

2.3 RDF Types and RDF Schema in RuleML

The rdf:type of a resource in RuleML is regarded as the relation of its describing atom. Again via a web reference it points to an RDF Schema definition.

Illustrating the type-relation correspondence (omitting namespace declarations):

<rdf:Description about="http://www.w3.org">
  <rdf:type resource="http://schema.org/StandardsBody"/>
  <dc:title>World Wide Web Consortium</dc:title>
  <eg:director rdf:resource="http://www.w3.org/People/Berners-Lee"/>
</rdf:Description>

<Atom>
  <oid><Ind wlab="http://www.w3.org"/></oid>
  <opr><Rel wref="http://schema.org/StandardsBody"/></opr>
  <slot><Ind wref="dc:title"/><Data>World Wide Web Consortium</Data></slot> 
  <slot><Ind wref="eg:director"/><Ind wref="http://www.w3.org/People/Berners-Lee"/></slot>
</Atom>

For multiple types of a resource, an atom with multiple relations can be used, which provides a useful shortcut even in the absence of an oid.

2.4 Blank Nodes as Skolem Constants

Blank Nodes have recently been introduced to RuleML for complete RDFizing: Skolem constants are marked up as <Skolem/> (anonymous) or <Skolem>...</Skolem> (named), and adopt the Yang/Kifer model theory [5].

3 Two Kinds of Negation in RDF/RuleML

While the previous section showed how RuleML caught up with RDF expressiveness, the current section discusses RuleML sublanguages also proposed as RDF extensions.

In his visionary article [2], Tim Berners-Lee identified two fundamental issues for the Semantic Web:

negation and inconsistency handling
open-world versus closed-world assumptions

It is disappointing, therefore, that neither in RDF nor in OWL these issues have been addressed so far. RDF does not even have any kind of negation, while OWL has a limited form of negation only. Neither the current RDF nor OWL are able to deal with Closed-World assumptions, nor do they have any feature for handling inconsistency. In [3], Tim Berners-Lee says: "We remove the centralized concepts of absolute truth, total knowledge, and total provability, and see what we can do with limited knowledge". This is exactly what has been done in RuleML by providing two kinds of negation on the basis of partial logic. Unlike classical logic, which is the basis of OWL, partial logic allows to handle truth value gaps (partiality) and truth value clashes (inconsistency).

RuleML includes the computational construct of negation-as-failure (NAF) for expressing local completeness (Closed-World) assumptions. And it includes a more conservative negation connective (NEG), also called strong negation, which corresponds to Kleene negation in 3-valued logic or to Boolean negation, depending on the semantic nature of the predicate beeing negated. With these computational logic facilities, RuleML supports more real-world knowledge representation tasks than RDF and OWL, which are based on the highly idealized classical (2-valued) logic.

The following is an example of a rule using both kinds of negation. Here, the predicate "requiresService" does not allow Closed-World inference, while the predicate "is AssignedToRentalContract" does allow it, and, hence, the former is negated with NEG and the latter with NAF.

<Implies>
  <body>

    <And>
      <Atom>
        <Rel>RentalCar</Rel>
        <Var>Car</Var>
      </Atom>
      <Neg>
        <Atom>
          <Rel>requiresService</Rel>
          <Var>Car</Var>
        </Atom>
      </Neg>
      <Naf>
        <Atom>
          <Rel>isAssignedToRentalContract</Rel>
          <Var>Car</Var>
        </Atom>
      </Naf>
    </And>
  </body>

  <head>

    <Atom>

      <Rel>isAvailable</Rel>

      <Var>Car</Var>

    </Atom>

  </head>
</Implies>

These semantics are reflected by RuleML sublanguage schemas with NAF, NEG, and both. RDF can be extended by adding both forms of negation, too, as has been shown in [1].

4 F-logic And TRIPLE Rules in RDF/RuleML

With the advent of OO RuleML [4], molecules, the most fundamental feature of F-logic (and its early RDF-compliant version, SiLRI) and TRIPLE, became representable.

For TRIPLE's model (or view) feature, which allows RDF statements to be "@"-associated with a name (similar to contexts in Cwm or named graphs), a RuleML module role (on Atom, Implies, etc.) is proposed in analogy to the oid role, which can contain an Individual.

The following example shows the proposed RuleML serialization for a TRIPLE molecule about W3C in a module context (omitting namespace declarations):

'http://www.w3.org':''[rdf:type -> s:StandardsBody;
  dc:title -> "World Wide Web Consortium";
  eg:director -> p:'Berners-Lee']@c:mod1.

<Atom>
  <module><Ind wref="c:mod1"/></module>
  <oid><Ind wlab="http://www.w3.org"/></oid>
  <opr><Rel wref="s:StandardsBody"/></opr>
  <slot><Ind wref="dc:title"/><Data>World Wide Web Consortium</Data></slot> 
  <slot><Ind wref="eg:director"/><Ind wref="p:Berners-Lee"/></slot>
</Atom>

Paramterized TRIPLE views, which proved to be very useful for representing ontology mappings, semantics definitions, etc., can then be serialized in RuleML with a module role that contains a Complex term.

TRIPLE/RuleML rules can be built from such Atoms in the head and body, and also employ the explicit quantifiers Forall and Exists introduced in FOL RuleML.

5 SWRL Rules in RDF/RuleML

In the SWRL submission to W3C an RDF Schema for SWRL (swrl.rdf) was published to provide a partial description of the syntax of SWRL. A corresponding RuleML version has recently been provided as swrl.ruleml (with a KQML-like top-level performative 'Assert' ).

SWRL rules in OWL RDF/XML syntax are interoperable with an RDFized RuleML version, where, e.g., the IndividualPropertyAtom element corresponds to a normal Atom element with a swrl:IndividualPropertyAtom attribute.

Illustrating SWRL Example 6.1-1 in RDFized RuleML (omitting namespace declarations):

<Implies>
  <oid><Ind wlab="http://www.w3.org/Submission/2004/SUBM-SWRL-20040521/#Example6.1-1"/></oid>

  <body>

    <And>

      <Atom>

        <opr><Rel wref="swrl:IndividualPropertyAtom"/></opr>

        <slot><Ind wref="swrl:propertyPredicate"/><Ind wref="eg:hasParent"/></slot>

        <slot><Ind wref="swrl:argument1"/><Var wref="eg:x1"/></slot>

        <slot><Ind wref="swrl:argument2"/><Var wref="eg:x2"/></slot>

      </Atom>

      <Atom>

        <opr><Rel wref="swrl:IndividualPropertyAtom"/></opr>

        <slot><Ind wref="swrl:propertyPredicate"/><Ind wref="eg:hasSibling"/></slot>

        <slot><Ind wref="swrl:argument1"/><Var wref="eg:x2"/></slot>

        <slot><Ind wref="swrl:argument2"/><Var wref="eg:x3"/></slot>

      </Atom>

      <Atom>

        <opr><Rel wref="swrl:IndividualPropertyAtom"/></opr>

        <slot><Ind wref="swrl:propertyPredicate"/><Ind wref="eg:hasSex"/></slot>

        <slot><Ind wref="swrl:argument1"/><Var wref="eg:x3"/></slot>

        <slot><Ind wref="swrl:argument2"/><Ind wref="eg:male"/></slot>

      </Atom>

    </And>

  </body>

  <head>

    <Atom>

      <opr><Rel wref="swrl:IndividualPropertyAtom"/></opr>

      <slot><Ind wref="swrl:propertyPredicate"/><Ind wref="eg:hasUncle"/></slot>

      <slot><Ind wref="swrl:argument1"/><Var wref="eg:x1"/></slot>

      <slot><Ind wref="swrl:argument2"/><Var wref="eg:x3"/></slot>

    </Atom>

  </head>
</Implies>

6 Conclusions

This paper demonstrates the high level of RDF/RuleML interoperability achieved along with extensions in close reach from RDF and RuleML.

7 References

1. A. Analyti, G. Antoniou, C. V. Damásio and G. Wagner. Negation and Negative Information in the W3C Resource Description Framework. Annals of Mathematics, Computing & Teleinformatics, vol 1, no 2, 2004, pp 25-34.

2. T. Berners-Lee. Design issues - architectual and philosophical points. Personal notes, 1998. Available at http://www.w3.org/DesignIssues/.

3. T. Berners-Lee. What the semantic web can represent. Personal notes, 1998. Available at http://www.w3.org/DesignIssues/RDFnot.html.

4. H. Boley, B. Grosof, M. Kifer, M. Sintek, S. Tabet, G. Wagner. Object-Oriented RuleML, 2004. Available at http://www.ruleml.org/indoo.

5. G. Yang and M. Kifer. Reasoning about Anonymous Resources and Meta Statements on the Semantic Web. Journal of Data Semantics, 2004.