Converging SCL's XCL and SWRL's RuleML for FOL Extensions

From: Boley, Harold (Harold.Boley@nrc-cnrc.gc.ca)
Date: 06/08/04

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    Hi JC Colleagues,
    as we envisaged in today's Joint Committee telecon,
    the XML notation for SCL, XCL (http://www.altheim.com/specs/xcl/1.0/),
    and the XML notation for SWRL rules, RuleML (http://www.ruleml.org/inspec/),
    could be converged for the FOL extensions to SWRL.
    Today we also discussed the (URI-)naming of layered FOL subsets
    that contain the current Horn/DL combination.
    One such FOL subset could add explicit, nested quantifiers to SWRL rules
    (as suggested for the Issues List); another could add disjunction /
    classical negation.
    Implications in XCL could be converged to the RuleML Horn-rule syntax.
    Formulas beyond SWRL's Horn/DL combination could benefit from XCL.
    Appended is an example using an implication from the above XCL draft.
    Best,
    Harold
    
    XCL, Section 3.3. Core Elements, uses a sorted notation:
    (FORALLx:TrailerTruck) => eighteenWheeler(x)
    
        <xcl xmlns="http://purl.org/xcl/1.0/">
          <formula>
            <conn name="implies">
              <quant name="forall" variable="x">
                <type>TrailerTruck</type>
              </quant>
              <pred name="eighteenWheeler">
                <term name="x"/>
              </pred>
            </conn>
          </formula>
        </xcl>
    
    To keep things simple, let's use TrailerTruck as a unary predicate here:
    
    FORALL(?x)TrailerTruck(?x) => eighteenWheeler(?x)
    
    The current RuleML 0.85 assumes implicit quantifiers, obtaining:
    
    <imp>
      <_body>
        <atom>
          <_opr><rel>TrailerTruck</rel></_opr>
          <var>x</var>
        </atom>
      </_body>
      <_head>
        <atom>
          <_opr><rel>eighteenWheeler</rel></_opr>
          <var>x</var>
        </atom>
      </_head>
    </imp>
    
    For RuleML 0.9 explicit quantifiers are envisaged as an option, here
    introducing a type tag <forall> with role tags <_bind> and <_form>
    for its 'variable-binding' child and its 'formula' child, respectively:
    
    <forall>
      <_bind>
        <var>x</var>
      </_bind>
      <_form>
        <imp>
          <_body>
            <atom>
              <_opr><rel>TrailerTruck</rel></_opr>
              <var>x</var>
            </atom>
          </_body>
          <_head>
            <atom>
              <_opr><rel>eighteenWheeler</rel></_opr>
              <var>x</var>
            </atom>
          </_head>
        </imp>
      </_form>
    </forall>
    
    The type tag <exists> can employ the same child elements.
    


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