OWL 2 罗化

在描述逻辑中，有一个概念叫“rolification”（OWL 和规则，第 3.2 节）。它将概念（类）转换为角色（属性）。例如，当我们滚动时R(x)，我们得到r(x,x)。该技术对于在深度学习中表达一些规则很有用。

我们如何在 OWL 2 中做到这一点？似乎没有直接支持roolification猫头鹰2规范.

您链接到的论文第 3.2 节说：

It is indeed possible to translate this rule into OWL 2—however this involves a transformation which we call rolification: The rolification of a concept A is a (new) role R_A defined by the axiom A ≡ ∃R_A.Self. Armed with rolification, we can now express rule (1) by the axiom …

OWL2 不支持表达这样的公理大象(x) & 楔子;鼠标(y) → 大于(x,y)直接地。据我了解，你manually使用本文描述的罗化过程产生一个可以直接用 OWL2 表达的新公理。

罗化

As to the specific process, if you want to express something like Elephant(x) ∧ Mouse(y) → biggerThan(x,y), you first rolify the classes Elephant and Mouse. This means that you introduce new roles (properties) R_Elephant and R_Mouse (but you do not delete the classes Elephant and Mouse). These new roles are such that R_Elephant(x,x) if and only if Elephant(x). This is enforced by adding the axioms

        Elephant ≡ ∃R_Elephant.Self

        Mouse ≡ ∃R_Mouse.Self

其中每一个都可以用 OWL2 来表达。有了这两个公理，您最终可以添加子属性链公理

        R_Elephant • topObjectProperty • R_Mouse ⊑ biggerThan

这也可以用 OWL2 来表达。因为对于任何大象e和任何鼠标m，我们有那个

        R_Elephant(e,e)

顶部对象属性(e,m)

        R_Mouse(m,m)

然后根据子财产链公理，我们有

大于(e,m)

这正是我们想要表达的。

公理语法

在Protege接受的输入语法中，这些公理的写法如下。

大象相当于R_大象一些自我
老鼠相当于R_鼠标一些自我
R_大象o顶部对象属性oR_鼠标子属性大于

在 Protege 中，它们如下所示。

In N3:

@prefix :        <http://www.example.org/rolification#> .
@prefix rdfs:    <http://www.w3.org/2000/01/rdf-schema#> .
@prefix owl:     <http://www.w3.org/2002/07/owl#> .
@prefix xsd:     <http://www.w3.org/2001/XMLSchema#> .
@prefix rdf:     <http://www.w3.org/1999/02/22-rdf-syntax-ns#> .

:Elephant
      a       owl:Class ;
      owl:equivalentClass
              [ a       owl:Restriction ;
                owl:hasSelf "true"^^xsd:boolean ;
                owl:onProperty :R_Elephant
              ] .

:R_Elephant
      a       owl:ObjectProperty .

:biggerThan
      a       owl:ObjectProperty ;
      owl:propertyChainAxiom
              (:R_Elephant owl:topObjectProperty :R_Mouse) .

:Mouse
      a       owl:Class ;
      owl:equivalentClass
              [ a       owl:Restriction ;
                owl:hasSelf "true"^^xsd:boolean ;
                owl:onProperty :R_Mouse
              ] .

<http://www.example.org/rolification>
      a       owl:Ontology .

:R_Mouse
      a       owl:ObjectProperty .

在 RDF/XML 中：

<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns="http://www.example.org/rolification#"
    xmlns:xsd="http://www.w3.org/2001/XMLSchema#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#">
  <owl:Ontology rdf:about="http://www.example.org/rolification"/>
  <owl:Class rdf:about="http://www.example.org/rolification#Elephant">
    <owl:equivalentClass>
      <owl:Restriction>
        <owl:onProperty>
          <owl:ObjectProperty rdf:about="http://www.example.org/rolification#R_Elephant"/>
        </owl:onProperty>
        <owl:hasSelf rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean"
        >true</owl:hasSelf>
      </owl:Restriction>
    </owl:equivalentClass>
  </owl:Class>
  <owl:Class rdf:about="http://www.example.org/rolification#Mouse">
    <owl:equivalentClass>
      <owl:Restriction>
        <owl:onProperty>
          <owl:ObjectProperty rdf:about="http://www.example.org/rolification#R_Mouse"/>
        </owl:onProperty>
        <owl:hasSelf rdf:datatype="http://www.w3.org/2001/XMLSchema#boolean"
        >true</owl:hasSelf>
      </owl:Restriction>
    </owl:equivalentClass>
  </owl:Class>
  <owl:ObjectProperty rdf:about="http://www.example.org/rolification#biggerThan">
    <owl:propertyChainAxiom rdf:parseType="Collection">
      <owl:ObjectProperty rdf:about="http://www.example.org/rolification#R_Elephant"/>
      <rdf:Description rdf:about="http://www.w3.org/2002/07/owl#topObjectProperty"/>
      <owl:ObjectProperty rdf:about="http://www.example.org/rolification#R_Mouse"/>
    </owl:propertyChainAxiom>
  </owl:ObjectProperty>
</rdf:RDF>