OWL Example with RDF Graph

Let us illustrate the use of OWL vocabulary on an example ontology (inspired by OWL Pizzas): "Pizza has PizzaBase as its base; Pizza is disjoint with PizzaBase; NonVegetarianPizza is exactly Pizza that is not VegetarianPizza; isIngredientOf is a transitive property; isIngredientOf is inverse of hasIngredient". The example expressed in the description logic syntax follows:

The same example expressed using OWL Abstract Syntax formulates the same information using LISP-like notation, and in addition uses URI for identification of all classes and properties:

      Namespace(p = <http://example.com/pizzas.owl#>)
      Ontology( <http://example.com/pizzas.owl#>
        Class(p:Pizza partial
          restriction(p:hasBase someValuesFrom(p:PizzaBase)))
        DisjointClasses(p:Pizza p:PizzaBase)
        Class(p:NonVegetarianPizza complete
          intersectionOf(p:Pizza complementOf(p:VegetarianPizza)))
        ObjectProperty(p:isIngredientOf Transitive
          inverseOf(p:hasIngredient))
      )

When embedding the example OWL ontology to RDF, every statement must be converted to triples - see the figure below. For example, the ∃R.C restriction is formed by anonymous resource of type owl:Restriction. This anonymous resource (blank node) is a subject for two properties owl:onProperty and owl:someValuesFrom that relate the restriction relation (property) and concept (class). The anonymous resource is then used to be related to the constrained class (by rdfs:subClassOf in our case). The example expressed in triples and serialized in N3 follows:

Pizza OWL ontology expressed in RDF triples

      @prefix :     <http://example.com/pizzas.owl#> .
      @prefix rdf:  <http://www.w3.org/1999/02/22-rdf-syntax-ns#> .
      @prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
      @prefix owl:  <http://www.w3.org/2002/07/owl#> .
      
      :Pizza rdfs:subClassOf
              [ a owl:Restriction ;
                owl:onProperty :hasBase ;
                owl:someValuesFrom :PizzaBase ] ;
             owl:disjointWith :PizzaBase .
      
      :NonVegetarianPizza  owl:equivalentClass
              [  owl:intersectionOf
                  (  [owl:complementOf :VegetarianPizza]
                     :Pizza  )  ] .
      
      :isIngredientOf
            a owl:TransitiveProperty , owl:ObjectProperty ;
            owl:inverseOf :hasIngredient .

The OWL DL uses all the SHOIN(D) features. The overview of the possible descriptions, data ranges, properties, individuals and data values is shown in the table in the previous page. The DL description of the semantics was introduced in one of the previous sections. The domain of individuals in the model is Δ^I, the domain of data values Δ^I_D was added to specify semantics of data ranges.

The ontology is formed by constraints on a model. The axioms that can be used to constrain a model are summarized in the table in the previous page.

In addition to the standard description logic features there are so called annotation properties added. In addition to RDFS annotation properties (such as rdfs:comment and rdfs:label) there are properties that allow to state for example version information, state compatibility or incompatibility between ontologies. There is also a construct owl:imports that allows to state that an ontology imports another ontology.