Creating an OWL sub-class based on the equality of two object properties

Question

Consider that I have classes A and B in OWL. There are two different object properties P1 and P2 whose ranges are class C and domains A and B respectively.

I want to create a class D which represents any A that contains an object property P1 whose value is equal to any object property P2 contained by B.

Is it possible to describe this using OWL?

"They both have two different object properties P1 and P2 whose ranges are class C." What do you mean by this? Properties don't belong to classes; OWL isn't an object-oriented programming language. Do you mean that the *domains* of P1 and P2 are A and B, respectively? — Joshua Taylor, Feb 13 '15 at 20:52
Yes, exactly, that's what i meant. New in this domain as it can be observed. — user1364591, Feb 14 '15 at 23:12

Joshua Taylor · Answer 1 · 2015-02-13T21:05:35.237

I want to create a class D which represents any A that contains an object property P1 whose value is equal to any object property P2 contained by B.

I think you're looking for a class expression like this (in DL and Manchester syntaxes):

D ≡ A &sqcap; ∃ p₁.(∃ p₂^-1.B)

D equivalentClass (A and (p1 some (inverse(p2) some B)))

This says that something is a D if and only if it is an A, and has some value for p1 that is the p2 value of some instance of B.

If the domains of p1 and p2 are A and B, respectively, then you can actually simplify that to:

D ≡ ∃ p₁.∃ p₂^-1

D equivalentClass p1 some (inverse(p2) some Thing)

Here's what the first one looks like in the N3 RDF serialization of OWL.

@prefix :      <http://stackoverflow.com/q/28506192/1281433/> .
@prefix rdf:   <http://www.w3.org/1999/02/22-rdf-syntax-ns#> .
@prefix owl:   <http://www.w3.org/2002/07/owl#> .
@prefix xsd:   <http://www.w3.org/2001/XMLSchema#> .
@prefix rdfs:  <http://www.w3.org/2000/01/rdf-schema#> .

:A      a       owl:Class .
:B      a       owl:Class .

:p      a       owl:ObjectProperty .
:q      a       owl:ObjectProperty .

:D      a                    owl:Class ;
        owl:equivalentClass  [ a                   owl:Class ;
                               owl:intersectionOf  ( :A _:b0 )
                             ] .

_:b0    a                   owl:Restriction ;
        owl:onProperty      :p ;
        owl:someValuesFrom  [ a                   owl:Restriction ;
                              owl:onProperty      [ owl:inverseOf  :q ] ;
                              owl:someValuesFrom  :B
                            ] .

If you have the domain and range axioms, so that you can use the simpler form, it'd be:

@prefix :      <http://stackoverflow.com/q/28506192/1281433/> .
@prefix rdf:   <http://www.w3.org/1999/02/22-rdf-syntax-ns#> .
@prefix owl:   <http://www.w3.org/2002/07/owl#> .
@prefix xsd:   <http://www.w3.org/2001/XMLSchema#> .
@prefix rdfs:  <http://www.w3.org/2000/01/rdf-schema#> .

:A      a       owl:Class .
:B      a       owl:Class .

:p      a            owl:ObjectProperty ;
        rdfs:domain  :A .
:q      a            owl:ObjectProperty ;
        rdfs:domain  :B .

:D      a                    owl:Class ;
        owl:equivalentClass  [ a                   owl:Restriction ;
                               owl:onProperty      :p ;
                               owl:someValuesFrom  [ a                   owl:Restriction ;
                                                     owl:onProperty      [ owl:inverseOf  :q ] ;
                                                     owl:someValuesFrom  owl:Thing
                                                   ]
                             ] .

Creating an OWL sub-class based on the equality of two object properties

1 Answers1