owl:equivalentClass is a built-in property that links a
class description to another class description. The meaning of such a class
axiom is that the two class descriptions involved have the same class extension
(i.e., both class extensions contain exactly the same set of individuals).
owl:equivalentClass has owl:Class as domain and as range.
In its simplest form, an equivalentClass axiom states the equivalence (in terms of their class extension) of two named classes. An example:
AXIOM SCHEMA: class description
owl:equivalentClass class description
A class axiom may contain (multiple) owl:equivalentClass statements.
NOTE: The use of
owl:equivalentClass does not imply
class equality. Class equality means that the classes have the same intensional
meaning (denote the same concept). In the example below, the concept of
"President of the US" is related to, but not equal to the concept of the
principal resident of a certain estate. Real class equality can only be
expressed with the
As this requires treating classes as individuals, class equality can only be
expressed in OWL Full.
owl:equivalentClass can also be used to define an
enumerated class by linking a type 1 class description (a class identifier) to a
type 2 class description (an enumeration). An example:
This class axiom defines the class of operas that together represent the "Da Ponte operas of Mozart" (a popular subject in musicology). By using the equivalentClass construct we can state necessary and sufficient conditions for class membership, in this case consisting of an enumeration of three individuals, no less, no more.
Note that relating two classes via
owl:sameAs is a very different
thing to relating them via
owl:equivalentClass. The former says
that the two objects are in fact the same, is actually an example of class
as instance, and thus pushes the ontology out of OWL DL. The latter is an
assertion that the extension (e.g. the collection of members) of the classes is
equivalent. OWL DL does not put any constraints on the types of class
descriptions that can be used as subject and object of an
owl:equivalentClass statement. In OWL Lite the subject must be a
class name and the object must be either a class name or a property restriction.
NOTE: Although in principle different types of class descriptions are allowed as the subject of an owl:equivalentClass statement, in practice it usually is some class identifier. This is also true for the examples in this section.
It is possible to have multiple equivalentClass axioms about the same class. However, this requires care. Both axioms must lead to the same outcome, i.e. exactly the same class extension. For example, an alternate equivalentClass axiom for Mozart's "Da Ponte operas" could be the following one:
This states that the class extension of the Da Ponte operas of Mozart corresponds exactly to those operas which are composed by Mozart and for which the libretto is written by Da Ponte (note: intersection = "and"). This axiom indeed defines a class with exactly the same instances as the previous axiom.
NOTE: If we wanted to "upgrade" an axiom of the form "A subClassOf B" to "A equivalentClass B" (meaning that the class extension of A is not just any subset, but in fact the same set as the class extension of B), we could add a second subClassOf axiom of the form (B subClassOf A), which by definition makes the two class extensions equivalent (and thus has the same meaning as "A equivalentClass B"). Such subClassOf "cycles" are explicitly allowed. As OWL is usable in a distributed environment, this can be a useful feature.
We have already seen that class expressions can be the targets of
rdfs:subClassOf constructors. They can also be the target of
owl:equivalentClass. Again, this avoids the need to contrive names for
every class expression and provides a powerful definitional capability based on
satisfaction of a property.
<owl:onProperty rdf:resource="#locatedIn" />
<owl:someValuesFrom rdf:resource="#TexasRegion" />
TexasThings are exactly those things located in the Texas
region. The difference between using
owl:equivalentClass here and using
rdfs:subClassOf is the difference between a necessary condition and a
necessary and sufficient condition. With rdfs:subClassOf, things that are
located in Texas are not necessarily TexasThings. But, using
owl:equivalentClass, if something is located in Texas, then it must be
in the class of TexasThings.