In creating their first OWL ontology, there are at least two aspects of EquivalentTo
and SubClassOf
that perplex users. The first is when to use EquivalentTo
and when to use SubClassOf
. The second problem is best illustrated by the following example:
ObjectProperty: a_to_b
Class: A1
EquivalentTo: (a_to_b some B)
Class: A2
SubClassOf: (a_to_b some B)
Class: B
Individual: b1
Types:
B
Individual: x
Facts:
a_to_b b1
When running a reasoner on this example, the individual x
is inferred to be of type A1
. What perplex users sometimes is that x
is not inferred to be of type A2
as well. This is shown in the next figure.

The difference between EquivalentTo
and SubClassOf
The first thing to be aware of wrt equivalentTo
is that
Class: C EquivalentTo: D
is an abbreviation for
Class: C SubClassOf: D Class: D SubClassOf: C
The semantics of SubClassOf
is subset. Thus, the above states that the set C
is a subset of the set D
and the set D
is a subset of the set C
. Which means that the sets C
and D
are exactly the same set. We say they are equivalent.
Note that if I know that the classes C1
and C2
are both subclasses of class C
, there is nothing more I can say about how class C1
relates to class C2
. This is a bit like knowing that bicycles and trucks are both vehicles – I can say nothing more about how bicycles relate to trucks beyond knowing that they are both vehicles.
Back to our initial example
Understanding the semantics of EquivalentTo
we can see that indeed the individual x
is an instance of A1
. Understanding the semantics of SubClassOf
helps us to understand why x
is not inferred to be of type A2
. We know that A2
is a subclass of a_to_b some B
and that x
is an instance of a_to_b some B
, but there is nothing that can force the reasoner to infer that x
is necessarily an instance of the class A2
. This is illustrated in the next figure.
When to use EquivalentTo
versus SubClassOf
EquivalentTo
is used for definitions. That is when you want to state the necessary and sufficient conditions for a concept.
SubClassOf
is used when you want to define a hierarchy from the most general to the most specific. I.e., it is typically what you see in taxonomies or in object oriented programming languages where one can define class hierarchies. In fact there is a strong relation between OWL 2 ontologies and object orientation which I explore here in more detail.
Conclusion
In this post I explained the difference between EquivalentTo
versus SubClassOf
and how they are used, as well as some inferences thatmay be confusing to new users. You can find the example ontology on GitHub.