Object Property Axioms

Object properties link individuals to individuals.

A set of instances connected to the property is called a property extension.

SubObjectPropertyOf axioms count

This axiom says that a property is a subproperty of another property. It also means that the instances of the subproperty are subsets to the property extension of the second property.

This Axiom can equally be used on object properties and data properties.

Equivalent object property axioms count

Equivalent property axioms exist when two properties have the same property extension.

This Axiom can equally be used on object properties and data properties.

Inverse object properties axioms count

Properties have a direction defined with domain to range, the inverseof term is used to mirror the direction.

This Axiom can equally be used on object properties and data properties.

Disjoint object properties axioms count

Two properties are disjoint when they don't have individuals in common.

Functional object properties axioms count

A functional property is a property which can only have one value. E.g. a woman can have at most one husband.

This Axiom can equally be used on object properties and data properties.

Transitive object property axioms count

Transitive means that if a property contains the pair(x,y)and the pair (y,z) then we can conclude that the pair(x,z) is also part of der property.

$\begin{align}
            &\forall a,b,c \in A\colon\\
            &(a,b) \in R \,\land\, (b,c) \in R\\
            &\Rightarrow\; (a,c) \in R
        \end{align}$

Symmetric object property axioms count

If a property is symmetric it means that if a pair(x,y) exists, then there is also a pair (y,x).

Asymmetric object property axioms count

A asymmetric property has a pair(x,y) but never a pair(y,x).

Reflexive object property axioms count

Reflexiv means that a property relates to itself.

$R$ is reflexive :$\Longleftrightarrow \forall x \in M: xRx$

Irreflexive object property axioms count

Subsequently irreflexive means that no individual relates to itself.

$R$ is irreflexive :$\Longleftrightarrow \forall x \in M: \neg \ xRx$

Object property domain axioms count

The domain links a property to a class description.

There can be more than one domain for a property.

Object property range axioms count

The range links the property to either a class description or a data range.

There can be more than one range for a property.

SubPropertyChainOf axioms count

These axioms are used to create a chain of multiple properties. E.g. two hasParents properties are linked by a chain thus a hasGrandparents property will be identified.

Sources

1. https://www.w3.org/TR/owl-ref/#Property
2. https://www.w3.org/TR/owl2-primer/