So they are either related by one of these Properties, e.g. via R or via S, i.e. one of them, but they are never be related with both Properties. Then these two Properties are defined as
Disjoint Properties. If these Properties are disjoint one can define one Property for example as
hasParent as an
ObjectProperty and one states that on the same hand that this should be disjoint with the Property
hasChild via the
owl:propertyDisjointWith Property. Thus
propertDisjoinWith defines two disjoint Properties.
There is a shortcut to make clear that several Properties are disjoint of each other. For example, one defines Set or a Collection of Properties and one states that all of these are disjoint. For this one defines a Class that is of type
owl:DisjointProperties and the members of this are part of this Collection.
:hasParent a owl:ObjectProperty ; owl:propertyDisjointWith :hasChild .
 rdf:type owl:AllDisoinProperties owl:members ( :hasParent :hasChild :hasGrantchild ) .
One can make a Property Hierarchy where one Property is at the top and another one at the bottom, which means that one has a top property of which all other Properties are Subproperties of but which is never a Subproperty of any other Property and one might have a Bottom Property which is always Subproperty of any other Property, but never any other Property is Subproperty of this Bottom Property. Therefore on can define Top Properties and Bottom Properties. Because of the distinction that one can has Object Properties and Datatype Properties, one has four different special Properties which are the
topObjectProperty that related each potential Individuals and is SuperClass of all Object Properties and one has the
owl:BottomObjectProperty which connects no Individuals at all, which is the Subclass of all Object Properties. For the Datatype Properties one has the
owl:topDatatypeProperty which means relates all Individual with all possible typed Literals and which is Superclass to all Datatype Properties and one has on the bottom the
owl:bttomDatatypeProperty which connects no Individual and no typed Literal and it is of course Subclass of all possible Datatype Properties.
owl:topObjectPropertyrelates each potential pair of individuals, superclass for Object Properties
owl:bottomObjectPropertyconnects no Individuals, subclass of all Object Properties
owl:topDatetypePropertyrelates all Individuals with all typed Literals, Superclass for all Datatype Properties
owl:bottomDatatypePropertyconnects no Individual and no types literal, subclass of all Datatypes Properties