Protege: Anonymous class to subsume all classes not participate in a relation

Question

Suppose there is 4 classes: a,b,c, d. and we have a has_relation some b.

I can define c as : has_relation some b to subsume a as its subclass.

but what if i want that the c to have d as its subclass.

(I know not(a has_relation some b) is not a true answer as d is not explicitly defined to has or has not any relation)

Answer 1

Strictly speaking this is not possible to infer due to the open world assumption. Thus, the only way to achieve this is by asserting that A is not related to B. Depending on the inferences you need, there are different ways to achieve this. In all cases you will need 2 relations: the first relation states that the relation does exist and the second relation states that the relation does not exist.

Option 1

If the inferences you require need to be applied to individuals, then you can specify it as follows:

ObjectProperty: isRelatedByRelationXOption1
    DisjointWith: 
        isNotRelatedByRelationXOption1

ObjectProperty: isNotRelatedByRelationXOption1
    DisjointWith: 
        isRelatedByRelationXOption1

If you then specify that individuals x1 and y1 are related via both these relations, the reasoner will indicate an inconsistency:

Individual: x1
    Facts:  
        isNotRelatedByRelationXOption1  y1,
        isRelatedByRelationXOption1  y1

Individual: y1

The potential disadvantage of defining the relations like this is that the following will not result in an inconsistency:

Class: A
    SubClassOf: 
        isRelatedByRelationXOption1 some B

Class: B

Class: C
      SubClassOf: 
          A,
          isNotRelatedByRelationXOption1 some B

If you want an inconsistency in this case, you will need to make use of Option 2.

Option 2

When we define the relations as below, class C will be unsatisfiable. Note that it is also not necessary to define the relations as Disjoint, except if you still want to detect individuals using both relations.

ObjectProperty: isRelatedByRelationXOption2
    Domain: 
        A

ObjectProperty: isNotRelatedByRelationXOption2
    Domain: 
        not (A)

 Class: A
    SubClassOf: 
         isRelatedByRelationXOption2 some B

 Class: B

 Class: C
     SubClassOf: 
         A,
         isNotRelatedByRelationXOption2 some B

Option 3

If you do not need to use Protege, you may want to consider using SHACL. See my answer on this Stackoverflow question.