This pattern helps resolving a logical inconsistency triggered by a situation of disjoint classes subsuming a common sub-class. When we need to define – for some modeling issues related to domain of interest – a class as a sub-class of two disjoint classes, a disjointness inconsistency is caused. The problem can be illustrated by the following scenario: let’s consider a class Sub_Class defined as a sub-class of a class Disjoint_Class 2; and a class Disjoint_Class 1 disjoint with the Disjoint_Class 2 (see diagram in attached file). If we need to add a sub-class relation between the Sub_Class and the Disjoint_Class 1, this generates a disjointness inconsistency:

- If the extension of the Sub_Class contains individuals instantiating this sub-class, the logical inconsistency will be extended to the knowledge base; - If the Sub_Class is not instantiated to individuals, it will be diagnosed as an unsatisfiable class.

To solve this inconsistency, one can think about deleting the disjointness axiom. However, this can alter the semantics expressed in the ontology, and negatively affect consistency checking and automatic evaluation of existing individuals as explained in [1]. This pattern tackles the questions of how to resolve the inconsistency caused by such kind of subsumption while preserving existing knowledge.

[1] Völker, J., Vrandecic, D., Sure, Y., Hotho, A.: Learning Disjointness. In F., Enrico, K., Michael, May. Wolfgang (Eds.). Proceedings of the 4th European Semantic Web Conference, ESWC 2007. LNCS: Vol. 4519 pp: 175-189. (2007)

Covered Requirements: The pattern solves a problem of disjointness inconsistency caused by a subsumption relation without deleting the disjointness axiom so that existing knowledge can be preserved.

The application of the solution can be described by the following process (see diagram in attached file):

1.The pattern defines a Hybrid Class as a union of the definitions of the disjoint classes implicated in the inconsistency to be resolved; 2.The pattern defines a subsumption between the most specific common super-class of the disjoint classes implicated in the inconsistency, and the Hybrid Class created; 3.The pattern defines a subsumption between the Hybrid Class and the sub-class involved in the inconsistency.

Consequences: The application of the pattern resolves the disjointness inconsistency (even if the involved sub-class is instantiated by individuals) and preserves existing knowledge. As a Logical OP, this pattern is independent from a specific domain of interest. However, it depends on the expressivity of the logical formalism used for the representation of the ontology. Therefore, the language of the targeted ontology should allow expressing class union.

ID of the sub-class (Sub_Class). ID of the first disjoint class (Disjoint_Class 1). ID of the second disjoint class (Disjoint_Class 2). ID of the most specific common super-class of the disjoint classes involved (Common_Super_Class).

{Animal ⊑Fauna-Flora, Plant ⊑Fauna-Flora, Carnivorous-Plant ⊑Plant, Plant ⊑ Not(Animal)}

If we apply a change to the ontology defining Carnivorous-Plant class as a sub-class of the class Animal, we cause a disjointness inconsistency. The proposed pattern resolves this kind of inconsistency.

1.The pattern defines a class Animal_Plant as a union of the definitions of the disjoint classes Animal and Plant; 2.The pattern defines a subsumption between the most specific common super-class of the disjoint classes Fauna-Flora and the hybrid class created Animal_Plant; 3.The pattern defines a subsumption between the defined hybrid class Animal_Plant and the sub-class Carnivorous-Plant involved in the inconsistency.