The pattern “Define Hybrid Class Resolving Disjointness due to Subsumption” is proposed as a Logical Ontology Design Pattern (Logical OP) solving a problem of disjointness inconsistency caused by a subsumption relation. Further away from solving design problems where the primitives of the representation language do not directly support certain logical constructs, this pattern helps resolving a logical inconsistency triggered by a situation of disjoint classes subsuming a common subclass. The solution presented by the pattern resolves the inconsistency while preserving existing knowledge, i.e. a resolution alternative avoiding axiom deletion.
In this section, we specify the problem that the pattern deals with and the requirements covered by it; we detail the description of the solution given by this pattern and the consequences of its application; and we illustrate the pattern by an example problem and its corresponding solution.
The pattern “Define Hybrid Class Resolving Disjointness due to Subsumption” is proposed to solve a problem of disjointness inconsistency caused by a subsumption relation. 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 (Fig. 1). If we need to add a subclass 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. {Disjoint}
Disjoint_Class 2
Sub_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
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This pattern tackles the questions of how to resolve the inconsistency caused by such kind of subsumption while preserving existing knowledge.
Intent The purpose of this pattern is to support the semantics of a subsumption defined under two disjoint classes and resolve the resulting inconsistency. 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 pattern resolves a disjointness inconsistency –due to a subsumption–by defining a Hybrid Class based on the definition of disjoint classes implicated in the inconsistency; and redistributing correctly sub-class relations between the sub-class, the hybrid class, and the most specific common super-class of the disjoint classes implicated. The definition of the Hybrid Class is the union (OR) of the definitions of the disjoint classes.
The application of the solution can be described by the following process (Fig. 2): 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; 2 3. The pattern defines a subsumption between the Hybrid Class and the sub-class involved in the inconsistency.
Common_Super_Class
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.
axioms: To explain pattern application, we present in this section, an example problem and its corresponding solution according to the pattern.
Let’s consider the OWL ontology O defined by the following {Animal Fauna-Flora, Plant
Plant, Plant Animal}
Fauna-Flora, Carnivorous-Plant
If we apply a change to the ontology defining Carnivorous-Plant class as a subclass of the class Animal, we cause a disjointness inconsistency. The proposed pattern resolves this kind of inconsistency.
Example Solution The application of the pattern to resolve the example above is performed as follow: 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;
The proposed – Logical OP – pattern “Define Hybrid Class Resolving Disjointness
due to Subsumption” is applied as an Alternative Resolution Pattern in an ontology
evolution approach ONTO-EVOAL, guided by Change Management Patterns (CMP)
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The purpose of this pattern is to support the semantics of a subsumption defined under two disjoint classes and resolve the resulting inconsistency without removing existing knowledge. This pattern can be extended and adapted to resolve disjointness inconsistency due to instantiation.