Alignment Coherence Measure

The core mechanism verifies that no class in the merged ontology becomes unsatisfiable—meaning it cannot have any instances. An alignment that maps a class from Ontology A to a class in Ontology B that has a disjointness axiom with A's superclass creates a logical contradiction. Coherence measures invoke a description logic reasoner to detect these violations automatically.

A coherent alignment must respect the conservativity principle: the mapping should not introduce new subsumption relationships between named classes that did not exist in either source ontology. Violations occur when an alignment causes a class to become a subclass of another class in ways that contradict the original taxonomic structure. This is a stricter constraint than mere satisfiability.

Many ontologies explicitly declare classes as disjoint—meaning an individual cannot belong to both simultaneously. A coherence measure flags alignments that map an entity to two classes declared as disjoint in the merged ontology. For example, mapping ex:Cat to both ex:Mammal and ex:Reptile triggers a violation if those classes are disjoint.

Rather than a binary coherent/incoherent judgment, advanced measures produce a weighted score reflecting alignment quality. Each unsatisfiable class or conservativity violation is assigned a severity weight based on its depth in the class hierarchy or the confidence of the original correspondence. The final coherence measure is a normalized value, often between 0 (fully incoherent) and 1 (fully coherent).

Coherence measures are tightly coupled with alignment repair algorithms. When violations are detected, the measure identifies the minimal set of correspondences—called the conflict set—that must be removed to restore coherence. Systems like LogMap use this iterative diagnosis-and-repair loop to produce logically sound alignments from initially noisy mappings.

Beyond basic satisfiability, coherence measures analyze the subsumption hierarchy of the merged ontology. They detect cycles in the class hierarchy (e.g., A is a subclass of B, B is a subclass of A) and validate that the domain and range restrictions of properties remain consistent when classes from different ontologies are equated through owl:sameAs or equivalence mappings.