Ontology Alignment

The core output of alignment is a set of mappings (or alignments) that define the logical relationship between entities in a source ontology and a target ontology. These are not just simple equality checks.

• Equivalence (≡): The connected classes or properties have exactly the same meaning and extension.
• Subsumption (⊑): The source entity is more specific than the target entity.
• Disjointness (⊥): The entities share no logical overlap.
• Overlap (∩): The entities share some instances but are not equivalent.

Every alignment carries a confidence value (typically [0,1]) representing the degree of trust in the match. This is derived from composite similarity measures.

• Lexical Similarity: String-based metrics like Levenshtein distance or Jaccard index on labels and synonyms.
• Structural Similarity: Analyzing the graph neighborhood; if two nodes have similar parent and child relationships, they are likely similar.
• Extensional Similarity: Comparing the sets of instances (individuals) that belong to each class. High overlap suggests a strong match.

The logical complexity of a mapping is defined by its cardinality, which dictates how many entities in the source can map to entities in the target.

• 1-to-1 (1:1): A single source class maps to a single target class. The simplest and most stable alignment.
• 1-to-N (1:N): A single source class maps to a combination (union or intersection) of multiple target classes.
• N-to-1 (N:1): Multiple source classes collapse into a single, more general target class.
• N-to-M (N:M): The most complex mapping, requiring complex logical constructors to define the correspondence.

The process of discovering alignments can be automated, manual, or hybrid. The strategy chosen directly impacts the recall and precision of the resulting knowledge graph.

• Terminological Matchers: Rely solely on string normalization and external thesauri (e.g., WordNet) to find lexical overlaps.
• Structural Matchers: Use graph homomorphism algorithms to find similar sub-graph topologies.
• Semantic Matchers: Employ satisfiability (SAT) solvers and description logic reasoners to check if a mapping introduces logical inconsistencies in the merged ontology.

A critical characteristic of robust alignment is the ability to detect and resolve logical incoherence. A mapping is incoherent if it causes a class to become unsatisfiable (it can never have instances).

• MIRA (Minimal Incoherence Repair Algorithm): Identifies the minimal set of mappings that must be removed to restore logical consistency.
• Weighted Repair: Automatically removes mappings with the lowest aggregated confidence scores first to resolve conflicts while preserving the maximum semantic overlap.

Simple alignments link single entities, but complex alignments express relationships between compound concepts using expressive constructors.

• Union Mappings: SourceClass ≡ (TargetClassA ∪ TargetClassB).
• Property Restriction Mappings: SourceClass ≡ (TargetClass ⊓ ∃hasProperty.TargetValue).
• Transformation Functions: Mappings that include unit conversion (e.g., Celsius to Fahrenheit) or string manipulation (e.g., concatenating first and last name) to bridge data property differences.