Alignment Repair

The systematic identification of logical contradictions introduced by a candidate alignment. When two ontologies are merged using generated correspondences, the resulting union may contain unsatisfiable classes—classes that cannot have any instances without violating axioms. Detection algorithms traverse the merged TBox to pinpoint the minimal set of conflicting correspondences responsible for the inconsistency. This often involves computing MUPS (Minimal Unsatisfiability-Preserving Sub-TBoxes), which isolate the exact subset of axioms causing a specific class to become incoherent.

A primary source of logical conflict occurs when an alignment maps a class from one ontology to a class in another that is declared disjoint from it. For example, if Ontology A maps Protein to Ontology B's ChemicalEntity, but Ontology B asserts Protein is disjoint from ChemicalEntity, the merged ontology becomes incoherent. Repair algorithms must identify and remove these disjointness axioms or the offending correspondences. Tools like LogMap use a Horn propositional logic representation to efficiently compute the minimal repair plan that resolves all disjointness conflicts while preserving as many correct mappings as possible.

A stricter logical constraint applied during repair to ensure the alignment does not alter the original classification hierarchies. The conservativity principle mandates that a mapping should not introduce new subsumption relationships between named classes that were not derivable in the original ontologies independently. Violations occur when a correspondence causes a class in Ontology A to become a subclass of a class in Ontology A that it was not previously classified under, solely due to the imported axioms from Ontology B. Repair under conservativity removes correspondences that cause these unintended structural changes.

Repair algorithms often incorporate the confidence scores assigned by the initial matcher to prioritize which correspondences to remove. The goal is to maximize the aggregate confidence of the retained alignment while restoring full logical coherence. This is typically formulated as a weighted Max-SAT problem or a hitting set problem over the set of conflicting correspondence clusters. The algorithm iteratively selects the lowest-confidence correspondence from each minimal conflict set until all conflicts are resolved, producing a coherent alignment with the highest possible total confidence score.

The repair process relies heavily on description logic reasoners such as HermiT, ELK, or Pellet to compute the logical closure of the merged ontology. These reasoners perform tasks including consistency checking (does the merged ontology have a model?), classification (computing the inferred class hierarchy), and realization (finding the most specific types for individuals). The reasoner output reveals all entailments, including unintended ones, that the repair algorithm must address. Scalable repair for large biomedical ontologies like SNOMED CT and the Gene Ontology often uses the EL profile of OWL 2, which trades expressivity for polynomial-time reasoning.

Fully automated repair can be overly aggressive, removing correct but logically conflicting correspondences due to modeling errors in the source ontologies. Interactive repair frameworks present the detected conflicts and proposed resolutions to a domain expert for validation. The user can override the algorithm's decisions, mark specific correspondences as infallible (must be preserved), or adjust the underlying ontology axioms to resolve the conflict at the schema level. This human-in-the-loop approach is critical for high-stakes domains like biomedical data integration, where removing a correct mapping can have downstream clinical consequences.

A quantitative evaluation metric that assesses the logical consistency of an alignment by checking if the merged ontology introduces unsatisfiable classes or disjointness violations. This measure is the primary diagnostic tool that triggers the repair process.

• Detects classes that cannot have any instances under the merged axioms
• Flags violations where a class is simultaneously asserted as a subtype of two disjoint classes
• Provides a numerical score indicating the severity of logical conflicts

A logical constraint in alignment repair stipulating that a mapping should not introduce new subsumption relationships between named classes in the original ontologies. This principle ensures that the alignment does not alter the intended semantics of either source ontology.

• Prevents the merged ontology from implying class hierarchies absent in both source ontologies
• Violations indicate that at least one correspondence is logically incompatible
• Serves as a guiding heuristic for selecting which mappings to remove during repair

A family of formal knowledge representation languages that form the logical foundation of OWL, enabling decidable reasoning over ontologies through constructors like intersection, union, and existential restriction. Alignment repair relies on description logic reasoners to detect inconsistencies.

• Provides the formal semantics against which coherence is evaluated
• Reasoners like HermiT, Pellet, and ELK compute the logical closure of merged ontologies
• The specific DL profile (e.g., OWL 2 EL, OWL 2 QL) determines reasoning tractability

An algorithmic solution applied to ontology matching that finds a stable one-to-one mapping between two sets of entities based on mutual preference scores. When integrated with repair, it optimizes global alignment cardinality while respecting logical constraints.

• Ensures no two unmatched entities would prefer each other over their current mapping partners
• Reduces the search space for repair by enforcing structural cardinality constraints
• Originally derived from Gale-Shapley algorithm for matching residency placements

A W3C submission combining OWL with rule-based logic to express Horn-like rules, enabling the deduction of new relationships beyond description logic expressivity. SWRL rules can introduce additional logical dependencies that repair algorithms must account for.

• Extends OWL axioms with if-then implications over ontology instances
• Can create indirect conflicts when rules interact with imported alignments
• Repair systems must consider the deductive closure of both OWL axioms and SWRL rules