Conservativity Principle

The Conservativity Principle stipulates that an alignment must not introduce new subsumption relationships (i.e., A rdfs:subClassOf B) between named classes within either the source or target ontology that did not logically hold before the alignment was applied. It ensures the mapping only bridges two independent models without rewriting their internal taxonomic structure. Violations typically occur when a class in Ontology 1 is mapped to a class in Ontology 2, and the reasoning engine infers a new, invalid parent-child link between two classes in Ontology 1 based on Ontology 2's axioms.

Consider two ontologies:

• Ontology A: Student and Professor are disjoint siblings under Person.
• Ontology B: Thesis Advisor is a sub-class of Professor.

An alignment maps Thesis Advisor in B to Student in A. A reasoner will now infer that Student is a sub-class of Professor in Ontology A, violating the original disjointness axiom. This is a conservativity violation because the mapping introduced a new subsumption (Student ⊑ Professor) within Ontology A that did not exist pre-alignment.

Conservativity is a stricter requirement than logical consistency (or coherence). A merged ontology can be consistent—meaning it contains no logical contradictions—yet still violate conservativity. In the example above, the merged ontology is technically consistent (it is not impossible for a Student to also be a Professor), but it is non-conservative because it adds a new, unintended taxonomic relationship to Ontology A. Conservativity preserves the original designer's intent for the class hierarchy.

Detecting violations requires computing the deductive closure of the original ontologies independently and comparing it to the closure of the merged ontology. The process involves:

• Pre-computation: Calculate all entailed subsumptions within Ontology 1 alone.
• Post-computation: Calculate all entailed subsumptions within the merged ontology (Ontology 1 + Ontology 2 + Alignment).
• Diff: If the post-computation set contains a subsumption between two named classes of Ontology 1 that was absent in the pre-computation set, a violation is flagged. Tools like LogMap use this method for automated repair.

Conservativity is a primary driver for alignment repair algorithms. When a matcher generates a high-recall mapping, many correspondences are logically sound but non-conservative. The repair step iteratively removes the minimal set of mappings to restore conservativity. This is often framed as a root cause analysis problem: identifying the specific mapping(s) that trigger the unintended inference. The goal is to maximize the number of retained correct mappings while eliminating all violations.

Strict logical conservativity is computationally expensive (EXPTIME-complete) for expressive ontologies. In practice, systems use approximate conservativity by limiting the type of inferences checked. For example, checking only violations that involve the classification hierarchy (rdfs:subClassOf) rather than all possible complex role restrictions. This trade-off allows scalable repair for large biomedical ontologies like SNOMED CT and the Gene Ontology while catching the most semantically damaging mapping errors.