|Approaches used by tools supporting ontology mapping are mostly based on schema mapping methods. But ontology has its own peculiarity. Schemas simulate entities of a domain, their conceptual structure, relationships and behavior and used for system development and implementation. Schemas often include properties of several entities or auxiliary information in a single abstract type. Ontology specifies a conceptualization, its foreground is concepts of a subject domain. Ontological information is structured not so arbitrarily. Structural specification of an ontology is not intended for storing and performing data, but reflects a place of concepts in a concept system, out of which a separate concept cannot exist.
Schema mapping tools usually include abstract type similarity evaluation by verbal and structural specifications. That is not sufficient for ontological concept semantics. The paper is dedicated to approaches that formally discover concept similarities on semantic level. Some of them specify additional concept semantics and don’t depend on structural specifications.
Supposing that well specified ontologies precisely reflect concept semantics, we apply a formal criterion to be sure that semantics is saved during mapping. This criterion is specification refinement relation taken from programming theory. It means that refining specification can be transparently used in place of refined one. This relation is formally defined for abstract data types and may be proved. Subsumption relation is a case of specification refinement defined over concept extents. Today’s ontological models support automatic inference of subsumption.
In addition to verbal and structural specifications of concept semantics, it’s useful for mapping to have specifications considering ontologies from a common point of view.
One of such approaches is using common underlying metaontology. Every concept of ontologies (as well as every relation or property if possible) becomes an instance of metaontology class or of a class expression in terms of metaontology. So ontological concepts are sorted into classes by their semantics in terms of the metaontology. Formally, in the mapping task, subsuming (refining) concept must belong to a subclass or to the same class of the metaontology with subsumed (refined) concept. Self specifications of concepts and specifications in terms of metaontology are independent since they use different levels of classification hierarchy. Metalevel approaches take their birth in conceptual modeling and become more actual in ontological modeling.
N. Guarino’s ontology gives much attention to various kinds of concept properties. There is a set of metaproperties, any concept may be evaluated by. They are essence, rigidity, identity, dependency, unity, properties of mereologyically related concepts and others. These metaproperties are formally defined, so metaproperty conflicts between mapped concepts mean incorrectness of mapping.
Metaproperty approach is partly related to the approach using top level ontology as a common top hierarchy for ontologies being mapped. Particular values of metaproperties correspond to fundamental concepts of the top level ontology.
One more approach adding semantic methods to ontology mapping is using instances of concepts as classes. It uses objects of real world, sample models, or data well classified using ontologies. Formally, in mapping task, conflict of a single instance in classes defined by related concepts means incorrectness of established relation. Such extensional approach “by example” is useful for search of relevant concepts or for verification of mapping.
Efforts of working groups on ontology development often take years. So conflicts of ontologies are conflicts of deeply thought out decisions. Ontology mapping needs tools supporting intelligent work of experts.
All the represented approaches may be implemented to be formal. But they are only helping tools for manual work of experts on ontology mapping. There are assumptions in any formal method: sufficiency of concept semantics of specifications, correctness of concept specification in terms of a metaontology and metaproperties, correctness of relating of real world object samples to ontological concepts and so on.
A protocol of experts’ work on ontology mapping requires participation of experts representing every ontology (as well as experts of metaontology and fundamental metaproperties) because ontologies have been often developed by different workgroups. Experts may make decisions on mentioned assumption in fields of their competences.
Some semantic conflicts may be discover in process of expert discussions as a result of application same additional metainformation or same instances of concepts to every ontology. Every represented approach helps experts to effectively discover hidden conflicts of ontologies. They may be implemented as a multiexpert interactive tool supporting ontology mapping or as a verbal discussion protocol for experts.