Ontologies are formal, declarative knowledge representation models, forming a semantic foundation for many domains. As the Semantic Web gains attention as the next generation of the Web, ontologies' importance increases accordingly. Different ontologies are heterogeneous, which can lead to misunderstandings, so there is a need for them to be related. The suggested approaches can be categorized as either rule-based or learning-based. The former works on ontology schemas, and the latter considers both schemas and instances. This book makes 6 assumptions to bound the matching problem, then presents 3 systems towards the mutual reconciliation of concepts from different ontologies: (1) the Puzzle system belongs to the rule-based approach; (2) the SOCCER (Similar Ontology Concept ClustERing) system is mostly a learning-based solution, integrated with some rule-based techniques; and (3) the Compatibility Vector system, although not an ontology-matching algorithm by itself, instead is a means of measuring and maintaining ontology compatibility, which helps in the mutual understanding of ontologies and determines the compatibility of services (or agents) associated with these ontologies.

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