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.