It is generally acknowledged that use of the Web and the Internet to retrieve information will continue to expand. With the large amount of knowledge available through the Internet, users are starting to look for effective ways to filter through the information, to find only the information relevant to their work. This article offers a formal treatment of the semantics for the ontologies underlying knowledge bases. We define methods which allow an interoperability between knowledge bases created by different knowledge engineers. Our goal is to filter out information retrieved from a knowledge base by using an ontology created by the user, in order to retrieve only the tailored information that the user is after. This will require defining means to compare, link or merge ontologies. This work is significant in that our formal definition of ontology dispenses with the class/instance boundary, thus saving complexity, while allowing a filtering mechanism for facilitating interoperability.