Ontologies explicate the contents, essential properties, and relationships between terms in a knowledge base. Many sources are now accessible with associated ontologies. Most prior work on the use of ontologies relies on the construction of a single global ontology covering all sources. Such an approach is not scalable and maintainable especially when the sources change frequently. We propose a scalable and easily maintainable approach based on the interoperation of ontologies. To handle user queries crossing the boundaries of the underlying information systems, the interoperation between the ontologies should be precisely defined. Our approach is to use rules that cross the semantic gap by creating an articulation or linkage between the systems. The rules are generated using a semi-automatic articulation tool with the help of a domain expert. To make the ontologies amenable for automatic composition, based on the accumulated knowledge rules, we represent them using a graph-oriented model extended with a small algebraic operator set. ONION, a user-friendly toolkit, aids the experts in bridging the semantic gap in real-life settings. Our framework provides a sound foundation to simplify the work of domain experts, enables integration with public semantic dictionaries, like Wordnet, and will derive ODMG-compliant mediators automatically.