Checking for properties of Web ontologies is important for the development of reliable Semantic Web systems. Software specification and verification tools can be used to complement the Knowledge Representation tools in reasoning about Semantic Web. The key to this approach is to develop sound transformation techniques from Web ontology to software specifications so that the associated verification tools can be applied to check the transformed specification models. Our previous work has demonstrated a practical approach to translating Web ontologies to Z specifications. However, from a sound engineering point of view, the translation is lacking the theoretical work that can formally relate the respective underlying logical systems of OWL and Z. In this paper, we take the advantage that the logics underlying OWL and Z can be represented as institutions and we show that the institution comorphism provides a formal semantic foundation for the transformation from OWL to Z. 1.

The Semantic Web (SW) is viewed as the next generation of the Web that enables intelligent software agents to process and aggregate data autonomously. Ontology languages provide basic vocabularies to semantically markup data on the SW. We have witnessed an increase of numbers of SW languages in the last years. These languages, such as RDF, RDF Schema (RDFS), the OWL suite of languages, the OWL − suite, SWRL, are based on different semantics, such as the RDFS-based, description logic-based, Datalog-based semantics. The relationship among the various semantics poses a challenge for the SW community for making the languages interoperable. Institutions provide a means of reasoning about software specifications regardless of the logical system. This makes it an ideal candidate to represent and reason about the various languages in the Semantic Web. In this paper, we construct institutions for the SW languages and use institution morphisms to relate them. We show that RDF framework together with the RDF serializations of SW languages form an indexed institution. This allows the use of Grothendieck institutions to combine Web ontologies described in various languages.

The correctness of the Z semantics of OWL is the theoretical foundation of using software engineering techniques to verify Web ontologies. As OWL and Z are based on di#erent logical systems, we use institutions to represent their underlying logical systems and use institution morphisms to prove the correctness of the Z semantics for OWL DL.