The Web Service Modeling Language (WSML) is a language for the specification of different aspects of Semantic Web Services. It provides a formal language for the Web Service Modeling Ontology WSMO which is based on well-known logical formalisms, specifying one coherent language framework for the description of Semantic Web Services, starting from the intersection of Datalog and the Description Logic SHIQ. This core language is extended in the directions of Description Logics and Logic Programming in a principled manner with strict layering. The most expressive language in the WSML family, namely WSML-Full, is basically for the integration of semantically heterogeneous ontologies that are written in otherwise semantically incompatible WSML languages. Hence, it must combine First-order Logics Semantics with certain non-monotonic features, like default negation. At present, the semantics of WSML-Full is not well-defined and the respective definition is an open research problem. The purpose of this project is to investigate semantics of First-order Logics and various non-monotonic Logics such as auto-epistemic Logics and based on this survey to develop a suitable formal semantics for WSML-Full Ontologies. The semantics should be defined in model-theoretic terms.
The aspects that should be covered by the project are the following:

• Investigation of Semantics of First-order Logics and Non-monotonic Logics 
• Development of an adequate model-theoretic semantics that combines both worlds Discussion of the properties of the proposed semantics (in terms of complexity, relation to semantics of less expressive WSML languages etc.)
• One potential path for extension or future work in an additional thesis would be definition of a correct calculus for the given semantics, an investigation on the completeness properties of the calculus and a prototypical implementation. Another possible path of research is what query answering means in WSML-Full under such a semantics and how it can be achieved in an efficient way.