Abstract. A common practice in conceptual modeling is to separate the intensional from the extensional model. Although very intuitive, this approach is inadequate for many complex domains, where the borderline between the two models is not clear-cut. Therefore, OWL-Full, the most expressive of the Semantic Web ontology languages, allows combining the intensional and the extensional model by a feature we refer to as metamodeling. In this paper, we show that the semantics of metamodeling adopted in OWL-Full leads to undecidability of basic inference problems, due to free mixing of logical and metalogical symbols. Based on this result, we propose two alternative semantics for metamodeling: the contextual and the HiLog semantics. We show that SHOIQ — a description logic underlying OWL-DL — extended with metamodeling under either semantics is decidable. Finally, we show how the latter semantics can be used in practice to axiomatize the logical interaction between concepts and metaconcepts. 1

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Abstract. In recent years ontologies – shared conceptualizations of some domain – are increasingly seen as the key to further automation of information processing. Although many approaches for representing and applying ontologies have already been devised, they haven’t found their way into enterprise applications. In this paper we argue that ontology-based systems lack critical technical features, such as scalability, reliability, concurrency and integration with existing data sources, as well as the support for modularization and meta-concept modeling from the conceptual modeling perspective. We present a conceptual modeling approach that balances some of the trade-offs to more easily integrate into existing enterprise information infrastructure. Our approach is implemented within KAON, the Karlsruhe Ontology and Semantic Web tool suite. 1

Metaclasses provide a useful mechanism for abstraction in object-oriented languages. But most languages that support metaclasses impose severe restrictions on their use. Typically, a metaclass is allowed to have only a single instance and all metaclasses are required to share a common superclass [6]. In addition, few languages that support metaclasses include a static type system, and none include a type system with nominal subtyping (i.e., subtyping as defined in languages such as the Java TM Programming Language or C#). To elucidate the structure of metaclasses and their relationship with static types, we present a core calculus for a nominally typed object-oriented language with metaclasses and prove type soundness over this core. To our knowledge, no previous formalization of metaclasses in a language with nominal subtyping exists. This calculus is presented as an adaptation of Featherweight GJ [13], and is powerful enough to capture metaclass relationships beyond those expressible in common object-oriented languages, including arbitrary metaclass hierarchies and classes as values. We also describe how the addition of metaclasses allow for integrated and natural expression of several common design patterns.