Using category theoretic notions, in particular diagrams and their colimits, we provide a common semantic backbone for various notions of modularity in structured ontologies, and outline a general approach for representing (heterogeneous) combinations of ontologies through interfaces of various kinds, based on the theory of institutions. This covers theory interpretations, (definitional) language extensions, symbol identifications, and conservative extensions. In particular, we study the problem of inheriting conservativity between sub-theories in a diagram to its colimit ontology, and apply this to the problem of localisation of reasoning in ‘modular ontology languages’ such as DDLs or E-connections.

We present an overview of the landscape of ontology languages, mostly pertaining to the first-order paradigm. In particular, we present a uniform formalisation of these languages based on the institution theoretical framework, allowing a systematic treatment and analysis of the translational relationships between the various languages and a general analysis of properties of such translations. We also discuss the importance of language translation from the point of view of ontological modularity and logical pluralism, and for the borrowing of tools and reasoners between languages.

Abstract. Several modularity concepts for ontologies have been studied in the literature. Can they be brought to a common basis? We propose to use the language of category theory, in particular diagrams and their colimits, for answering this question. We outline a general approach for representing combinations of logical theories, or ontologies, through interfaces of various kinds, based on diagrams and the theory of institutions. In particular, we consider theory interpretations, language extensions, symbol identification, and conservative extensions. We study the problem of inheriting conservativity between sub-theories in a diagram to its colimit ontology. Finally, we apply this to the problem of conservativity when composing DDLs or E-connections. 1

This paper systematically applies tools and techniques from the area of algebraic specification theory to corresponding ontology structuring and design tasks. We employ the heterogeneous structuring mechanisms of the heterogeneous algebraic specification language HetCasl for defining an abstract notion of structured heterogeneous ontology. This approach enables the designer to split up a heterogeneous ontology into semantically meaningful parts and employ dedicated reasoning tools to them. In particular, we distinguish three fundamentally different kinds of combining heterogeneous ontologies: integration, connection, and refinement.

Abstract. We present a general framework for the design of formal ontologies, resting on two main principles: firstly, we endorse Rudolf Carnap’s principle of logical tolerance by giving central stage to the concept of logical heterogeneity, i.e. the use of a plurality of logical languages within one ontology design. Secondly, to structure and combine heterogeneous ontologies in a semantically well-founded way, we base our work on abstract model theory in the form of institutional semantics, as forcefully put forward by Joseph Goguen and Rod Burstall. The theoretical foundation in institution theory establishes a close link to algebraic specification theory. We explore this link by systematically applying tools and techniques from this area to corresponding ontology structuring and design tasks, in particular employ the structuring mechanisms of the heterogeneous algebraic specification language HetCasl for defining an abstract notion of structured heterogeneous ontology, leading to the idea of a hyperontology, a heterogeneous, distributed,

Abstract. The Distributed Ontology Language (DOL) is a recent development within the ISO standardisation initiative 17347 Ontology Integration and Interoperability (OntoIOp). In DOL, heterogeneous and distributed ontologies can be expressed, i.e. ontologies that are made up of parts written in ontology languages based on various logics. In order to make the DOL meta-language and its semantics more easily accessible to the wider ontology community, we have developed a notion of institute which are like institutions but with signature partial orders and based on standard set-theoretic semantics rather than category theory. We give an institute-based semantics for the kernel of DOL and show that this is compatible with institutional semantics. Moreover, as it turns out, beyond their greater simplicity, institutes have some further surprising advantages over institutions. 1