Colimits are a useful tool for the combination of specifications and logical theories. We generalize the notion of colimit to a heterogeneous multi-logic setting. For practically realistic cases, the notion has to be weakened. We describe an algorithm that approximates the weaker notion but obtains a colimit whenever possible. This algorithm is being implemented as part of the Heterogeneous Tool Set HETS.

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 approach for representing, composing, and computing alignments, based on the category theoretic notions of diagram, pushout, and colimit. This generalises the possible ‘shapes ’ of alignments that have been introduced previously in similar approaches. We use the theory of institutions to represent heterogeneous ontologies, and show how the tool Hets can be employed to compute the colimit ontology of an alignment diagram. 1

Abstract. Systematic engineering design processes have many aspects in common

testing for refinement

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Abstract. We present a general approach for representing and combining alignments and computing these combinations, based on the category theoretic notions of diagram, pushout, and colimit. This generalises the possible ‘shapes ’ of alignments that have been introduced previously in similar approaches. We use the theory of institutions to represent heterogeneous ontologies, and show how the tool Hets can be employed to compute the colimit ontology of an alignment diagram. 1

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Abstract. We present the integration of refinement method of VSE verification tool, successfully used in industrial applications, in the Heterogeneous Tool Set HETS. The connection is done via introducing the dynamic logic underlying VSE and two logic translations in the logic graph of HETS. Thus the logic-independent layers of HETS are not modified and its proof management formalism can be applied to VSE specifications. 1