Based on work done in collaboration

(Mestre) Disserta,c~ao para Obten,c~ao do Grau de Doutor em Matem'atica

Two notions are becoming increasingly important in ontological engineering: modularity and heterogeneity. Whilst heterogeneity al-lows ontologies to be specified in different logical formalisms and thus calls for sophisticated integration and combination techniques, various notions of modularity have been envisaged in the literature in order to support maintenance and reuse of (parts of) ontologies. Can these de-mands 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 ap-proach for representing (heterogeneous) combinations of logical theories, or ontologies, through interfaces of various kinds, based on diagrams and the theory of institutions. In particular, we cover theory interpreta-tions, (definitional) language extensions, symbol identifications, and con-servative extensions. We study the problem of inheriting conservativity between sub-theories in a diagram to its colimit ontology. Finally, we ap-ply this to the problem of localisation of reasoning in ‘modular ontology languages’ such as DDLs or E-connections.

Abstract not found