Abbreviations

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Modularity in logical theories and ontologies

Modularity of logical theories is a classical subject in mathematical logic and philosophy of science. Due to the ever increasing size and complexity of logical theories that are used to represent ontologies and software specifications, the problem of defining appropriate notions of modularity and of providing reasoning support for dealing with modularity has recently become an important research topic also in these areas. In this course, we introduce and survey recent progress in the field. The course starts with a general introduction to modularity in the context of propositional and first-order logic, highlighting also the connection to classical notions such as conservative extensions and interpolation. We then switch to ontologies and description logics, introduce different notions of modularity, analyze their interrelation and possible use, and consider a variety of reasoning tasks such as the extraction of a module from an ontology. Concrete applications to medical ontologies are also presented.