In this paper, we propose a set of tasks that are relevant for the modular reuse of ontologies. In order to formalize these tasks as reasoning problems, we introduce the notions of conservative extension, safety and module for a very general class of logic-based ontology languages. We investigate the general properties of and relationships between these notions and study the relationships between the relevant reasoning problems we have previously identified. To study the computability of these problems, we consider, in particular, Description Logics (DLs), which provide the formal underpinning of the W3C Web Ontology Language (OWL), and show that all the problems we consider are undecidable or algorithmically unsolvable for the description logic underlying OWL DL. In order to achieve a practical solution, we identify conditions sufficient for an ontology to reuse a set of symbols ``safely''---that is, without changing their meaning. We provide the notion of a safety class, which characterizes any sufficient condition for safety, and identify a family of safety classes--called locality---which enjoys a collection of desirable properties. We use the notion of a safety class to extract modules from ontologies, and we provide various modularization algorithms that are appropriate to the properties of the particular safety class in use. Finally, we show practical benefits of our safety checking and module extraction algorithms.
