Many real world applications of ontologies call for reasoning with modular ontologies. We describe a tableau-based reasoning algorithm based on Package-based Description Logics (P-DL), an modular ontology language that extends description logics. Unlike Classical approaches that assume a single centralized, consistent ontology, the proposed algorithm adopts a federated approach to reasoning with modular ontologies wherein each ontology module has associated with it, a local reasoner. The local reasoners communicate with each other as needed in an asynchronous fashion. Hence, the proposed approach offers an attractive approach to reasoning with multiple, autonomously developed ontology modules, in settings where it is neither possible nor desirable to integrate all involved modules into a single centralized ontology.