Recognizing and supporting human activities is an important challenge for ambient assisted living. In this paper we introduce a novel argumentation-based approach for dealing with human activity recognition. By considering a model of the world and a set of observations of the world, hypothetical fragments of activities are built. The hypothetical fragments of activities will be goal-oriented actions and they will be considered defeasible. Therefore we consider extension-based argumentation semantics for local selection of hypothetical fragments of activities. By considering degrees of fulfillment of activities and local selection, a global selection of hypothetical fragments of the activities is defined. Therefore, we can make explicit statements about why one hypothetical activity was performed.