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Recognition of activities of daily living (ADLs) is an enabling technology for several ubiquitous computing applications. Most activity recognition systems rely on supervised learning to extract activity models from labeled datasets. A problem with that approach is the acquisition of comprehensive activity datasets, which is an expensive task. The problem is particularly challenging when focusing on complex ADLs characterized by large variability of execution. Moreover, several activity recognition systems are limited to offline recognition, while many applications claim for online activity recognition. In this paper, we propose POLARIS, a framework for unsupervised activity recognition. POLARIS can recognize complex ADLs exploiting the semantics of activities, context data, and sensors. Through ontological reasoning, our algorithm derives semantic correlations among activities and sensor events. By matching observed events with semantic correlations, a statistical reasoner formulates initial hypotheses about the occurred activities. Those hypotheses are refined through probabilistic reasoning, exploiting semantic constraints derived from the ontology. Our system supports online recognition, thanks to a novel segmentation algorithm. Extensive experiments with real-world datasets show that the accuracy of our unsupervised method is comparable to the one of supervised approaches. Moreover, the online version of our system achieves essentially the same accuracy of the offline version.