Recognising the human context in terms of ongoing human activities is of major importance to ensure an efficient context-aware assistance. In this paper, a hybrid approach combining deep learning and probabilistic commonsense reasoning is proposed for anticipating human activities in AmI environments. Deep learning models are exploited for recognising environment objects, human hands and user’s indoor locations. To implement probabilistic commonsense reasoning, probabilistic fluents are introduced in the formalism of event calculus formulated in answer set programming (ECASP). The reasoning axiomatization is based on an ontology describing the user’s context when performing an activity. Using reasoning based on temporal projection and abduction enables an eXplainable AI (XAI) approach for activity anticipation. Experimental results show the high accuracy of inferences in terms of activity anticipation and a very low computation time in knowledge-intensive scenarios, rendering the system compatible with real-time applications.