The evolution of consumer electronics, telecommunications and computing has empowered ambient intelligence into an emerging field of research bringing new possible solutions to many problems of human life. One of them is the technological assistance of elders who are suffering from a cognitive deficit with the execution of their everyday life activities inside what is called a smart home. To enable this technology, the first challenge to overcome is the recognition of the resident's activities of daily living (ADLs). This problem consists of inferring the minimal set of possible ongoing ADLs using templates (plans) of activities defined in a library. To successfully achieve that goal, we must exploit constraints of different natures (logical, temporal, etc.) in order to reject a maximal number of hypotheses. However, only a minority of works exploited the elementary spatial aspects related to objects and to their relations in the smart environment. In this paper, we propose a novel recognition model exploiting the fundamental qualitative spatial reasoning approach of Egenhofer to discriminate implausible ongoing activities. Furthermore, the model is validated through extensive testing of realistic scenarios based on clinical trials conducted at our laboratory with both normal and impaired subjects.