In this paper, we propose a non-quantitative logical approach to ADL recognition in a smart home, dedicated to Alzheimer's patients. Our formal framework for the recognition process is based on lattice theory and action description logic. Our framework reduces the uncertainty about the prediction of the observed patient's behaviour, allowing the assistant agent to anticipate the opportunities for assistance. This is achieved by dynamically generating the future potentially incoherent intentions of the patient, which result from the symptoms of their cognitive impairments (disorientation, memory lapse, etc.). This approach offers an effective solution to actual recognition of ADL in a smart home, in order to provide assistance to persons suffering from Alzheimer's disease.