In recent years there has been a growing interest in solutions for the delivery of clinical care for the elderly because of the large increase in aging population. Monitoring a patient in his home environment is necessary to ensure continuity of care in home settings, but, to be useful, this activity must not be too invasive for patients and a burden for caregivers. We prototyped a system called Secure and INDependent lIving (SINDI), focused on (a) collecting a limited amount of data about the person and the environment through Wireless Sensor Networks (WSN), and (b) inferring from these data enough information to support caregivers in understanding patients' well-being and in predicting possible evolutions of their health. Our hierarchical logic-based model of health combines data from different sources, sensor data, tests results, common-sense knowledge and patient's clinical profile at the lower level, and correlation rules between health conditions across upper levels. The logical formalization and the reasoning process are based on Answer Set Programming. The expressive power of this logic programming paradigm makes it possible to reason about health evolution even when the available information is incomplete and potentially incoherent, while declarativity simplifies rules specification by caregivers and allows automatic encoding of knowledge. This paper describes how these issues have been targeted in the application scenario of the SINDI system.