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Smart Homes (SH) have emerged as a viable solution capable of providing assistive living for the elderly and disabled. Nevertheless, it still remains a challenge to assist the inhabitants of a SH in performing the correct action(s) at the correct time in the correct place. To address this challenge, this paper introduces a novel logic-based approach to cognitive modeling based on a highly developed logical theory of actions - the Event Calculus. Cognitive models go beyond behavioral models in that they govern an inhabitant's behavior by reasoning about its knowledge, actions and events. We present a formal cognitive model for a SH and describe the mechanisms for its use in facilitating assistive living. In addition we present a system architecture and demonstrate the use of the proposed approach through a real world daily activity.