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Home-based health monitoring systems are currently being used to support early detection of abnormal conditions and prevention of its serious consequences. Many patients can benefit from continuous ambulatory monitoring as a part of a diagnostic procedure, optimal maintenance of a chronic condition or during supervised recovery from an acute event or surgical procedure. An evolution of this approach is the use of the mobile infrastructure and wearable technology, which mainly provides more freedom to their users. While these approaches use mobile communication devices just as a router of health information, we argue that such devices can make use of reasoning mechanisms so that they can take decisions and provide a better health care support to their users. This paper discusses the specification of a deductive health monitoring system, where its components are represented by assistant agents running in mobile devices and using a low cost wireless communication protocol (SMS) to exchange knowledge with a central root. Requirements for communication protocol and agent reasoning, based on a production system, are shown in details together with some practical experiments.