With the increasing availability of medical sensors and Internet of Things (IoT) devices for personal use, it becomes feasible to maintain a repository of measurements for personal health conditions. Consequently, it is tempting to analyze in-progress diseases and to identify the development of potential diseases with the measurement repository. However, there are a number of technical challenges in developing such applications, modeling the relationships between diseases and acquired measurements, representing medical expertise in machine-readable forms, and high complexity in diagnosing disease methods. We adopt a semantic-based approach to resolve the first two challenges, and utilize the concept of cloud computing to tackle with the last challenge. In this paper, we present a cloud platform which provides a core set of functionality needed to enable personal medical diagnosis over the network. We believe that the presented platform provides a comprehensive core functionality needed for various types of personal healthcare IoT applications.