A novel approach for building autonomic computing systems is presented.Autonomic computing systems are systems which are self-managed, self-healing, self- organised, ultra-reliable, robust, and flexible. These systems have multiple ways of accomplishing their purpose,and are capable of reconfiguring themselves in order to optimise their performance, achieve their goals under varying and unpredictable conditions, recover from internal faults and protect themselves. The presented approach for building autonomic computing systems is based on an extension of Bunge ontology and the Bunge- Wand-Weber (BWW) models. An extended ontology is presented which models a system as an organised whole exhibiting a coherent and useful overall behaviour. Ontological component models captured using software engineering diagrams enable these systems to have self- awareness on their construction, their available resources, their external environment, and their goals. Self-organisation, self-adaptation and self-healing are achieved by employing a controller synthesis algorithm based on the Ramadge and Wonham supervisory control theory of discrete event systems.