This dissertation addresses the intersection of personal wireless technology and computational intelligence. The primary research issue addressed is the organization of radio domain knowledge into data structures processable in real-time that integrate machine learning and natural language processing technology into software radio. The thesis defines and develops the cognitive radio architecture. The features needed in the architecture are derived from cognitive radio use cases. These include inferring user communications context, shaping access-network demand, and realizing a protocol for real-time radio spectrum rental. Mathematical foundations for the knowledge-representation architecture are derived by applying point-set topology to the requirements of the use cases. This results in the set-theoretic ontology of radio knowledge defined in the Radio Knowledge Representation Language (RKRL). The mathematical analysis also demonstrates that isochronous radio software is not Turing-computable. Instead, it is constrained to a bounded-recursive subset of the total functions. A rapid-prototype cognitive radio, CR1, was developed to apply these mathematical foundations in a simulated environment. CR1 demonstrated the principles of cognitive radio and focused the research issues. This led to an important contribution of this dissertation, the cognitive radio architecture. This is an open architecture framework for integrating agent-based control, natural language processing, and machine learning technology into software-defined radio platforms.