Aerospace systems are connected with the operational environment and other systems in general. The focus in aerospace product development is consequently shifting from a singular system perspective to a System-of-Systems (SoS) perspective. This increasing complexity gives rise to new levels of uncertainty that must be understood and managed to produce aerospace solutions for an ever-changing future. This paper presents an approach to using architecture frameworks, and ontologies with description logic reasoning capabilities, to break down SoS needs into required capabilities and functions. The intention of this approach is to provide a consistent way of obtaining the functions to be realized in order to meet the overarching capabilities and needs of an SoS. The breakdown with an architecture framework results in an initial design space representation of functions to be performed. The captured knowledge is then represented in an ontology with description logic reasoning capabilities, which provides a more flexible way to expand and process the initial design space representation obtained from the architecture framework. The proposed approach is ultimately tested in a search and rescue case study, partly based on the operations of the Swedish Maritime Administration. The results show that it is possible to break down SoS needs in a consistent way and that ontology with description logic reasoning can be used to process the captured knowledge to both expand and reduce an available design space representation.