This paper presents an approach to system-of-systems engineering for product development with the use of ontology. A proposed method for building as well as using ontology to generate and explore system-of-systems design spaces based on identified system-of-system needs is presented. The method is largely built to cover the first levels of related work, where a process for system of systems in the context of product development is introduced. Within this work, it is shown that scenarios for a system-of-systems can be used to identify needs and subsequently the system-of-systems capabilities that fulfils them. The allocation of capabilities to possible constituent systems is used to show the available design space. The proposed method of this paper therefore addresses these initial challenges and provides a framework for approaching the system-of-systems design space creation using ontology. A case study is used to test the method on a fictitious search and rescue scenario based on available resources and information from the Swedish Maritime Administration. The case study shows that a representation of a system-of-systems scenario can be created in an ontology using the method. The ontology provides a representation of the involved entities from the fictitious scenario and their existing relationships. Defined ontology classes containing conditions are used to represent the identified needs for the system-of-systems. The invocation of a description logic reasoner is subsequently used to classify and create an inferred ontology where the available system-of-systems solutions are represented as sub-classes and individuals of the defined classes representing the needs. Finally, several classes representing different possible system-of-systems needs are used to explore the available design space and to identify the most persistent solutions of the case study.