This paper describes the step-by-step processes towards the formalization of a core ontology for missions and capabilities in systems of systems, and the development of a specific system of systems domain ontology from the formalized ontology. The study traces the ontology development process through the SABIOx methodology's requirements, setup, capture, design, and implementation phases. In this process, we demonstrate the core ontology's usability and reusability. Usability refers to the ontology's adequacy for specific use as a reference point for SoS knowledge exploration for development and operational purposes, and reusability refers to the ontology's adequacy for several uses, such as facilitating the understanding of different domain-specific systems of systems. This demonstration is done in three steps: formalization of the core ontology, exploration of the usefulness of this formalization, and development of a domain ontology from the core ontology. These result in: the incorporation of systematic ontology development processes; the application of ontology tools for machine readability; coherence and consistency checking of the ontology artifact; querying support for the ontology knowledge base; and testing of the core knowledge with a domain-specific system of systems. An alignment of these aspects provides different points of view of how a system of systems can be formulated, how the concepts collectively describe the development of an SoS emergent behavior, and how the ontology knowledge base can be explored to support decision frameworks guiding a system of systems.