## 3 Development of SoS Metamodels and Ontologies
### Mission-Centric SoS Metamodel Based on DMM  
The traditional SysML requirement diagram decomposes requirements in SE, but its use in analyzing the SoS mission should consider the SoS context [39]. SoS mission management guides the entire process of UAF development [28]. Architecture development stages should interact with mission management to ensure domains align with the mission and to update missions iteratively. The decomposition of SoS missions can be achieved by mission-related attributes [39] or the ontology-based mission decomposition method [37]. While detailed sub-missions can be derived from top-level missions, over-complicating the mission phase by adding too many attributes for formalization and decomposition should be avoided. Furthermore, analyzing relevant attributes in the mission phase alone may be insufficient, requiring the support of multiple perspectives.  
We propose that one of the intentions of SoS Afs is to translate the SoS mission into SE requirements. To enhance consistency among various SoS stakeholders, UAF defines multiple domains, including strategic (St) and operational (Op), which can be utilized to refine mission analysis. The St domain's capability element is critical in an SoS architecture [40] because it assists in developing solutions-based capabilities [41], and architecture-based capability engineering aids in conceptualizing the capabilities expected to be achieved by the SoS architecture [42]. Therefore, the proposed metamodel in this study supports SoS architecture modeling by describing the Op domain from structural and behavioral perspectives, and capabilities in the St domain bridge these two perspectives.  
The UAF Domain Meta Model (DMM) provides the foundation for implementing UAF and is widely used in many applications [10; 33; 43]. It comprises six elements: Individual, Type, Abstract, Tuple, Enumeration, and External Type, and their meanings are based on concepts proposed in the International Defense Enterprise Architecture Specification (IDEAS) [44]. The proposed SoS metamodel, based on DMM, indicates that missions can be achieved by capabilities from both structural and behavioral perspectives, as depicted in Figure 1. In the SoS metamodel, the asterisks appearing at either end of an association relationship serve to denote the multiplicity of the relationship, indicating the number of instances of one element that can be related to one or more instances of another element.  
The representation of a mission in the metamodel, denoted by Type, is linked to other elements through three distinct sets of relationships defined by Tuple. These relationships include trace, refine, and satisfy, which respectively outline the capabilities required to achieve the mission, operational activities needed for behavioral analysis, and resource allocation from a structural perspective. To represent the constituent systems (CS) of the SoS, the Performer is used, which can be physical resources (ResourcePerformer) or logical resources (OperationalPerformer). As SoS is a collective term for multiple CSs, there is no single CS in the metamodel to represent the concept of SoS. Instead, the metamodelinvestigates how CSs implement their capabilities to comprehend and describe the SoS. The Process can be captured as an OperationalActivity to represent a logical process or function specified within the context of a ResourcePerformer capable of performing it.