With the increasing complexity of engineered systems, digital twins (DTs) have been widely used to support integrated modeling, simulation, and decision-making of the system of systems (SoS). However, when integrating DTs of each constituent system, it is challenging to implement complexity management, interface definition, and service integration across DTs. This study proposes a new concept called cognitive twin (CT) to support SoS development and operation. CTs have been defined as DTs with augmented semantic capabilities for promoting the understanding of interrelationships be-tween virtual models and enhancing the decision-making. First, CTs aim to integrate the information description of DTs across constituent systems using a unified ontology and semantic modeling technique. Second, CTs provide integrated simulations among DTs for decision-making of the SoS based on a high-level architecture (HLA). Finally, through reasoning ontology models, CTs provide decision-making options for the operations of real constituent systems. A case study on unmanned aerial vehicles (UAVs) landing on unmanned surface vehicles (USVs) is used to verify the flexibility of this approach. From the results, we find that the CT based on the proposed ontology provides a unified formalism of DTs across UAVs and USVs. Moreover, the reasoning based on the CT provides decision-making capabilities for UAVs by implementing cognitive computing to select target USVs for landing.