In this paper we introduce our vision of a Cognitive Computing Continuum to address the changing IT service provisioning towards a distributed, opportunistic, self-managed collaboration between heterogeneous devices outside the traditional data center boundaries. The focal point of this continuum are cognitive devices, which have to make decisions autonomously using their on-board computation and storage capacity based on information sensed from their environment. Such devices are moving and cannot rely on fixed infrastructure elements, but instead realise on-the-fly networking and thus frequently join and leave temporal swarms. All this creates novel demands for the underlying architecture and resource management, which must bridge the gap from edge to cloud environments, while keeping the QoS parameters within required boundaries. The paper presents an initial architecture and a resource management framework for the implementation of this type of IT service provisioning.