A lot of today's data is generated incrementally over time by a large variety of producers. This data ranges from quantitative sensor observations produced by robot systems to complex unstructured human-generated texts on social media. With data being so abundant, making sense of these streams of data through reasoning is challenging. Reasoning over streams is particularly relevant for autonomous robotic systems that operate in a physical environment. They commonly observe this environment through incremental observations, gradually refining information about their surroundings. This makes robust management of streaming data and its refinement an important problem. Many contemporary approaches to stream reasoning focus on the issue of querying data streams in order to generate higher-level information by relying on well-known database approaches. Other approaches apply logic-based reasoning techniques, which rarely consider the provenance of their symbolic interpretations. In this thesis, we integrate techniques for logic-based spatio-temporal stream reasoning with the adaptive generation of the state streams needed to do the reasoning over. This combination deals with both the challenge of reasoning over streaming data and the problem of robustly managing streaming data and its refinement. The main contributions of this thesis are (1) a logic-based spatio-temporal reasoning technique that combines temporal reasoning with qualitative spatial reasoning; (2) an adaptive reconfiguration procedure for generating and maintaining a data stream required to perform spatio-temporal stream reasoning over; and (3) integration of these two techniques into a stream reasoning framework. The proposed spatio-temporal stream reasoning technique is able to reason with intertemporal spatial relations by leveraging landmarks. Adaptive state stream generation allows the framework to adapt in situations in which the set of available streaming resources changes. Management of streaming resources is formalised in the DyKnow model, which introduces a configuration life-cycle to adaptively generate state streams. The DyKnow-ROS stream reasoning framework is a concrete realisation of this model that extends the Robot Operating System (ROS). DyKnow-ROS has been deployed on the SoftBank Robotics NAO platform to demonstrate the system's capabilities in the context of a case study on run-time adaptive reconfiguration. The results show that the proposed system – by combining reasoning over and reasoning about streams – can robustly perform spatio-temporal stream reasoning, even when the availability of streaming resources changes.