The development of the Semantic Web of Things (SWoT) is challenged by the nature of IoT deployment architec-tures, where constrained devices collect data processed remotely by powerful Cloud servers. Such a deployment pattern introduces bottlenecks constituting a hurdle for scalability, and increases response time. This hinders the development of a number of critical and time-sensitive applications. Enabling the deployment of the Semantic Web stack closer to the constrained devices of the IoT may foster the development of time-sensitive interoperable applications, while reducing forwarding the user data to remote third party Cloud servers. The approach we develop in this paper is a contribution towards this direction, and aims to enable rule-based reasoning closer to sensors producing IoT data. For this purpose, we define a distributed scalable semantic processing algorithm by dynamically propagating deduction rules on Fog nodes. Our goal is to shorten the time needed to deliver high level information deduced from the collected data. This approach is evaluated on a smart building use case where both distribution and scalability have been considered.