The advancements in the smart space research bring us closer and closer to a future, in which the living standards of people are greatly enhanced. Smart spaces are composed of heterogeneous networks of embedded devices that communicate, perform computations and actuate. From a system point of view, a smart space is a specific type of ubiquitous system. Like any ubiquitous system, a smart space is usually heterogeneous, i.e. it is made up of embedded devices with various hardware, software and communication platforms. There is need for information exchange and interoperability between these embedded devices and their services. However, embedded devices in a smart space vary in terms of their sensing, actuation and control capabilities, as well as their resources of processing, storage, and networking. For an interoperability solution, this paper proposes a semantic interoperability architecture for smart spaces. The description details of an ontology model and interoperability interactions between smart objects are explained. An example implementation of a heterogeneous smart lighting system as a smart space using the proposed semantic interoperability architecture is discussed.