Identifying the functionality in objects means to be able to associate a purpose with them in a specific environment. The purpose depends on the intention of the agent and on the applicability of the object in a particular task. In our investigation of functionality we focus on functionalities which involve changes of physical relation and properties between objects in the environment. A formal model, based on Discrete Event Dynamic System Theory (DEDS), is introduced to define an interactive task for recovering and describing functionality. To observe and control the recovery process we introduce the notion of piecewise observability of a task by different sensors. This allows the description of a dynamic system in which neither all events nor the time of their occurrence may be predicted in advance. We have developed an experimental system consisting of actuators and both force and position sensors, for carrying out the interactive recovery of functionality. In particular, we demonstrate how this approach can be used by carrying out some experiments investigating the functionality of piercing. Furthermore, we discuss the importance of a multisensory approach for the observation and interpretation of functionality.