In this paper we focus on understanding and defining a methodology for object description and recognition both in terms of its geometrical, material and functional specifications. We define functionality in an object as its applicability toward the achievement of a task. We emphasize and develop an interactive and performatory approach to functionality recovery. Furthermore, we introduce the distinction between Inherent, Intended and Imposed functionality. By analyzing interaction and manipulation tasks as goal-oriented recognition processes we propose to identify and characterize functionalities of objects. This interaction is not only a means of verification of the hypothesized presence of functionality in objects but also a way to actively and purposively recognize the object. In order to accomplish our goal, we introduce a formal model, based on Discrete Event Dynamic System Theory, to define a task for recovering and describing functionality. We extend the recovery process to an algebra of tasks. We describe how a more complex task call be composed from a set of primitive ones. This constructive approach allows a task to be built from simpler ones in an stepwise fashion. Once the manipulatory task has been described in the formal model, it must be instantiated in a context. In such a context, the behavior of the system in which the interactio between a Manipulator, a Tool and a Target object must be observed. Thus, the description of tasks themselves provide must for means of addressing observability through different sensor modalities. For this purpose, we introduce the notion of Partial Observability of a task. This allows the description of a plant in which not all events and the time of their occurrence might he modelled and therefore predictable in advance.