Describing, structuring and implementing objects

The popularity of the notion of object for structuring (the specification of) systems has not been accompanied by the necessary formalisation of the concepts and constructions involved. We have a well developed theory of abstract data types that explains how to structure specifications based on the notion of value, but objects involve imperative notions such as those of action and state which are not well captured in an applicative way. In this paper, we focus on the development of an alternative framework to support systems design based on the concept of object. We provide a notion of object signature around which we define the notion of locality (encapsulation). We adopt a deontic action logic for the description of objects. We define the notion of morphism between object descriptions, and show how these notions can be used to combine object descriptions and, in this way, define the behaviour of societies of interacting objects. And, finally, we show by means of an example how object descriptions may be reified by implementing descriptions of objects at one level (of abstraction) in terms of object descriptions at the level below.