Canonical Institutions of Behaviour

Abstract

The concept of behaviour plays a central role in the specification of a considerable number of different kinds of systems. In these settings a “behaviour” is seen as a possible evolution (or life-cycle) of the system, whereas the system itself is considered to be defined by the set of all its possible behaviours.

Examples of this kind of situation are common. Maybe the most well known and studied is that of concurrency theory: a behaviour is e.g. a stream of actions and the system is a process (in this case, a set of streams of actions).

If institutions are used as the way for specifying the systems, then it is customary to start by creating an institution for individual behaviours (where each model corresponds to a possible behaviour) from which the “system institution” - or “institution of behaviour”, in our terminology - where each model is a set of behaviours is built.

The new institution is tightly bound to the base institution, sharing signatures and languages. Also, because the models are obtained from the base institution’s models, the satisfaction relation is defined in terms of the base satisfaction relation.

In this paper it is shown that the construction of these institutions of behaviour can be carried out in a canonical way. Indeed, the construction does not depend in any way at all on the particular base institution chosen. It is also shown that several institutions presented since the 90’s in WADT workshops and elsewhere arise as particular cases of this canonical construction [4][2][3][6][8].

It is hoped that the proposed construction can be used as a shortcut for defining new useful institutions of behaviour.