On the Emergence of Properties in Component-Based Systems

When several components are interconnected to form a complex system, they may exhibit more properties (individually) than they had when considered in isolation. When we consider a category SPEC of component specifications taken as theories in some logic, properties are expressed as sentences of the underlying logic, and emergence of properties can be characterised by the fact that the morphisms that connect component specifications to the system specification are not conservative. Depending on the relationship that can be established between SPEC and a corresponding category PROG of programs, we show that such emergence phenomena can be interpreted in more than one way: (1) considering an individual component, the rest of the system is acting as a “regulator” for that component which, therefore, has a more constrained behaviour and exhibits more properties; (2) the overall good behaviour of the system requires cooperation of the components (some sort of sociability with regard to the rest of the system) which gives rise to the emergence of new properties. Some of these forms of sociability are characterised and related to well known properties of concurrent systems such as fairness and, more generally, to the assumptions that are made on the environment in rely-guarantee styles of specification.