Reasoning About Adaptivity of Agents and Multi-agent Systems

Although adaptivity is a central feature of agents and multi-agent systems (MAS), there is no precise definition of it in the literature. What does it mean for an agent or for a MAS to be adaptive? How can we reason about and measure the ability of agents and MAS to adapt? In this paper, we provide a formal definition of adaptivity of agents and MAS aimed at addressing these issues. The definition is independent of any particular mechanism for ensuring adaptivity. It is qualified by the environmental actions to which the agents adapt, and quantified by the number of actions needed for adaptivity. It is formalised using a simple extension to labelled transitions systems allowing it to be applied to specifications of MAS in a wide range of existing formal notations. We show by a simple example how it can be used to detect design flaws which lead to situations in which a system is unable to adapt.