Formal Reasoning about Emergent Behaviours of Multi-Agent Systems

Abstract. Emergent behaviour (EB) is a common phe-nomenon in multi-agent systems (MAS) where autono-mous agents perform certain actions with only limited access to local information and make decisions individu-ally, while the whole system demonstrates properties and behaviours that have strong global features. Because of the huge gap between individual agents’ properties and behaviours and those of the whole system, specifying and reasoning about EBs are difficult. In this paper, we pro-pose a framework to the specification of and reasoning about EBs based on our previous work on the SLABS language for the formal specification of MAS. We investi-gate the uses of the scenario specification in SLABS for the definition of EBs of MAS and study the properties of scenario inclusion, scenario transition and scenario up-date. The uses of these properties in the proofs of MAS’ EBs are illustrated by an example. 1. Motivation In the development of software for service-oriented and Grid computing, it is essential but difficult to under-stand how the system as a whole will behave while its components behave autonomously. On the other hand the specification and design of each individual component must take into consideration of the state and behaviour of the whole system, which is the environment that individ-ual components execute in and operate on. There is a wide gap between individual components’ properties and be-haviours and the whole system’s properties and behav-iours. This is known as the emergent behaviour (EB) problem; c.f. [1]. This paper proposes a formal system to facilitate the specification of and reasoning about systems that consist of multiple autonomous agents. EB is a common phenomenon in multi-agent systems (MAS), such as in the Amalthaea system for web informa-tion retrieval and filtering [2], the ecosystem for resource allocation in a distributed environment [3], as well as in e-commerce (such as online auctions), simulation (such as ant colony optimisation), and many other application areas. Therefore, understanding EBs and facilitating the specifi-cation of and reasoning about EBs of MAS are very im-portant to the development of MAS. In the past few years, intensive research on EB of MAS has been done in artificial intelligence. Various mathematical models of specific types of MAS in particu-lar application areas have been developed and studied, e.g. [3]. Formal logics of belief, desire and intension of intel-ligent agents were proposed, c.f. [4]. Formal specification of agent in Z notation was also investigated [5]. In our previous work, a formal specification language SLABS was proposed for engineering MAS [6, 7]. It has also be used in formal specification of evolutionary MAS [8]. However, we are still lack of a general formal logic sys-tem for specifying and reasoning about the EBs of MAS. This paper reports our work on such a logic system based on SLABS and the notion of scenarios. The remainder of the paper is organised as follows. Section 2 briefly review the formal specification language SLABS. Section 3 studies the properties of scenarios and illustrates its uses in the specification of and reasoning about EBs. Section 4 concludes the paper with a discus-sion of further work.