Perhaps the most successful agent architectures, and certainly the best known, are those based on the Belief-Desire-Intention (BDI) framework. Despite the wealth of research that has accumulated on both formal and practical aspects of this framework, however, there remains a gap between the formal models and the implemented systems. In this paper, we build on earlier work by Rao aimed at narrowing this gap, by developing a strongly-typed, formal, yet computational model of the BDI-based AgentSpeak(L) language. AgentSpeak(L) is a programming language, based on the Procedural Reasoning System (PRS) and the Distributed Multi-Agent Reasoning System (dMARS), which determines the behaviour of the agents it implements. In developing the model, we add to Rao's work, identify some omissions, and progress beyond the description of a particular language by giving a formal speci cation of a general BDI architecture that can be used as the basis for providing further formal speci cations of m...