We present a formalism for representing the formation of intentions by agents engaged in cooperative activity. We use a syntactic approach presenting a formal logical calculus that can be regarded as a meta-logic that describes the reasoning and activities of the agents. Our central focus is on the evolving intentions of agents over time, and the conditions under which an agent can adopt and maintain an intention. In particular, the reasoning time and the time taken to subcontract are modeled explicitly in the logic. We axiomatize the concept of agent interactions in the meta-language, show that the meta-theory is consistent and describe the unique This research was supported by NSF under grant IIS-0222914 and by the Air Force Office of Scientific Research, and the Office of Naval Research. Preliminary version appeared in the proceedings of AAAI-2002. We wish to thank the referees for many helpful comments and suggestions. 1