This paper presents a temporal belief logic called LTB. In addition to the usual connectives of linear discrete temporal logic, LTB contains an indexed set of modal belief connectives, via which it is possible to represent the belief systems of resource-bounded reasoning agents. The applications of LTB in general, and its use for representing the dynamic properties of multi-agent AI systems in particular, are discussed in detail. A tableau-based decision procedure for LTB is then described, and some examples of its use are presented. The paper concludes with a discussion and future work proposals.