Belief-Desire-Intention (BDI) agents have been investigated by many researchers from both a theoretical specification perspective and a practical design perspective. However, there still remains a large gap between theory and practice. The main reason for this has been the complexity of theorem-proving or model-checking in these expressive specification logics. Hence, the implemented BDI systems have tended to use the three major attitudes as data structures, rather than as modal operators. In this paper, we provide an alternative formalization of BDI agents by providing an operational and proof-theoretic semantics of a language AgentSpeak(L). This language can be viewed as an abstraction of one of the implemented BDI systems (i.e., PRS) and allows agent programs to be written and interpreted in a manner similar to that of horn-clause logic programs. We show how to perform derivations in this logic using a simple example. These derivations can then be used to prove the properties satisfied by BDI agents.