We present a new model of knowledge, belief, desire and intention, called the interpreted KBDI-system model (or KBDI-model for short). The key point of the interpreted KBDI-system model is that we express an agent’s knowledge, belief, desire and intention as a set of runs (computing paths), which is exactly a system in the interpreted system model, a well-known agent model due to Halpern and his colleagues. Our KBDI-model is computationally grounded in that we are able to associate a KBDI-model with a computer program, and formulas, involving agents’ knowledge, belief, desire (goal) and intention, can be understood as properties of program computations. With KBDI-model, we have two different semantics to interpret our logic of knowledge, belief, desire and intention. Moreover, with respect to each semantics, we present a sound and complete proof system.