From the last decade, modeling of cognitive agents have drawn great attention and provide a new paradigm for addressing fundamental questions in cognitive science. In this paper, a logical model for reasoning about cognitive agent’s three attitudes Belief, Capability and Promise is proposed. A formalization is provided based on the modal logic to specify and analyze dependencies between the three attitudes. By adopting a set of constraints that describe how the three attitudes are related to each other, we can draw a number of properties of the model. To show the potential applications of the model, we apply the BCP model to a decision-making example in trading agent competition for supply chain management(TAC SCM). The logical model proposed here provides a rigorous semantic basis for modeling cognitive agent and reasoning about multi-agent interactions.