BDI (Beliefs, Desires, Intentions) is one of the most popular intelligent agent architectures which was inspired by multi-modal BDI logics. The main idea behind BDI is to implement system’s behaviour by specifying it as a set of mental objects. This allows designing systems at a high level of abstraction which come closer to a human-like thinking. Although this architecture has been rapidly developing for about 20 years, its relevance to BDI logic is still arguable. This paper describes the basics of modal logic and main inference algorithms. Main concepts of BDI agents are presented and their relationships with BDI logic are discussed. Finally advantages and disadvantages of implementing BDI interpreter as a theorem prover are discussed.