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The study of formal theories of agents has intensified over the last decade since such formalisms can be viewed as providing the specifications for building agent-based systems. One such theory views agents as having beliefs, desires and intentions (BDI). The BDI paradigm provides us with the means of describing different types of agents; a desirable quality, since agent-based systems are employed in various domains with diverse characteristics and therefore different requirements. This is accomplished by adopting a set of constraints that describe how the three attitudes are related to each other, called a notion of realism. Although three such notions have been explored in the literature, namely strong realism, realism and weak realism, no systematic attempt has been undertaken to study other available options. In this paper we explore the dynamics and possible interrelations between the three attitudes and we propose notions of realism for heterogeneous BDI agents. We explore a wider range of possibilities by considering a combination of the types of relations between accessible worlds. Moreover, we distinguish between two broad categories of agents, bold and circumspect, according to the relation between beliefs and intentions. We explore several interesting notions of realism for such agents and we argue that these come close to the desiderata for rational BDI agents.