This paper discusses the formal specification of properties that determine the behavior of component based BDI agents, i.e. classical BDI agents in which the mental attitudes are conditional and represented by interconnected components. Some properties, such as realism and commitment strategies, have already been discussed in the BDI literature and can be formally specified by for example Rao and Georgeff’s BDI_ctl formalism. Other properties are specific to component based cognitive agents and cannot be specified by existing BDI_ctl formalisms. We focus here on the so-called functional dependencies between mental attitudes where a mental attitude is considered to be a function of one or more other mental attitudes. To formally specify the properties of functional dependencies we extend Rao and Georgeff’s BDI_ctl formalism. In particular, for functional dependencies we introduce ‘only belief’, ‘only desire’and ‘only intend’ operators in the tradition of Levesque’s ‘all I know’ operator, and for components we distinguish between ‘belief in’and ‘belief out’, ‘desire in’and ‘desire out’, and ‘intention in’ and ‘intention out’ operators. We show how our extended formalism can be used to specify functionality properties such as conservativity, monotonic ity, and self-boundedness, as well as properties related to the connections between and control of the components.