It may border on scandalous that the cardinality of the set of all dedicated—computational or otherwise—logics of attention is apparently \(\approx \) 3; and of logics of attention-and-perception the cardinality is that of \(\emptyset \) . We have introduced and through a number of years of effort refined and implemented a class of computational logics marked by high extensional and intensional expressivity: cognitive calculi, as they have now long been known. Unfortunately, at this point in time only some simplistic reasoning involving perception has been formalized in some of these calculi. To start to change this state-of-affairs, the present essay prepares the way for the subsequent full specification, implementation, and simulation of the cognition of (rational) artificial agents that premeditatedly attend and perceive, in extreme environments. More specifically, after briefly explaining the nature of cognitive calculi, and setting out our desiderata for a new attention-and-perception cognitive calculus, we introduce a new sub-space of cognitive calculi: the attention-perception cognitive calculus ( \({\mathcal {{APCC}}}\) ).