Recently, much interest has been directed towards software defined radios and embedded intelligence in telecommunication devices. However, no fundamental basis for cognitive radios has ever been proposed. In this paper, we introduce a fundamental vision of cognitive radios from a physical layer viewpoint. Specifically, our motivation in this work is to embed human-like intelligence in mobile wireless devices, following the three century-old work on Bayesian probability theory, the maximum entropy principle and minimal probability update. This allows us to partially answer such questions as, what are the signal detection capabilities of a wireless device, when facing a situation in which most parameters are missing, how to react and so on. As an introductory example, we will present previous works from the same authors following the cognitive framework, and especially the multi-antenna channel modeling and signal sensing.