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\section{Bayesian Inference}  One very natural way of representing beliefs $b$ and $\phi$ mathematically is as subjective probability functions. In this case, we may restrict our theories of rationality to those which are consistent with Bayesian inference.  Assume that a belief $b$ actually corresponds to a probability function $\mathbb{B}$ representing a belief about the instantaneous state $Z_t$ $z_t$  of a ``phenomenal world'' variable $Z$, and how the world's next state $Z_{t+1}$ $z_{t+1}$  is co-distributed with instantaneous action $a_t$ and sensation $s_{t+1}$. \[ \mathbb{B} : (Z \times Z \times A \times S) \to [0, 1] \]