deletions | additions       diff --git a/section_Bayesian_Inference_One_very__.tex b/section_Bayesian_Inference_One_very__.tex  index d6c80e7..766fcb5 100644  --- a/section_Bayesian_Inference_One_very__.tex  +++ b/section_Bayesian_Inference_One_very__.tex 
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\[ b : (Z \times Z \times A \times S) \to [0, 1] \]  We will denote the underlying probability space as $\mathbb{B}$.  We can then define a Bayesian theory of rationality $R$ as one in which beliefs change according to Bayes' rule: rule, and the ``laws of physics'' remain constant:  \[ R(\mathbb{B}(Z_t), d, \phi, s, a) = (\mathbb{B}(Z_{t+1} \given Z_t, S_t=s, A_t=a), d^*, a^*) \\  \mathbb{B}^*(Z_t=z') = \mathbb{B}(Z_{t+1} = z' \given Z_t, S=s, A=a)  \mathbb{B}^*(Z_{t+1} = z' \given Z_{t} = z, S=s, A=a) = \mathbb{B}(Z_{t+1} = z' \given Z_t = z, S=s, A=a) \]  \] ...where $d^*$ and $a^*$ are still arbitrary sets of rational desires and actions.     
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