J(1). Note: Compactness means that one knows the explanation of one state, iff one knows the explanation for the other state. Then we can use a single variable J or J’.
Definition: A state s is said to be caused by chance iff a situation of s and unsound belief J’(s) are stable. It is said then that there is a hidden cause linking J(s) to s.
Definition: If the sound information concerns a model then we can denote J in binary values, with 1 = ‘the model is known’ and 0 = ‘the model isn’t known’, rather than use the whole list of statements. With binary information, compactness J(0)
J(1) becomes J(0) = J(1).
Remark: Consider the example of the Roman emperor. His model is ‘sacrifice
fortune’ (and if fortune slips after a sacrifice, then apparently more sacrifices are required). One of his basic informations is BI(~fortune, fortune) = {‘sacrifice