Axiom: Let "unknown" be a value that indicates a state in which there is no information about the value.
Axiom: Value a and value A, value b and value B are assumed to be corresponding values, and if there is no information on value A or value B, the closer the distance between value a and value b, the greater the difference between value A and value B. Assuming it's close.
"Corresponding" means that if the value a is determined, the value A is uniquely determined.
"No information" means that no inference can be made by deduction or induction.
If axiom 3 of induction can be partially inferred, only the remaining part is inferred by axiom 2 of induction.
Any value that satisfies the axiom of distance can be used for the "close distance" distance.
Axiom: We assume that the original probability distribution of the uninformed belonging to the set is equal to the original distribution of the set.
Due to the principle of indiscrimination, applying a uniform distribution or maximum entropy distribution is not inductive reasoning.
It is just substituting the assumed value for "unknown", and it is considered as deduction.
It is unavoidable to do it unavoidably, but it is a process to be done after giving up when no further inductive reasoning can be done, so it is distinguished.
Bias inference is just inductive inference of "unknown".
There is no need to set new axioms.