#### Supplement to Defeasible Reasoning

## Popper Functions

A Popper function is a function from pairs of propositions to real numbers that satisfies the following conditions:

- For some
*D*,*E*,*P*[*D*|*E*] ≠ 1. *P*[*A*|*A*] = 1.*P*[*A*|(*C*&*B*)] =*P*[*A*|(*B*&*C*)].*P*[(*B*&*A*)|*C*] =*P*[(*A*&*B*)|*C*].*P*[*A*|*B*] +*P*[¬*A*|*B*] = 1, or*P*[*C*|*B*] = 1.*P*[(*A*&*B*)|*C*] =*P*[*A*|(*B*&*C*)] ×*P*[*B*|*C*].