## Popper Functions

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

1. For some $$D, E, P[D\mid E] \ne 1$$.
2. $$P[A\mid A] = 1$$.
3. $$P[A\mid (C \amp B)] = P[A\mid (B \amp C)$$].
4. $$P[(B \amp A)\mid C] = P[(A \amp B)\mid C$$].
5. $$P[A\mid B] + P[\neg A\mid B] = 1$$, or $$P[C\mid B] = 1$$.
6. $$P[(A \amp B)\mid C] = P[A\mid (B \amp C)] \times P[B\mid C$$].