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. $P[(A \amp B)\mid C] = P[A\mid (B \amp C)] \times P[B\mid C$].