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