On requirements for conditional probability functions

Abstract

Let the prepositional calculus (PC) be cast in the following form: (a) The primitive signs of PC are to be a denumerably infinite hst of propositional letters, the two connectives ‘∼’ and ‘&’, and the two parentheses ‘(‘and’)’; (b) The formulas of PC, referred to hereafter by ‘A’, ‘B’, ‘C’, and ‘D,’ are to be all finite sequences of primitive signs of PC; (c) The well-formed formulas (wffs) of PC are to be all propositional letters, all formulas of the form ∼A, where A is a wff of PC, and all formulas of the form (A&B), where A and B are wffs of PC; (d) (A⊃B) is to be short for ∼(A&∼B), (AνB) short for ∼(∼A&∼B), and (A ≡ B) short for (((A ⊃B)&(B⊃A)).