The powerset operator, P, is compared with other operators of similar type and logical complexity. Namely we examine positive operators whose defining formula has a canonical form containing at most a string of universal quantifiers. We call them ∀-operators. The question we address in this paper is: How is the class of ∀-operators generated? It is shown that every positive ∀-operator Γ such th...

Most spam filters are configured for use at a very low falsepositive rate. Typically, the filters are trained with techniques that optimize accuracy or entropy, rather than performance in this configuration. We describe two different techniques for optimizing for the low false-positive region. One method weights good data more than spam. The other method uses a two-stage technique of first find...