  Primal logic arose in access control; it has a remarkably efficient (linear
time) decision procedure for its entailment problem. But primal logic is a
general logic of information. In the realm of arbitrary items of information
(infons), conjunction, disjunction, and implication may seem to correspond
(set-theoretically) to union, intersection, and relative complementation. But,
while infons are closed under union, they are not closed under intersection or
relative complementation.
  It turns out that there is a systematic transformation of propositional
intuitionistic calculi to the original (propositional) primal calculi; we call
it Flatting. We extend Flatting to quantifier rules, obtaining arguably the
right quantified primal logic, QPL. The QPL entailment problem is
exponential-time complete, but it is polynomial-time complete in the case, of
importance to applications (at least to access control), where the number of
quantifiers is bounded.
