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.

翻译：原始逻辑产生于访问控制领域；其蕴含问题的判定过程具有极高的效率（线性时间复杂度）。但原始逻辑是一种通用的信息逻辑。在任意信息项（信息子）的范畴中，合取、析取与蕴涵在集合论意义上似乎分别对应并集、交集与相对补集。然而，尽管信息子对并运算封闭，却对交运算或相对补运算不封闭。研究发现，从命题直觉主义演算到原始命题演算存在一种系统性变换，我们称之为“扁平化”。我们将扁平化扩展至量词规则，从而得到了较为合理的量化原始逻辑QPL。QPL的蕴含问题具有指数时间完备性，但在量词数量有界（对应用场景——至少对访问控制——具有重要价值）的情况下，该问题表现为多项式时间完备性。