Relationships between Specified and Underspecified Quantification by the Theory of Acyclic Recursion

The paper introduces a technique for representing quantifier relations that can have different scope order depending on context. The technique is demonstrated by classes of terms denoting relations, where each of the arguments of a relation term is bound by a different quantifier. We represent a formalization of linking quantifiers with the corresponding argument slots that they bind, across lambda-abstractions and reduction steps. The purpose of the technique is to represent underspecified order of quantification, in the absence of a context and corresponding information about the order. Furthermore, it is used to represent subclasses of larger classes of relations depending on order of quantification or specific relations.