On the Semantics of Branching Quantifier Sentences

Abstract

An example of a branching quantifier sentence is (1) Some friend of each townsman and some neighbor of each villager envy each other

The intended reading of such sentences [3] is that the choice of the friend should be made independent of the choice of the neighbor. There has been discussion whether such sentences are grammatical and/or have the meaning attributed to them (e.g. [1]), but we will accept both points. Our aim is to investigate the formal analysis given to such sentences and argue that they do not formalize the intended reading: the desired independence is not captured. As for an application of branching quantifiers in physics, the same will be argued.