DPL’s semantics ensures that, unlike in classical logic, the last occurrence of x is bound by the existential quantifier. The way this works is that DPL analyzes sentence meanings in terms of variable assignments, which are manipulated by the logical constants in such as way that [1] is true in a model M iff M’s domain features an individual which, when assigned to the variable x, makes each of the atomic sentences in [1] come out true in M. Formally, this is implemented by stipulating that the meaning of a sentence is a relation between variable assignments.