 The key to understanding the DPL account of discourse anaphora lies in understanding its semantics of the existential quantifier and conjunction. Let’s begin with existential quantification. The basic idea here it that when we interpret an existential quantifier, the output of that interpretation may affect the interpretation of subsequent expressions. In standard predicate logic, the interpretation of an existential quantifier is a set of assignment functions. In DPL, it is a set of ordered pairs of input and output assignment functions. The output assignment functions act as the input to subsequent formulas. Take for example the simple formula “\((\exists x)(\mbox{man } x)\)”. In DPL, such a formula takes all the input functions g, and for each one outputs all the possible assignment functions h such that they differ from g at most in that they assign x to an object in the interpretation of “man” (i.e., they assign x to a man). More generally, accounting for possibly more complex formulas in the scope of the existential (including another quantifier), a pair of sequences \(\langle g, h\rangle\) is in the interpretation of an existential formula “\((\exists x)\Phi\)” just in case there is an assignment function k differing from g at most on x such that \(\langle k,h\rangle\); is in the interpretation of “\(\Phi\)”.[16]  So note how interpreting the existential quantifier results in shifting from the input function g to k, where k is now the input to “\(\Phi\)”. This makes the existential quantifier internally dynamic, capable of affecting the interpretation of expressions within its syntactic scope. Further, the fact that the output assignment functions of interpreting the whole existentially quantified sentence are allowed to be different from the input to the interpretation means that the processing of the existentially quantified formula may affect the interpretation of expressions after the existentially quantified formula, and hence outside the scope of the existential quantifier. This is to say that the existential quantifier is externally dynamic, capable of affecting the interpretation of expressions outside its syntactic scope. As we will see, an expression can be internally dynamic and externally static (as well as internally and externally static). At any rate, putting things very roughly, the idea here is that once the existential quantifier “resets” the value of “x” so that it satisfies the formula the quantifier embeds, that value stays reset (unless there is a subsequent existential quantifier attached to the same variable) and can affect the interpretation of subsequent formulas.