Because anaphora are able to operate on an intersentential level, the traditional method of assigning closed formulas to sentences caused problems for discourse processing, and one had to resort to a number of ad hoc techniques for constructing the first-order formulas for natural language discourses.
an appropriate firstorder logic formula for the sentence a woman snorts would be ∃x(WOMaN(x)∧SNORT(x)), but if one continues the discourse with She collapses, there is a need to alter the formula into something of the form: one has to extend the scope of the existential quantifier introduced in the translation of the first sentence to cover elements introduced in the second sentence.