3.1.6 Quantifying In: An Example

Let's look at our example from before: Suppose we chose the variable for the pronoun ``her''. But we want to be able to use this pronoun like a quantified NP that would usually stand in the same place. Eventually, it should end up in the second argument slot of . So we will wrap it in a -expression as follows: . This should ring a bell - we did the same thing for proper names, for example when translating ``John'' as .

Introduce a pleaceholder...

In effect, the sentence ``Every man loves her'' yields the representation

which can be -reduced to:

So what remains to be done? We still have to process the antecedent for our pronoun, namely the phrase ``a woman'', translated as . And of course, our pronoun variable should be connected to this antecedent: We eventually want the second argument position of to be bound by the existential ``woman-quantifier''. This is achieved by -abstracting over the pronoun variable and then applying the translation of ``a woman'' to the resulting abstraction:

...and eliminate it again.

This reduces to:

We've finally got the reading where ``a woman'' has scope over ``every man''. The basic trick was to find a way to delay processing the NP ``a woman'' until we have processed ``every man'', thus lifting the existential quantifier above the universal. Implementing this trick of course required quite a piece of sophisticated -programming.