5.1.7 Other Traditional Solutions

Other Traditional Solutions.

So we have managed to construct the second reading for our sentence. At a price, though: in order to solve a semantic problem, we had to postulate an alternative syntactic analysis for no obvious syntactic reason - and a rather unintuitive and strange one at that; one that employs a pronoun that doesn't surface in the sentence itself. The fundamental problem that each syntactic analysis still can have only one possible meaning remains.

A more Elegant Solution

In 1975, Robin Cooper proposed a much more elegant mechanism to solve this problem. It became known as Cooper storage . This mechanism took up Montagues idea of lifting quantifiers by using ``placeholders'' (like pronoun variables) as arguments instead of quantified NPs, and accessing these placeholders later at different points during the semantic construction process. Cooper started with a syntax tree whose leaves had been annotated with the -terms representing the semantics of the words. Then he performed bottom-up semantic composition as we have seen it above, but whenever he had to combine an NP and a verb or VP, he could not only immediately apply the NP semantics to the verb semantics, but alternatively use a placeholder and put the NP semantics into a quantifier store . This way, he could potentially collect a lot of quantifiers whose application he wanted to delay on his way up in the tree. Whenever he hit a sentence node, his algorithm could pick some or all of the quantifiers and apply them to the current semantics, in any order, thus generating all possible permutations of quantifiers.

A Pseudo-reading

Cooper's algorithm was a big step forward, but it suffered from an overgeneration problem. For example, it generated a sixth reading for the three-quantifier sentence we've seen above. The problem with Cooper's approach was that it liberally assumed that you can obtain readings by simply permuting the quantifiers, and that each formula obtained that way would represent a possible reading as well. In this respect it did not differ too much from Montague's technique of quantifying in. However, this assumption is not true. Look at the following formula. It is another permutation of the three quantifiers in our siamese-cat-example, but it is not a possible reading.

Advanced Solutions

In 1988, Keller managed to fix this overgeneration problem in a modified Cooper storage mechanism called Nested Cooper storage (or simply Keller storage ). By the mid-Eighties, algorithms like this one or Hobbs and Shieber's (1987) scoping algorithm allowed to enumerate the readings of a scope ambiguity reasonably well.