16.1.2 Scope Underspecification

For instance, the following sentence contains a lot of scope ambiguities even though its its syntactically unambiguous.

A politician can fool most voters on most issues most of the time, but no politician can fool all voters on every single issue all of the time.

There are 5!*5! = 14400 possible permutations of the scope bearing elements (though not all permutations lead to semantically different readings).

One way to remedy this problem is to under-specify the semantic representation of constituents. This technique has been put to use in particular, for scope ambiguities i.e. sentences such as:

Every yogi has a guru

where either there is one guru for all yogis, or one guru per yogi. These two readings are captured by different scopes for the quantifiers every yogi and a guru so that the two meanings of the above sentence are given by the following FOL formulae:

$\begin{array}{ll} \mbox{Reading 1:}& \forall x (yogi(x) \rightarrow \exists y (guru(y) \wedge has(x,y))) \\ \mbox{Reading 2:}& \exists y (guru(y) \wedge \forall x (yogi(x) \rightarrow has(x,y))) \end{array}$

Note that in both cases, we have the same components namely, the yogi-quantifier, the guru-quantifier and the verb semantics. What varies is the order in which the two quantifiers occur.