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Quantifier interaction in the temporal structure of extended eventualities

Focussing on the temporal structures of the events described by language, the sentence 'Simmer the soup stirring occasionally for fifteen minutes'
is ambiguous between five semantic interpretations. Some of these readings can only be found if we take the view, argued by Moltmann, that temporal measure adverbials play the role of part quantifiers, rather than the more traditional approach of treating them as predicates. 
In this paper I describe first of all the justification for adopting the quantifier view of measure adverbials, and argue for its extension in including object quantifiers. I then demonstrate how this is used in a computational system to expose some ambiguity that would otherwise remain hidden.