In alternative semantics, expressions denote alternative sets, understood as sets of objects of the same semantic type.
For instance, while the word "Lena" might denote Lena herself in a classical semantics, it would denote the singleton set containing Lena in alternative semantics.
The framework was introduced by Charles Leonard Hamblin in 1973 as a way of extending Montague grammar to provide an analysis for questions.
In this framework, a question denotes the set of its possible answers.
Since the 1970s, it has been extended and adapted to analyze phenomena including focus,[1] scope, disjunction,[2] NPIs,[3][4] presupposition, and implicature.