Exhaustivity

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In linguistics, exhaustivity is the phenomenon where a proposition can be strengthened with the negation of certain alternatives. For example, in response to the question "Which students got an A?", the utterance "Ava got an A" has an exhaustive interpretation when it conveys that no other students got an A. It has a non-exhaustive interpretation when it merely conveys that Ava was among the students who got an A.

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Exhaustivity is a major topic in the linguistic subfields of semantics and pragmatics. Research on the topic aims to explain when and why expressions receive exhaustive interpretations. Particular factors include focus, [1] disjunction, [2] questions, [3] and polarity items. [4] A major theoretical issue is whether exhaustivity is a semantic entailment encoded in the grammar, a pragmatic implicature arising from Gricean social cognition, or some combination of the two. [5] [6] [7] [8]

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Alternative semantics is a framework in formal semantics and logic. 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. Thus, if and are propositions, then is the denotation of the question whether or is true. Since the 1970s, it has been extended and adapted to analyze phenomena including focus, scope, disjunction, NPIs, presupposition, and implicature.

In formal semantics, a Hurford disjunction is a disjunction in which one of the disjuncts entails the other. The concept was first identified by British linguist James Hurford. The sentence "Mary is in the Netherlands or she is in Amsterdam" is an example of a Hurford disjunction since one cannot be in Amsterdam without being in the Netherlands. Other examples are shown below:

  1. #Tamina saw a Beatle or Paul McCartney.
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  3. #Is Wilbur a pig or an animal?

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