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What denotation do linguists assign to the predicate exists in order to make the right predictions about the truth conditions of sentences like

  1. Santa does not exist.
  2. Unicorns do not exist.
  3. My neighbor Bob exists.
  4. Dogs exist.

Obviously, the denotation would need to make (1) and (2) true, while also ensuring that sentences like (5) are true and sentences like (6) are false.

  1. Unicorns have exactly one horn.
  2. Unicorns have exactly two horns.

Also, how is the semantics of the predicate exists related to the semantics of the quantifier some?

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