Are scalar implicatures computed online?

; Some students in the audience liked the talk, but not all. The intuitive meaning of the sentences in (1) imposes restrictions (the material underlined in the glosses) that go beyond the meaning of logical disjunction or existential quantification: in formal logic, P ∨ Q is true if both disjuncts are, and ∃xP (x) is true if the P holds of all entities in the domain of quantification.
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