Journal of Semantics 37 (2):171-217 (2020)

Abstract
Many languages have particles that possess multiple logical functions. Take the Mandarin particle dou for example. Varying by the item it is associated with and the prosodic pattern of the environment it appears in, dou can trigger a distributivity effect, license a pre-verbal free choice item, or evoke an even-like inference. Considering universal grammar a simple system, we need to figure out, for a multi-functional particle, which of its functions is primary, what parametric variations are responsible for the alternations in function, and how these variations are conditioned. In this paper, I argue that the seemingly unrelated functions of dou share the same source: dou is a pre-exhaustification exhaustifier operating on sub-alternatives. Uniformly, dou affirms the truth of its propositional prejacent, negates the exhaustification of each sub-alternative, and presupposes a non-vacuity inference that there is at least one sub-alternative. Alternations in function result from minimal weakening operations on the semantics of sub-alternatives. In particular, sub-alternatives are primarily weaker alternatives, and the non-vacuity presupposition of dou yields a distributivity effect. When the semantics of sub-alternatives is weakened under particular syntactic or prosodic conditions, dou gains its other logical functions.
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DOI 10.1093/jos/ffz018
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A Theory of Focus Interpretation.Mats Rooth - 1992 - Natural Language Semantics 1 (1):75-116.
Scalar Implicatures in Complex Sentences.Uli Sauerland - 2004 - Linguistics and Philosophy 27 (3):367-391.
Economy and Embedded Exhaustification.Danny Fox & Benjamin Spector - 2018 - Natural Language Semantics 26 (1):1-50.

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