Abstract
The paper provides a compositional account of cumulative readings with non-increasing modified numerals (aka van Benthem’s puzzle), e.g., Exactly three boys saw exactly five movies. The main proposal is that modified numerals make two kinds of semantic contributions. Their asserted/at-issue contribution is a maximization operator that introduces the maximal set of entities that satisfies their restrictor and nuclear scope. The second contribution is a post-supposition, i.e., a cardinality constraint that needs to be satisfied relative to the context that results after the at-issue meaning is evaluated. We take contexts to be sets of variable assignments relative to which quantificational expressions are interpreted and which are updated as a result of their interpretation.
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Brasoveanu, A. (2010). Modified Numerals as Post-Suppositions. In: Aloni, M., Bastiaanse, H., de Jager, T., Schulz, K. (eds) Logic, Language and Meaning. Lecture Notes in Computer Science(), vol 6042. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14287-1_21
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DOI: https://doi.org/10.1007/978-3-642-14287-1_21
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