Modal auxiliaries and negation: A type-logical account
Yusuke Kubota, Bob Levine
April 2019

This paper proposes an analysis of modal auxiliaries in English in Type-Logical Grammar. The proposed analysis captures the scopal interactions between different types of modal auxiliaries and negation by incorporating the key analytic idea of Iatridou and Zeijlstra who classify English modal auxiliaries into PPI and NPI types. In order to technically implement this analysis, we build on Kubota and Levine’s treatment of modal auxiliaries as higher-order operators that take scope at the clausal level. The proposed extension of the Kubota/Levine analysis is shown to have several interesting consequences, including a formal derivability relation from the higher-order entry for auxiliaries to a lower-order VP/VP entry traditionally recognized in categorial grammar research. The systematic analysis of the scopal properties of auxiliaries and the somewhat more abstract meta-comparison between 'transformational' and 'non-transformational' analytic ideas that become possible in a type-logical setup highlight the value of taking a logical perspective on the syntax of natural language embodied in Type-Logical Grammar research.
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Reference: lingbuzz/004473
(please use that when you cite this article)
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keywords: modal auxiliary; negation; scope; type-logical grammar, semantics, syntax
previous versions: v1 [February 2019]
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