Optionality, scope, and licensing: An application of partially ordered categories

This paper uses a partially ordered set of syntactic categories to accommodate optionality and licensing in natural language syntax. A complex but well-studied data set pertaining to the syntax of quantifier scope and negative polarity licensing in Hungarian is used to illustrate the proposal. The presentation is geared towards both linguists and logicians. The paper highlights that the main ideas can be implemented in different grammar formalisms, and discusses in detail an implementation where the partial ordering on categories is given by the derivability relation of a calculus with residuated and Galois-connected unary operators.
Keywords Partial order  Residuation  Galois-connection  Boolean connectives  Typed feature structures  Natural language syntax  Scope  Polarity items  Licensing  Optionality
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DOI 10.1007/s10849-008-9060-y
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Joachim Lambek (1968). The Mathematics of Sentence Structure. Journal of Symbolic Logic 33 (4):627-628.

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