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Erschienen in:
2007 | OriginalPaper | Buchkapitel
Symmetries in Natural Language Syntax and Semantics: The Lambek-Grishin Calculus
verfasst von : Michael Moortgat
Erschienen in: Logic, Language, Information and Computation
Verlag: Springer Berlin Heidelberg
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In this paper, we explore the Lambek-Grishin calculus
$\textbf{LG}$
: a symmetric version of categorial grammar based on the generalizations of Lambek calculus studied in Grishin [1]. The vocabulary of
$\textbf{LG}$
complements the Lambek product and its left and right residuals with a dual family of type-forming operations: coproduct, left and right difference. The two families interact by means of structure-preserving distributivity principles. We present an axiomatization of
$\textbf{LG}$
in the style of Curry’s combinatory logic and establish its decidability. We discuss Kripke models and Curry-Howard interpretation for
$\textbf{LG}$
and characterize its notion of type similarity in comparison with the other categorial systems. From the linguistic point of view, we show that
$\textbf{LG}$
naturally accommodates non-local semantic construal and displacement — phenomena that are problematic for the original Lambek calculi.