A Geometrical Representation of the Basic Laws of Categorial Grammar

We present a geometrical analysis of the principles that lay at the basis of Categorial Grammar and of the Lambek Calculus. In Abrusci (On residuation, 2014) it is shown that the basic properties known as Residuation laws can be characterized in the framework of Cyclic Multiplicative Linear Logic, a...

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Bibliographic Details
Published in:Studia logica 2017-06, Vol.105 (3), p.479-520
Main Authors: Abrusci, V. Michele, Casadio, Claudia
Format: Article
Language:English
Subjects:
Computational Linguistics
Education
Logic
Mathematical Logic and Foundations
Philosophy
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Summary:We present a geometrical analysis of the principles that lay at the basis of Categorial Grammar and of the Lambek Calculus. In Abrusci (On residuation, 2014) it is shown that the basic properties known as Residuation laws can be characterized in the framework of Cyclic Multiplicative Linear Logic, a purely non-commutative fragment of Linear Logic. We present a summary of this result and, pursuing this Une of investigation, we analyze a well-known set of categorial grammar laws: Monotonicity, Application, Expansion, Type-raising, Composition, Geach laws and Switching laws.
ISSN:0039-3215
1572-8730
DOI:10.1007/s11225-016-9698-4