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A Geometrical Representation of the Basic Laws of Categorial Grammar

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Abstract

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 line of investigation, we analyze a well-known set of categorial grammar laws: Monotonicity, Application, Expansion, Type-raising, Composition, Geach laws and Switching laws.

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Authors and Affiliations

  1. Dipartimento di Matematica e Fisica, University Roma Tre, L.go S. L. Murialdo, 1, 00146, Rome, Italy

    V. Michele Abrusci

  2. Dipartimento di Scienze Filosoche, Pedagogiche ed Economico-quantitative, University Chieti and Pescara, Campus Universitario, Via dei Vestini 31, 00146, Chieti, Italy

    Claudia Casadio

Authors
  1. V. Michele Abrusci
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  2. Claudia Casadio
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Correspondence to Claudia Casadio.

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Abrusci, V.M., Casadio, C. A Geometrical Representation of the Basic Laws of Categorial Grammar. Stud Logica 105, 479–520 (2017). https://doi.org/10.1007/s11225-016-9698-4

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