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Multi-Sorted Residuation

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Categories and Types in Logic, Language, and Physics

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8222))

Abstract

Nonassociative Lambek Calculus (NL) is a pure logic of residuation, involving one binary operation (product) and its two residual operations defined on a poset [26]. Generalized Lambek Calculus GL involves a finite number of basic operations (with an arbitrary number of arguments) and their residual operations [7]. In this paper we study a further generalization of GL which admits operations whose arguments and values can be of different sorts. This logic is called Multi-Sorted Lambek Calculus mL. We also consider its variants with lattice and boolean operations. We discuss some basic properties of these logics (completeness, decidability, complexity and others) and the corresponding algebras.

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Author information

Authors and Affiliations

  1. The Adam Mickiewicz University in Poznań, Poland

    Wojciech Buszkowski

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  1. Wojciech Buszkowski
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Editors and Affiliations

  1. Department of Philosophy, Education and Quantitative Economics, Gabriele D’Annunzio University, Chieti-Pescara, Via dei Vestini 31, 60100, Chieti, Italy

    Claudia Casadio

  2. Department of Computer Science, Oxford University, Wolfson Building, Parks Road, OX1 3QD, Oxford, UK

    Bob Coecke

  3. Utrecht Institute of Linguistics OTS, Utrecht University, Trans 10,, 3512 JK, Utrecht, The Netherlands

    Michael Moortgat

  4. Department of Mathematics, University of Ottawa, 585 King Edward, K1N 6N5, Ottawa, ON, Canada

    Philip Scott

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Buszkowski, W. (2014). Multi-Sorted Residuation. In: Casadio, C., Coecke, B., Moortgat, M., Scott, P. (eds) Categories and Types in Logic, Language, and Physics. Lecture Notes in Computer Science, vol 8222. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54789-8_8

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  • DOI: https://doi.org/10.1007/978-3-642-54789-8_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-54788-1

  • Online ISBN: 978-3-642-54789-8

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