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Categories and Types in Logic, Language, and Physics pp 331–352Cite as

A Categorial Type Logic

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

Abstract

In logical categorial grammar [23,11] syntactic structures are categorial proofs and semantic structures are intuitionistic proofs, and the syntax-semantics interface comprises a homomorphism from syntactic proofs to semantic proofs. Thereby, logical categorial grammar embodies in a pure logical form the principles of compositionality, lexicalism, and parsing as deduction. Interest has focused on multimodal versions but the advent of the (dis)placement calculus of Morrill, Valentín and Fadda [21] suggests that the role of structural rules can be reduced, and this facilitates computational implementation. In this paper we specify a comprehensive formalism of (dis)placement logic for the parser/theorem prover CatLog integrating categorial logic connectives proposed to date and illustrate with a cover grammar of the Montague fragment.

This research was partially supported by an ICREA Acadèmia 2012, by BASMATI MICINN project (TIN2011-27479-C04-03) and by SGR2009-1428 (LARCA).

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Author information

Authors and Affiliations

  1. Universitat Politècnica de Catalunya, Spain

    Glyn Morrill

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  1. Glyn Morrill
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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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Morrill, G. (2014). A Categorial Type Logic. 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_18

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  • DOI: https://doi.org/10.1007/978-3-642-54789-8_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-54788-1

  • Online ISBN: 978-3-642-54789-8

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