Bracket Induction for Lambek Calculus with Bracket Modalities

  • Glyn Morrill
  • Stepan Kuznetsov
  • Max Kanovich
  • Andre Scedrov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10950)


Relativisation involves dependencies which, although unbounded, are constrained with respect to certain island domains. The Lambek calculus L can provide a very rudimentary account of relativisation limited to unbounded peripheral extraction; the Lambek calculus with bracket modalities Lb can further condition this account according to island domains. However in naïve parsing/theorem-proving by backward chaining sequent proof search for Lb the bracketed island domains, which can be indefinitely nested, have to be specified in the linguistic input. In realistic parsing word order is given but such hierarchical bracketing structure cannot be assumed to be given. In this paper we show how parsing can be realised which induces the bracketing structure in backward chaining sequent proof search with Lb.


Lambek calculus with brackets Bracket induction Categorial grammar 



We would like to thank the anonymous referees for their thoughtful comments and questions.

The research of Morrill was supported by the grant TIN2017-89244-R from MINECO (Ministerio de Economia, Industria y Competitividad). Glyn Morrill is also grateful to the University of Pennsylvania for support during his visit in February 2017. Kuznetsov’s research towards this paper was supported by the Young Russian Mathematics award, by the Program of the Presidium of the Russian Academy of Sciences No. 01 ‘Fundamental Mathematics and its Applications’ under grant PRAS-18-01, and by the Russian Foundation for Basic Research under grant 18-01-00822. Stepan Kuznetsov is also grateful to the University of Pennsylvania for support during his visit in April–May 2018, when the final version of this paper was prepared. Max Kanovich is grateful to the University of Pennsylvania for support during his visit in February 2017. The participation of Kanovich, Kuznetsov, and Scedrov in the preparation of this article was within the framework of the Basic Research Program at the National Research University Higher School of Economics (HSE) and supported within the framework of a subsidy by the Russian Academic Excellence Project ‘5-100’.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Glyn Morrill
    • 1
  • Stepan Kuznetsov
    • 2
    • 5
  • Max Kanovich
    • 3
    • 5
  • Andre Scedrov
    • 4
    • 5
  1. 1.Universitat Politècnica de CatalunyaBarcelonaSpain
  2. 2.Steklov Mathematical Institute of the RASMoscowRussia
  3. 3.University College LondonLondonUK
  4. 4.University of PennsylvaniaPhiladelphiaUSA
  5. 5.National Research University Higher School of EconomicsMoscowRussia

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