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2018 | OriginalPaper | Chapter

Bracket Induction for Lambek Calculus with Bracket Modalities

Authors : Glyn Morrill, Stepan Kuznetsov, Max Kanovich, Andre Scedrov

Published in: Formal Grammar 2018

Publisher: Springer Berlin Heidelberg

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Abstract

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.

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We use this notation because it prefigures a planned future extension to exponentials in which onsets are coded by lists of naturals representing the size of so-called stoups; the zeros in the coding of Lb essentially mean that here all stoups are empty.

In contrast to the present paper, the calculus in [5] allows empty antecedents, but imposing the Lambek’s restriction there is quite straightforward.

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Title: Bracket Induction for Lambek Calculus with Bracket Modalities
Authors: Glyn Morrill
Stepan Kuznetsov
Max Kanovich
Andre Scedrov
Publisher: Springer Berlin Heidelberg
Book: Formal Grammar 2018
Print ISBN: 978-3-662-57783-7

Electronic ISBN: 978-3-662-57784-4

Copyright Year: 2018
DOI: https://doi.org/10.1007/978-3-662-57784-4_5

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