article

The Displacement Calculus

Authors:

Oriol Valentín,

Mario FaddaAuthors Info & Claims

Journal of Logic, Language and Information, Volume 20, Issue 1

Pages 1 - 48

https://doi.org/10.1007/s10849-010-9129-2

Published: 01 January 2011 Publication History

Abstract

If all dependent expressions were adjacent some variety of immediate constituent analysis would suffice for grammar, but syntactic and semantic mismatches are characteristic of natural language; indeed this is a, or the, central problem in grammar. Logical categorial grammar reduces grammar to logic: an expression is well-formed if and only if an associated sequent is a theorem of a categorial logic. The paradigmatic categorial logic is the Lambek calculus, but being a logic of concatenation the Lambek calculus can only capture discontinuous dependencies when they are peripheral. In this paper we present the displacement calculus, which is a logic of intercalation as well as concatenation and which subsumes the Lambek calculus. On the empirical side, we apply the new calculus to discontinuous idioms, quantification, VP ellipsis, medial extraction, pied-piping, appositive relativisation, parentheticals, gapping, comparative subdeletion, cross-serial dependencies, reflexivization, anaphora, dative alternation, and particle shift. On the technical side, we prove that the calculus enjoys Cut-elimination.

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cover image Journal of Logic, Language and Information

Journal of Logic, Language and Information Volume 20, Issue 1

January 2011

136 pages

ISSN:0925-8531

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Copyright © Copyright © 2011 Springer Science+Business Media B.V.

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Kluwer Academic Publishers

United States

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Published: 01 January 2011

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Cited By

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https://doi.org/10.1007/978-3-031-62687-6_13
Morrill GValentín O(2019)Displacement logic for anaphoraJournal of Computer and System Sciences10.1016/j.jcss.2013.05.00680:2(390-409)Online publication date: 1-Jan-2019
https://dl.acm.org/doi/10.1016/j.jcss.2013.05.006
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Wurm C(2018)Language-Theoretic and Finite Relation Models for the (Full) Lambek CalculusJournal of Logic, Language and Information10.1007/s10849-017-9249-z26:2(179-214)Online publication date: 24-Dec-2018
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Morrill GKuznetsov SKanovich MScedrov A(2018)Bracket Induction for Lambek Calculus with Bracket ModalitiesFormal Grammar 201810.1007/978-3-662-57784-4_5(84-101)Online publication date: 11-Aug-2018
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