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Quantum Physics and LinguisticsA Compositional, Diagrammatic Discourse$
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Chris Heunen, Mehrnoosh Sadrzadeh, and Edward Grefenstette

Print publication date: 2013

Print ISBN-13: 9780199646296

Published to Oxford Scholarship Online: May 2013

DOI: 10.1093/acprof:oso/9780199646296.001.0001

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Proof Nets for the Lambek–Grishin Calculus

Proof Nets for the Lambek–Grishin Calculus

Chapter:
(p.283) CHAPTER 10 Proof Nets for the Lambek–Grishin Calculus
Source:
Quantum Physics and Linguistics
Author(s):

Moortgat Michael

Moot Richard

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199646296.003.0010

Grishin's generalization of Lambek's syntactic calculus combines a non-commutative multiplicative conjunction and its residuals (product, left and right division) with a dual family: multiplicative disjunction, right and left difference. Interaction between these two families takes the form of linear distributivity principles. We study proof nets for the Lambek–Grishin calculus and the correspondence between these nets and unfocused and focused versions of its sequent calculus.

Keywords:   syntactic calculus, ordered type algebras, residuation, linear distributivity, Grishin algebras, proof nets, focus, sequent calculus

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