Unified correspondence and proof theory for strict implication

Unified correspondence and proof theory for strict implication AbstractThe unified correspondence theory for distributive lattice expansion logics (DLE-logics) is specialized to strict implication logics. As a consequence of a general semantic consevativity result, a wide range of strict implication logics can be conservatively extended to Lambek Calculi over the bounded distributive full non-associative Lambek calculus ($\mathsf{BDFNL}$). Many strict implication sequents can be transformed into analytic rules employing one of the main tools of unified correspondence theory, namely (a suitably modified version of) the Ackermann lemma based algorithm $\mathsf{ALBA}$. Gentzen-style cut-free sequent calculi for $\mathsf{BDFNL}$ and its extensions with analytic rules, which are transformed from strict implication sequents, are developed. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Logic and Computation Oxford University Press

Unified correspondence and proof theory for strict implication

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Publisher
Oxford University Press
Copyright
© The Author, 2016. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com
ISSN
0955-792X
eISSN
1465-363X
D.O.I.
10.1093/logcom/exw012
Publisher site
See Article on Publisher Site

Abstract

AbstractThe unified correspondence theory for distributive lattice expansion logics (DLE-logics) is specialized to strict implication logics. As a consequence of a general semantic consevativity result, a wide range of strict implication logics can be conservatively extended to Lambek Calculi over the bounded distributive full non-associative Lambek calculus ($\mathsf{BDFNL}$). Many strict implication sequents can be transformed into analytic rules employing one of the main tools of unified correspondence theory, namely (a suitably modified version of) the Ackermann lemma based algorithm $\mathsf{ALBA}$. Gentzen-style cut-free sequent calculi for $\mathsf{BDFNL}$ and its extensions with analytic rules, which are transformed from strict implication sequents, are developed.

Journal

Journal of Logic and ComputationOxford University Press

Published: Apr 1, 2017

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