Editorial

Editorial One of the major trends in modern logic has been the move from logic to logics. This has created the need to develop general results applicable to enormous families of logical systems, while at the same time accounting for the specific features of each family member in a modular way. This volume focuses on canonicity and correspondence results for non-classical logics. Canonicity and correspondence are intimately related, and recently, general methodologies for obtaining such results have become very prominent. These methodologies extend the original Sahlqvist canonicity and correspondence theorem from the realm of model theory to the realm of algebra, coalgebra and Stone-type duality. This volume collects a small sample of results in this very vibrant research field. The first paper, entitled ‘The Canonical FEP Construction’, introduces a novel construction, based on canonical extensions. This construction is used to prove the finite embeddability property (FEP) for varieties of decreasing residuated lattice-ordered algebras defined by equations from a certain syntactically specified class. The finite algebras produces in this way are guaranteed to be internally compact, which is not the case with more traditional FEP constructions. The second paper, ‘Dual characterizations for finite lattices via correspondence theory for monotone modal logic’, http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Logic and Computation Oxford University Press

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Publisher
Oxford University Press
Copyright
© The Author, 2017. 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/exx013
Publisher site
See Article on Publisher Site

Abstract

One of the major trends in modern logic has been the move from logic to logics. This has created the need to develop general results applicable to enormous families of logical systems, while at the same time accounting for the specific features of each family member in a modular way. This volume focuses on canonicity and correspondence results for non-classical logics. Canonicity and correspondence are intimately related, and recently, general methodologies for obtaining such results have become very prominent. These methodologies extend the original Sahlqvist canonicity and correspondence theorem from the realm of model theory to the realm of algebra, coalgebra and Stone-type duality. This volume collects a small sample of results in this very vibrant research field. The first paper, entitled ‘The Canonical FEP Construction’, introduces a novel construction, based on canonical extensions. This construction is used to prove the finite embeddability property (FEP) for varieties of decreasing residuated lattice-ordered algebras defined by equations from a certain syntactically specified class. The finite algebras produces in this way are guaranteed to be internally compact, which is not the case with more traditional FEP constructions. The second paper, ‘Dual characterizations for finite lattices via correspondence theory for monotone modal logic’,

Journal

Journal of Logic and ComputationOxford University Press

Published: Apr 1, 2017

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