On Sahlqvist theory for hybrid logics

On Sahlqvist theory for hybrid logics AbstractWe develop a Sahlqvist theory by introducing the class of hybrid inductive formulas. Each hybrid inductive formula is shown to have an effectively calculable first-order local frame correspondent. We define two subclasses, called the nominally skeletal and skeletal hybrid inductive formulas. We show that members of these subclasses are, respectively, preserved under canonical extensions and Dedekind–MacNeille completions of certain hybrid algebras, which is enough to ensure that these formulas axiomatize relationally complete logics. The key methodological tool in proving these results is a hybrid version of the ALBA algorithm, which we formulate and call hybrid-ALBA. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Logic and Computation Oxford University Press

On Sahlqvist theory for hybrid logics

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Publisher
Oxford University Press
Copyright
© The Author, 2015. 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/exv045
Publisher site
See Article on Publisher Site

Abstract

AbstractWe develop a Sahlqvist theory by introducing the class of hybrid inductive formulas. Each hybrid inductive formula is shown to have an effectively calculable first-order local frame correspondent. We define two subclasses, called the nominally skeletal and skeletal hybrid inductive formulas. We show that members of these subclasses are, respectively, preserved under canonical extensions and Dedekind–MacNeille completions of certain hybrid algebras, which is enough to ensure that these formulas axiomatize relationally complete logics. The key methodological tool in proving these results is a hybrid version of the ALBA algorithm, which we formulate and call hybrid-ALBA.

Journal

Journal of Logic and ComputationOxford University Press

Published: Apr 1, 2017

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