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How to identify, translate and combine logics?

How to identify, translate and combine logics? AbstractWe give general definitions of logical frameworks and logics. Examples include the logical frameworks LF and Isabelle and the logics represented in them. We apply this to give general definitions for equivalence of logics, translation between logics and combination of logics. We also establish general criteria for the soundness and completeness of these. Our key messages are that the syntax and proof systems of logics are theories; that both semantics and translations are theory morphisms; and that combinations are colimits. Our approach is based on the Mmt language, which lets us combine formalist declarative representations (and thus the associated tool support) with abstract categorical conceptualizations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Logic and Computation Oxford University Press

How to identify, translate and combine logics?

Journal of Logic and Computation , Volume 27 (6) – Sep 1, 2017

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References (61)

Publisher
Oxford University Press
Copyright
© The Author, 2014. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com Published online December 14, 2014
ISSN
0955-792X
eISSN
1465-363X
DOI
10.1093/logcom/exu079
Publisher site
See Article on Publisher Site

Abstract

AbstractWe give general definitions of logical frameworks and logics. Examples include the logical frameworks LF and Isabelle and the logics represented in them. We apply this to give general definitions for equivalence of logics, translation between logics and combination of logics. We also establish general criteria for the soundness and completeness of these. Our key messages are that the syntax and proof systems of logics are theories; that both semantics and translations are theory morphisms; and that combinations are colimits. Our approach is based on the Mmt language, which lets us combine formalist declarative representations (and thus the associated tool support) with abstract categorical conceptualizations.

Journal

Journal of Logic and ComputationOxford University Press

Published: Sep 1, 2017

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