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Logic Journal of IGPL Advance Access originally published online on October 29, 2007
Logic Journal of IGPL 2008 16(2):155-174; doi:10.1093/jigpal/jzm058
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© The Author, 2007. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Sequent Calculi for Some Strict Implication Logics

Ryo Ishigaki

Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, O-okayama, Meguro, Tokyo 152-8522, Japan. E-mail: zan35044{at}nifty.com

Ryo Kashima

Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, O-okayama, Meguro, Tokyo 152-8522, Japan. E-mail: kashima{at}is.titech.ac.jp


  Abstract

We introduce various sequent systems for propositional logics having strict implication, and prove the completeness theorems and the finite model properties of these systems.The cut-elimination theorems or the (modified) subformula properties are proved semantically.

Key Words: strict implication • sequent calculus • completeness theorem • Kripke models

Received for publication 17 September 2007.
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