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Journal of Logic and Computation Advance Access originally published online on August 6, 2007
Journal of Logic and Computation 2007 17(4):767-794; doi:10.1093/logcom/exm026
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© The Author, 2007. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Articles

Classical Modal Display Logic in the Calculus of Structures and Minimal Cut-free Deep Inference Calculi for S5

Rajeev Goré

Computer Sciences Laboratory, The Australian National University, ACT 0200 Australia. E-mail: rajeev.gore{at}anu.edu.au

Alwen Tiu

Computer Sciences Laboratory, The Australian National University and NICTA, ACT 0200 Australia. E-mail: alwen.tiu{at}anu.edu.au

Received 4 May 2007.


  Abstract

We begin by showing how to faithfully encode the Classical Modal Display Logic (CMDL) of Wansing into the Calculus of Structures (CoS) of Guglielmi. Since every CMDL calculus enjoys cut-elimination, we obtain a cut-elimination theorem for all corresponding CoS calculi. We then show how our result leads to a minimal cut-free CoS calculus for modal logic S5. No other existing CoS calculi for S5 enjoy both these properties simultaneously.

Keywords: Calculus of structures; cut-free sequent calculi; deep inference; display logic; proof theory of modal logic


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