Formalizing Cut Elimination of Coalgebraic Logics in Coq

  • Hendrik Tews
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8123)


In their work on coalgebraic logics, Pattinson and Schröder prove soundness, completeness and cut elimination in a generic sequent calculus for propositional multi-modal logics [1]. The present paper reports on a formalization of Pattinson’s and Schröder’s work in the proof assistant Coq that provides machine-checked proofs for soundness, completeness and cut elimination of their calculus. The formalization exploits dependent types to obtain a very concise deep embedding for formulas and proofs. The work presented here can be used to verify cut elimination theorems for different modal logics with considerably less effort in the future.


Modal Logic Classical Logic Modal Rank Propositional Variable Proof Assistant 
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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Hendrik Tews
    • 1
  1. 1.Institute of Systems ArchitectureTU DresdenGermany

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