Archive for Mathematical Logic

, Volume 51, Issue 1–2, pp 71–92 | Cite as

Proof analysis in intermediate logics



Using labelled formulae, a cut-free sequent calculus for intuitionistic propositional logic is presented, together with an easy cut-admissibility proof; both extend to cover, in a uniform fashion, all intermediate logics characterised by frames satisfying conditions expressible by one or more geometric implications. Each of these logics is embedded by the Gödel–McKinsey–Tarski translation into an extension of S4. Faithfulness of the embedding is proved in a simple and general way by constructive proof-theoretic methods, without appeal to semantics other than in the explanation of the rules.


Sequent calculus Modal logic Intermediate logic Labelled deduction Modal companion 

Mathematics Subject Classification (2000)

03A99 03B20 03B45 03B55 03F03 03F05 


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.School of Computer ScienceSt. Andrews UniversitySt. AndrewsScotland
  2. 2.Department of PhilosophyUniversity of HelsinkiHelsinkiFinland

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