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The Gödel-Tarski Translations of Intuitionistic Propositional Formulas

  • Grigori Mints
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7265)

Abstract

The Gödel-Tarski operation that prefixes the necessity symbol to every subformula is a sound and faithful translation of intuitionistic propositional logic into modal logic S4. We characterize modal formulas equivalent in S4 to Gödel-Tarski translations of intuitionistic propositional formulas. It would be interesting to obtain a similar characterization for intuitionistic predicate formulas.

Keywords

modal logic intuitionistic logic Gödel-Tarski translation 

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References

  1. 1.
    Gödel, K.: Eine Interpretation des intuitionischen Aussagenkalküls. Ergebnisse Math. Colloq. 4, 39–40 (1933)zbMATHGoogle Scholar
  2. 2.
    McKinsey, J., Tarski, A.: Some theorems about the sentential calculi of Lewis and Heyting. J. Symb. Log. 13, 1–15 (1948)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Mints, G.: Embedding operations related to S. Kripke’s semantics. Seminars in Mathematics, V.A. Steklov Math. Inst. 4, 60–62 (1969)Google Scholar
  4. 4.
    Mints, G.: A Short Introduction to Intuitionistic Logic. Kluwer Publishers (2000)Google Scholar
  5. 5.
    Mints, G.: A Short Introduction to Modal Logic. CSLI Publications, Stanford (1992)zbMATHGoogle Scholar
  6. 6.
    Olkhovikov, G.: Model-theoretic characterization of predicate intuitionistic formulas, arxiv:1202.1195 (2012)Google Scholar
  7. 7.
    van Benthem, J.: Modal Logic for Open Minds. CSLI Publications (2010)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Grigori Mints
    • 1
  1. 1.Stanford UniversityStanfordUSA

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