Modal Renderings of Intuitionistic Propositional Logic

  • Nicholas Rescher
Part of the Synthese Library book series (SYLI, volume 17)


The two systems of non-standard propositional logic that have been most extensively studied to date are C. I. Lewis’ systems of ‘strict implication’ and the intuitionistic propositional logic as systematized by A. Heyting. The relationship between these systems, which has now been explored for over a generation, is of substantial interest. The aim of the present chapter is both to summarize and to extend what is known about this relationship. Its linkages with the established systems of modal logic represent one of the most significant bridges between modern intuitionistic logic and other branches of the subject whose historical rootings go far deeper.1


Modal Logic Propositional Logic Historical Rooting Modal Rendering Intuitionistic Propositional Calculus 
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  1. [1]
    A. Heyting,‘Die formalen Regeln der intuitionistischen Logik’, Sitzungsberichte der Preussischen Akademie der Wissenschaften (Physikalisch-mathematische Klasse) 1930, pp. 42–56.Google Scholar
  2. [2]
    C. I. Lewis and C. H. Langford, Symbolic Logic (New York, 1932; second edition, New York, 1959 ).Google Scholar
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    Kurt GöDEL, ‘Eine Interpretation des intuitionistischen Aussagenkalküls’, Ergebnisse eines mathematischen Kolloquiums 4 (1933) 39–40. Reporting results presented in 1931.Google Scholar
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    J. J. C. Mckinsey and Alfred TARSKI, ‘Some Theorems About the Sentential Calculi of Lewis and Heyting’, The Journal of Symbolic Logic 13 (1948) 1–15.CrossRefGoogle Scholar
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    A. Heyting, Intuitionism (Amsterdam, 1956 ).Google Scholar

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© Springer Science+Business Media Dordrecht 1968

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  • Nicholas Rescher

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