Classical and intuitionistic logic are asymptotically identical

Authors:
Hervé Fournier;Danièle Gardy;Antoine Genitrini;Marek Zaionc
Affiliations:
Laboratoire PRiSM, Université de Versailles St-Quentin en Yvelines, Versailles, France;Laboratoire PRiSM, Université de Versailles St-Quentin en Yvelines, Versailles, France;Laboratoire PRiSM, Université de Versailles St-Quentin en Yvelines, Versailles, France;Theoretical Computer Science, Jagiellonian University, Kraków, Poland
Venue:
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
Year:
2007

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Abstract

This paper considers logical formulas built on the single binary connector of implication and a finite number of variables. When the number of variables becomes large, we prove the following quantitative results: asymptotically, all classical tautologies are simple tautologies. It follows that asymptotically, all classical tautologies are intuitionistic.