Intuitionistic vs. classical tautologies, quantitative comparison

Authors:
Antoine Genitrini;Jakub Kozik;Marek Zaionc
Affiliations:
PRiSM, CNRS, UMR, Université de Versailles, Versailles cedex, France;Theoretical Computer Science, Jagiellonian University, Kraków, Poland;Theoretical Computer Science, Jagiellonian University, Kraków, Poland
Venue:
TYPES'07 Proceedings of the 2007 international conference on Types for proofs and programs
Year:
2007

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Abstract

We consider propositional formulas built on implication. The size of a formula is the number of occurrences of variables in it. We assume that two formulas which differ only in the naming of variables are identical. For every n ∈ N, there is a finite number of different formulas of size n. For every n we consider the proportion between the number of intuitionistic tautologies of size n compared with the number of classical tautologies of size n. We prove that the limit of that fraction is 1 when n tends to infinity.