| Issue |
RAIRO-Theor. Inf. Appl.
Volume 56, 2022
|
|
|---|---|---|
| Article Number | 9 | |
| Number of page(s) | 12 | |
| DOI | https://doi.org/10.1051/ita/2022009 | |
| Published online | 20 December 2022 | |
Almost all Classical Theorems are Intuitionistic
École Normale Supérieure de Lyon, LIP (UMR 5668 CNRS ENS Lyon UCBL),
46 allée d’Italie,
69364
Lyon,
France
* Corresponding author: pierre.lescanne@ens-lyon.fr
Received:
9
May
2022
Accepted:
7
October
2022
Canonical expressions represent the implicative propositions (i.e., the propositions with only implications) up-to renaming of variables. Using a Monte-Carlo approach, we explore the model of canonical expressions in order to confirm the paradox that says that asymptotically almost all classical theorems are intuitionistic. Actually we found that more than 96.6% of classical theorems are intuitionistic among propositions of size 100.
Mathematics Subject Classification: 11B73 / 03F55 / 06E30 / 05-04 / 05-08
Key words: Intuitionistic logic / classical logic / combinatorics / asymptotic / random generation / Bell number / Catalan number / Monte-Carlo method
© The authors. Published by EDP Sciences, 2022
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