Geodesic
Comparison of several proof systems of intuitionistic propositional logic
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (2005), pp. 25-30 
S. M. Sayadyan. Comparison of several proof systems of intuitionistic propositional logic. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (2005), pp. 25-30. http://geodesic.mathdoc.fr/item/UZERU_2005_2_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A fragment of hierarchy of the proof systems for intuitionistic propositional logic under the $p$-simulation relation is constructed. These systems are resolution system, natural, Hilbert-style system and sequence system. The obtained hierarchy is the same as the hierarchy for analogous systems of classical logic.

[1] S. R. Buss, “Polynomial size proofs of the propositional pigeonhole principle”, Journal of Symbolic Logic, 52:4 (1987), 916–927 | DOI | MR

[2] S. R. Buss, T. Pitassi, “Resolution and the Weak Pigeonhole Principle”, Annual Conference of the European Association for Computer Science Logic (August 23-29), 1997

[3] S. K. Klini, Vvedenie v metamatematiku, IL, Moskva, 1957

[4] G. E. Mints, “Ischisleniya rezolyutsii dlya neklassicheskikh logik”, Semiotika i informatika, 1985, no. 25, 120–125

[5] G. S. Tseitin, “O slozhnosti vyvoda v ischislenii vyskazyvanii”, Zapiski nauchnykh seminarov LOMI AN SSSR, 1968, no. 8, 234–259