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On proof normal forms for some systems of classical propositional logic
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 1 (2007), pp. 39-45.

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In this paper proof normal forms are given for some non-traditional systems of classical propositional logic. On basis of that forms the upper and lower bounds of proof complexity are given using the notion of $\varphi$-determinative disjunctive normal form. 
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S. R. Aleksanyan. On proof normal forms for some systems of classical propositional logic. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 1 (2007), pp. 39-45. http://geodesic.mathdoc.fr/item/UZERU_2007_1_a4/

[1] S. Buss, “Propositional Proof Complexity (Introduction)”, Handbook of Proof Theory, North-Holland, 1998 | MR

[2] A. A. Chubaryan, “Otnositelnaya effektivnost nekotorykh sistem dokazatelstv klassicheskoi propozitsionalnoi logiki”, Izvestiya NAN Armenii: Matematika, 37:5 (2002), 71–84 | MR | Zbl