Geodesic
On non-monotonous properties of some classical and nonclassical propositional proof systems
Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 54 (2020) no. 3, pp. 127-136

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We investigate the relations between the proof lines of non-minimal tautologies and its minimal tautologies for the Frege systems, the sequent systems with cut rule and the systems of natural deductions of classical and nonclassical logics. We show that for these systems there are sequences of tautologies $\psi_n$, every one of which has unique minimal tautologies $\varphi_n$ such that for each $n$ the minimal proof lines of $\varphi_n$ are an order more than the minimal proof lines of $\psi_n$.
Keywords: minimal tautology, Frege system, sequent system, natural deduction system, proof lines, proof sizes, monotonous and strongly monotonous system. 
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A. A. Chubaryan; A. A. Hambardzumyan. On non-monotonous properties of some classical and nonclassical propositional proof systems. Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 54 (2020) no. 3, pp. 127-136. http://geodesic.mathdoc.fr/item/UZERU_2020_54_3_a0/