On Sizes of Linear and Tree-Like Proofs for any Formulae Families in Some Systems of Propositional Calculus - Apinyan, Levon A.; Chubaryan, Anahit A. (Изд-во НАН РА)
The sizes of linear and tree-likeproofs for any formulae families are investigated in some systems of propositional calculus: in different sequent systems (with quantifier rules, with the substitution rule, with the cut rule, without the cut rule, monotone) and in the generalization splitting system. The comparison of results obtained here with the boundsobtained formerly for the steps of proofs for the same formulas in the mentioned systems shows the importance of the sizeof proof among the other characteristics of proofcomplexities.
Keywords: Mathematical cybernetics; Computer science