On Sizes of Linear and Tree-Like Proofs for any Formulae Families in Some Systems of Propositional Calculus

Abstract

The sizes of linear and tree-like proofs 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 bounds obtained formerly for the steps of proofs for the same formulas in the mentioned systems shows the importance of the size of proof among the other characteristics of proof complexities.