Archive for Mathematical Logic 45 (4):431-446 (2006)

Abstract
The paper considers a commonly used axiomatization of the classical propositional logic and studies how different axiom schemata in this system contribute to proof complexity of the logic. The existence of a polynomial bound on proof complexity of every statement provable in this logic is a well-known open question.The axiomatization consists of three schemata. We show that any statement provable using unrestricted number of axioms from the first of the three schemata and polynomially-bounded in size set of axioms from the other schemata, has a polynomially-bounded proof complexity. In addition, it is also established, that any statement, provable using unrestricted number of axioms from the remaining two schemata and polynomially-bounded in size set of axioms from the first scheme, also has a polynomially-bounded proof complexity
Keywords Mathematics   Mathematics, general   Algebra   Mathematical Logic and Foundations
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Reprint years 2006
DOI 10.1007/s00153-005-0325-8
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Introduction to Mathematical Logic.ALONZO CHURCH - 1944 - London: Oxford University PRess.

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