Naumov, Pavel (2006) Upper bounds on complexity of Frege proofs with limited use of certain schemata. Archive for Mathematical Logic, 45 (4), 431-446. (doi:10.1007/s00153-005-0325-8).
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.
This record has no associated files available for download.
More information
Identifiers
Catalogue record
Export record
Altmetrics
Contributors
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.