Upper bounds on complexity of Frege proofs with limited use of certain schemata

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.

• Type: Journal
• Year: 2006
• Where: AML
• Authors: Pavel Naumov
• Keywords: AML 2006, Axiom Schemata, Classical Propositional Logic, Proof Complexity