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

نویسنده

  • Pavel Naumov
چکیده

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.

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عنوان ژورنال:
  • Arch. Math. Log.

دوره 45  شماره 

صفحات  -

تاریخ انتشار 2006