Complexity of Proofs and Their Transformations in Axiomatic Theories
Author:   V. P. Orevkov
Publisher:   American Mathematical Society
Volume:   No. 128
ISBN:  

9780821845769


Pages:   153
Publication Date:   01 December 1994
Format:   Hardback
Availability:   In Print   Availability explained
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Complexity of Proofs and Their Transformations in Axiomatic Theories


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Overview

The aim of this work is to develop the tool of logical deduction schemata and use it to establish upper and lower bounds on the complexity of proofs and their transformations in axiomatized theories. The main results are: establishment of upper bounds on the elongation of deductions in cut eliminations; a proof that the length of a direct deduction of an existence theorem in the predicate calculus cannot be bounded above by an elementary function of the length of an indirect deduction of the same theorem; a complexity version of the existence property of the constructive predicate calculus; and, for certain formal systems of arithmetic, restrictions on the complexity of deductions that guarantee that the deducibility of a formula for all natural numbers in some finite set implies the deducibility of the same formula with a universal quantifier over all sufficiently large numbers.

Full Product Details

Author:   V. P. Orevkov
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
Volume:   No. 128
Weight:   0.510kg
ISBN:  

9780821845769


ISBN 10:   0821845764
Pages:   153
Publication Date:   01 December 1994
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print   Availability explained
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

Table of Contents

Introduction Upper bounds on deduction elongation in cut elimination Systems of term equations with substitutions Logical deduction schemata in axiomatized theories Bounds for the complexity of terms occurring in proofs Proof strengthening theorems References.

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