Gentzen's cut-elimination theorem is widely used as a tool for
meta-mathematical investigations. It is sometimes claimed however
that the theorem and its proof have interest which is independent
of these applications and derives from the information they supply
about the structure of proofs in general. Ungar investigates this
claim in the context of first order logic. Ungar gives an account
of Gentzen's theorem for various formalisms and discusses the
difficulties involved in treating these different versions
uniformly, as instances of a single theorem which is not tied to a
particular system of rules. By extending the theorem to a natural
deduction calculus whose derivations are allowed to have more than
one conclusion, Ungar argues that the different versions of the
theorem are more or less natural specializations of a single result
whose significance can be understood in terms of the proofs
represented by formal derivations. A concluding discussion focuses
on the relationship between proofs and formal derivations, and the
role proofs may play as part of a general theory of evidence.
General
Imprint: |
Centre for the Study of Language & Information
|
Country of origin: |
United States |
Series: |
Center for the Study of Language and Information Publication Lecture Notes, 28 |
Release date: |
February 1992 |
First published: |
June 1992 |
Authors: |
A.M. Ungar
|
Dimensions: |
228 x 152 x 21mm (L x W x T) |
Format: |
Hardcover - Cloth over boards
|
Pages: |
248 |
Edition: |
New |
ISBN-13: |
978-0-937073-83-4 |
Categories: |
Books >
Science & Mathematics >
Mathematics >
Mathematical foundations >
General
|
LSN: |
0-937073-83-0 |
Barcode: |
9780937073834 |
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