INTERNATIONAL STANDARD BOOK NUMBER
(Number (ISBN
9781107008953 (hardback)
NATIONAL BIBLIOGRAPHY NUMBER
Country Code
IR
Number
EN-52607
LANGUAGE OF THE ITEM
.Language of Text, Soundtrack etc
انگلیسی
COUNTRY OF PUBLICATION OR PRODUCTlON
Country of publication
IR
TITLE AND STATEMENT OF RESPONSIBILITY
Title Proper
Proof analysis
General Material Designation
[Book]
Other Title Information
:a contribution to Hilbert's last problem
First Statement of Responsibility
/ Sara Negri, Jan von Plato
.PUBLICATION, DISTRIBUTION, ETC
Place of Publication, Distribution, etc.
Cambridge, UK ;New York
Name of Publisher, Distributor, etc.
: Cambridge University Press,
Date of Publication, Distribution, etc.
, 2011.
PHYSICAL DESCRIPTION
Specific Material Designation and Extent of Item
xi, 265 p. , 26 cm.
NOTES PERTAINING TO PUBLICATION, DISTRIBUTION, ETC.
Text of Note
Electronic
INTERNAL BIBLIOGRAPHIES/INDEXES NOTE
Text of Note
Includes bibliographical references and index.
CONTENTS NOTE
Text of Note
Machine generated contents note: Prologue: Hilbert's Last Problem; 1. Introduction; Part I. Proof Systems Based on Natural Deduction: 2. Rules of proof: natural deduction; 3. Axiomatic systems; 4. Order and lattice theory; 5. Theories with existence axioms; Part II. Proof Systems Based on Sequent Calculus: 6. Rules of proof: sequent calculus; 7. Linear order; Part III. Proof Systems for Geometric Theories: 8. Geometric theories; 9. Classical and intuitionistic axiomatics; 10. Proof analysis in elementary geometry; Part IV. Proof Systems for Nonclassical Logics: 11. Modal logic; 12. Quantified modal logic, provability logic, and so on; Bibliography; Index of names; Index of subjects.
Text of Note
"We shall discuss the notion of proof and then present an introductory example of the analysis of the structure of proofs. The contents of the book are outlined in the third and last section of this chapter. 1.1 The idea of a proof A proof in logic and mathematics is, traditionally, a deductive argument from some given assumptions to a conclusion. Proofs are meant to present conclusive evidence in the sense that the truth of the conclusion should follow necessarily from the truth of the assumptions. Proofs must be, in principle, communicable in every detail, so that their correctness can be checked. Detailed proofs are a means of presentation that need not follow in anyway the steps in finding things out. Still, it would be useful if there was a natural way from the latter steps to a proof, and equally useful if proofs also suggested the way the truths behind them were discovered. The presentation of proofs as deductive arguments began in ancient Greek axiomatic geometry. It took Gottlob Frege in 1879 to realize that mere axioms and definitions are not enough, but that also the logical steps that combine axioms into a proof have to be made, and indeed can be made, explicit. To this purpose, Frege formulated logic itself as an axiomatic discipline, completed with just two rules of inference for combining logical axioms. Axiomatic logic of the Fregean sort was studied and developed by Bert-rand Russell, and later by David Hilbert and Paul Bernays and their students, in the first three decades of the twentieth century. Gradually logic came to be seen as a formal calculus instead of a system of reasoning: the language of logic was formalized and its rules of inference taken as part of an inductive definition of the class of formally provable formulas in the calculus"--Provided by publisher.
Text of Note
"This book continues from where the authors' previous book, Structural Proof Theory, ended. It presents an extension of the methods of analysis of proofs in pure logic to elementary axiomatic systems and to what is known as philosophical logic. A self-contained brief introduction to the proof theory of pure logic is included that serves both the mathematically and philosophically oriented reader. The method is built up gradually, with examples drawn from theories of order, lattice theory and elementary geometry. The aim is, in each of the examples, to help the reader grasp the combinatorial behaviour of an axiom system, which typically leads to decidability results. The last part presents, as an application and extension of all that precedes it, a proof-theoretical approach to the Kripke semantics of modal and related logics, with a great number of new results, providing essential reading for mathematical and philosophical logicians"--Provided by publisher.
TOPICAL NAME USED AS SUBJECT
Proof theory
LIBRARY OF CONGRESS CLASSIFICATION
Class number
E-BOOK
PERSONAL NAME - PRIMARY RESPONSIBILITY
Negri, Sara,1967-
PERSONAL NAME - SECONDARY RESPONSIBILITY
Von Plato, Jan
ORIGINATING SOURCE
Country
ایران
ELECTRONIC LOCATION AND ACCESS
Host name
9781107008953.pdf
Access number
عادی
Compression information
عادی
Date and Hour of Consultation and Access
9781107008953.pdf
Electronic Format Type
متن
old catalog
e
BL
1
a
Y
