Proof analysis: a contribution to Hilbert's last problem
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge University Press
2011
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Cover image Inhaltsverzeichnis |
| Item Description: | "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. -- "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... Includes bibliographical references and index |
| Physical Description: | XI, 265 S. |
| ISBN: | 9781107008953 |
Staff View
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Record in the Search Index
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| adam_text | PROOF ANALYSIS
/ NEGRI, SARA
: 2011
TABLE OF CONTENTS / INHALTSVERZEICHNIS
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.
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
| any_adam_object | 1 |
| author | Negri, Sara 1967- Plato, Jan von 1951- |
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| classification_rvk | CC 2600 SK 130 |
| ctrlnum | (OCoLC)779060359 (DE-599)BVBBV040128857 |
| dewey-full | 511.3/6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3/6 |
| dewey-search | 511.3/6 |
| dewey-sort | 3511.3 16 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Philosophie |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV040128857 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T00:17:32Z |
| institution | BVB |
| isbn | 9781107008953 |
| language | English |
| lccn | 2011023026 |
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| physical | XI, 265 S. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Cambridge University Press |
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| spelling | Negri, Sara 1967- Verfasser (DE-588)173487084 aut Proof analysis a contribution to Hilbert's last problem Sara Negri ; Jan von Plato 1. publ. Cambridge [u.a.] Cambridge University Press 2011 XI, 265 S. txt rdacontent n rdamedia nc rdacarrier "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. -- "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... Includes bibliographical references and index Proof theory MATHEMATICS / Logic bisacsh Beweistheorie (DE-588)4145177-6 gnd rswk-swf Beweistheorie (DE-588)4145177-6 s DE-604 Plato, Jan von 1951- Verfasser (DE-588)171423615 aut http://assets.cambridge.org/97811070/08953/cover/9781107008953.jpg Cover image LoC Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024986070&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Negri, Sara 1967- Plato, Jan von 1951- Proof analysis a contribution to Hilbert's last problem Proof theory MATHEMATICS / Logic bisacsh Beweistheorie (DE-588)4145177-6 gnd |
| subject_GND | (DE-588)4145177-6 |
| title | Proof analysis a contribution to Hilbert's last problem |
| title_auth | Proof analysis a contribution to Hilbert's last problem |
| title_exact_search | Proof analysis a contribution to Hilbert's last problem |
| title_full | Proof analysis a contribution to Hilbert's last problem Sara Negri ; Jan von Plato |
| title_fullStr | Proof analysis a contribution to Hilbert's last problem Sara Negri ; Jan von Plato |
| title_full_unstemmed | Proof analysis a contribution to Hilbert's last problem Sara Negri ; Jan von Plato |
| title_short | Proof analysis |
| title_sort | proof analysis a contribution to hilbert s last problem |
| title_sub | a contribution to Hilbert's last problem |
| topic | Proof theory MATHEMATICS / Logic bisacsh Beweistheorie (DE-588)4145177-6 gnd |
| topic_facet | Proof theory MATHEMATICS / Logic Beweistheorie |
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