Proof Analysis

A Contribution to Hilbert's Last Problem

By: Sara Negri, Jan von Plato

Write A Review

Hardcover | 29 September 2011 | Edition Number 1

At a Glance

Hardcover
278 Pages

Dimensions(cm)
25.4 x 17.78 x 1.91

Hardcover

RRP $187.95

$166.75

11%OFF

or 4 interest-free payments of $41.69 with

or

Ships in 5 to 7 business days

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.

Industry Reviews

"...provide a substantial contribution to the development of proof theory in mathematics.... The book covers a lot of useful material in a concise, efficient and very clearly structured manner. The chapters are written with a palpable intention to show how vast the applicability of the methods is. The results are uniform, general and require a high-level preparation in many different fields. This book can be seen as the stimulating continuation of the authors' introductory book Structural Proof Theory..." --F. Poggiolesi, Institut d'Histoire et Philosophie des Sciences, Paris, France, History and Philosophy of Logic

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

Orders over $79.00 qualify for free shipping.

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

More in Philosophy & Logic

Critical Thinking Skills

Effective Analysis, Argument and Reflection

Paperback

RRP $36.99

$35.75

Rationality

What It Is, Why It Seems Scarce, Why It Matters

Paperback

RRP $26.99

$22.99

15%
OFF

The Logic of Scientific Discovery

Routledge Classics

Paperback

RRP $34.99

$34.75

The Socratic Method

A Practitioner's Handbook

Paperback

RRP $34.99

$33.99

How Not to Be Wrong : The Power of Mathematical Thinking - Jordan Ellenberg

$20.75

10%
OFF

The Laws of Thought

The Quest for a Mathematical Theory of the Mind

Paperback

RRP $34.99

$28.75

18%
OFF

Critical Thinking Skills For Dummies

For Dummies

Paperback

RRP $32.95

$26.99

18%
OFF

Conjectures and Refutations : The Growth of Scientific Knowledge : The Growth of Scientific Knowledge - Karl Popper

$23.75

15%
OFF

The Philosophical Foundations of Bayesianism : An Opinionated Introduction - Kenny Easwaran

$77.75

An Introduction to Collective Intentionality

In Action, Thought, and Society

Hardcover

RRP $305.00

$263.75

14%
OFF

Recipes for Science : An Introduction to Scientific Methods and Reasoning - Angela Potochnik

$226.75

13%
OFF

Interdisciplinarity and the Art of Human Connection

Knowing in a Complex World

Hardcover

RRP $150.00

$134.75

10%
OFF

Analogy and Exemplary Reasoning in Legal Discourse

Paperback

RRP $90.99

$82.75

Objective Knowledge

An Evolutionary Approach

Hardcover

RRP $305.00

$263.75

14%
OFF

Objective Knowledge

An Evolutionary Approach

Paperback

RRP $54.99

$54.75

Quantum Gravity and Computation

1st Edition - Information, Pregeometry, and Digital Physics

Hardcover

RRP $305.00

$304.75

Inductive Probability

Routledge Revivals

Paperback

RRP $62.99

$60.99

Probability, Objectivity and Evidence

Routledge Revivals

Hardcover

RRP $189.00

$167.75

11%
OFF

Preface	p. ix
Prologue: Hilbert's last problem	p. 1
Introduction	p. 3
The idea of a proof	p. 3
Proof analysis: an introductory example	p. 4
Outline	p. 9
Proof Systems Based on Natural Deduction
Rules of proof: natural deduction	p. 17
Natural deduction with general elimination rules	p. 17
Normalization of derivations	p. 23
From axioms to rules of proof	p. 29
The theory of equality	p. 32
Predicate logic with equality and its word problem	p. 35
Notes to Chapter 2	p. 37
Axiomatic systems	p. 39
Organization of an axiomatization	p. 39
Relational theories and existential axioms	p. 46
Notes to Chapter 3	p. 49
Order and lattice theory	p. 50
Order relations	p. 50
Lattice theory	p. 52
The word problem for groupoids	p. 57
Rule systems with eigenvariables	p. 62
Notes to Chapter 4	p. 67
Theories with existence axioms	p. 68
Existence in natural deduction	p. 68
Theories of equality and order again	p. 71
Relational lattice theory	p. 73
Notes to Chapter 5	p. 82
Proof Systems Based on Sequent Calculus
Rules of proof: sequent calculus	p. 85
From natural deduction to sequent calculus	p. 85
Extensions of sequent calculus	p. 97
Predicate logic with equality	p. 106
Herbrand's theorem for universal theories	p. 110
Notes to Chapter 6	p. 111
Linear order	p. 113
Partial order and Szpilrajn's theorem	p. 113
The word problem for linear order	p. 119
Linear lattices	p. 123
Notes to Chapter 7	p. 128
Proof Systems for Geometric Theories
Geometric theories	p. 133
Systems of geometric rules	p. 133
Proof theory of geometric theories	p. 138
Barr's theorem	p. 144
Notes to Chapter 8	p. 145
Classical and intuitionistic axiomatics	p. 147
The duality of classical and constructive notions and proofs	p. 147
From geometric to co-geometric axioms and rules	p. 150
Duality of dependent types and degenerate cases	p. 155
Notes to Chapter 9	p. 156
Proof analysis in elementary geometry	p. 157
Projective geometry	p. 157
Affine geometry	p. 173
Examples of proof analysis in geometry	p. 180
Notes to Chapter 10	p. 181
Proof Systems for Non-Classical Logics
Modal logic	p. 185
The language and axioms of modal logic	p. 185
Kripke semantics	p. 187
Formal Kripke semantics	p. 189
Structural properties of modal calculi	p. 193
Decidability	p. 201
Modal calculi with equality, undefinability results	p. 210
Completeness	p. 213
Notes to Chapter 11	p. 219
Quantified modal logic, provability logic, & other non-classical logics	p. 222
Adding the quantifiers	p. 222
Provability logic	p. 234
Intermediate logics	p. 239
Substructural logics	p. 249
Notes to Chapter 12	p. 251
Bibliography	p. 254
Index of names	p. 262
Index of subjects	p. 264
Table of Contents provided by Ingram. All Rights Reserved.

Proof Analysis

A Contribution to Hilbert's Last Problem

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

Other Editions and Formats

Paperback

More in Philosophy & Logic

Critical Thinking Skills

Effective Analysis, Argument and Reflection

Rationality

What It Is, Why It Seems Scarce, Why It Matters

The Logic of Scientific Discovery

Routledge Classics

The Socratic Method

A Practitioner's Handbook

How Not to Be Wrong

The Power of Mathematical Thinking

True Facts That Sound Like Bull$#*t

500 Insane-But-True Facts That Will Shock and Impress Your Friends

The Laws of Thought

The Quest for a Mathematical Theory of the Mind

Critical Thinking Skills For Dummies

For Dummies

Conjectures and Refutations : The Growth of Scientific Knowledge

The Growth of Scientific Knowledge

Light on Yoga

The Definitive Guide to Yoga Practice [Thorsons Classics Edition]

The Philosophical Foundations of Bayesianism

An Opinionated Introduction

An Introduction to Collective Intentionality

In Action, Thought, and Society

An Introduction to Collective Intentionality

In Action, Thought, and Society

Recipes for Science

An Introduction to Scientific Methods and Reasoning

Contemporary Debates in African and Western Philosophy

Analytic and Intercultural Approaches

Interdisciplinarity and the Art of Human Connection

Knowing in a Complex World

Analogy and Exemplary Reasoning in Legal Discourse

Objective Knowledge

An Evolutionary Approach

Objective Knowledge

An Evolutionary Approach

Quantum Gravity and Computation

1st Edition - Information, Pregeometry, and Digital Physics

Inductive Probability

Routledge Revivals

Probability, Objectivity and Evidence

Routledge Revivals

How to Think More and Better

Being Reasonable in Unreasonable Times

Logic and Criticism

Routledge Revivals

This product is categorised by