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  • © 2011

Computational Logic and Set Theory

Applying Formalized Logic to Analysis

  • Presents the pioneering work of the late Professor Jacob (Jack) T. Schwartz

  • Introduces an unique system for automated proof verification in large-scale software systems

  • With a Foreword by Prof. Martin Davis of the Courant Institute of Mathematical Sciences, New York University

  • Includes supplementary material: sn.pub/extras

Buying options

eBook USD 69.99
Price excludes VAT (USA)
  • ISBN: 978-0-85729-808-9
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 89.95
Price excludes VAT (USA)
Hardcover Book USD 89.95
Price excludes VAT (USA)

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Table of contents (7 chapters)

  1. Front Matter

    Pages I-XVII
  2. Introduction

    • Jacob T. Schwartz, Domenico Cantone, Eugenio G. Omodeo
    Pages 1-35
  3. Propositional- and Predicate-Calculus Preliminaries

    • Jacob T. Schwartz, Domenico Cantone, Eugenio G. Omodeo
    Pages 37-91
  4. A Survey of Inference Mechanisms

    • Jacob T. Schwartz, Domenico Cantone, Eugenio G. Omodeo
    Pages 93-203
  5. More on the Structure of the Verifier System

    • Jacob T. Schwartz, Domenico Cantone, Eugenio G. Omodeo
    Pages 205-255
  6. A Closer Examination of the Sequence of Definitions and Theorems Presented in this Book

    • Jacob T. Schwartz, Domenico Cantone, Eugenio G. Omodeo
    Pages 257-311
  7. Undecidability and Unsolvability

    • Jacob T. Schwartz, Domenico Cantone, Eugenio G. Omodeo
    Pages 313-371
  8. A Self-contained Beginning for Ref’s Main Proof Scenario

    • Jacob T. Schwartz, Domenico Cantone, Eugenio G. Omodeo
    Pages 373-409
  9. Back Matter

    Pages 411-416

About this book

As computer software becomes more complex, the question of how its correctness can be assured grows ever more critical. Formal logic embodied in computer programs is an important part of the answer to this problem.

This must-read text presents the pioneering work of the late Professor Jacob (Jack) T. Schwartz on computational logic and set theory and its application to proof verification techniques, culminating in the ÆtnaNova system, a prototype computer program designed to verify the correctness of mathematical proofs presented in the language of set theory. Taking a systematic approach, the book begins with a survey of traditional branches of logic before describing in detail the underlying design of the ÆtnaNova system. Major classical results on undecidability and unsolvability are then recast for this system. Readers do not require great knowledge of formal logic in order to follow the text, but a good understanding of standard programming techniques, and a familiarity with mathematical definitions and proofs reflecting the usual levels of rigor is assumed.

Topics and features:

  • With a Foreword by Dr. Martin Davis, Professor Emeritus of the Courant Institute of Mathematical Sciences, New York University
  • Describes in depth how a specific first-order theory can be exploited to model and carry out reasoning in branches of computer science and mathematics
  • Presents an unique system for automated proof verification on the large scale
  • Integrates important proof-engineering issues, reflecting the goals of large-scale verifiers
  • Includes an appendix showing formalized proofs of ordinals, of various properties of the transitive closure operation, of finite and transfinite induction principles, and of Zorn’s lemma

This ground-breaking work is essential reading for researchers and advanced graduates of computer science.

Keywords

  • Automated Reasoning
  • Computer Systems
  • Program Verification Methods
  • Programming Logic

Reviews

From the book reviews:

“This is a text defining new formulae, theorems, lemmas, and sublanguages. Partition calculus and subset theory is well developed. … I recommend this book to all students and logicians.” (Joseph J. Grenier, Amazon.com, August, 2014)

“The contents of the book makes it inspiring and interesting both to mathematicians and to computer scientists. … This is one of a few recent books which promise to both make mathematicians aware of the possibilities opened by the recent progress in automated theorem proving and draw the attention of the researchers working in logic and automated theorem proving to the challenges and possibilities raised by interesting problems in mathematics.” (Viorica Sofronie-Stokkermans, Zentralblatt MATH, Vol. 1246, 2012)

Authors and Affiliations

  • New York University, New York, USA

    Jacob T. Schwartz

  • Dept. of Mathematics & Computer Science, University of Catania, Catania, Italy

    Domenico Cantone

  • Dept. of Mathematics & Computer Science, University of Trieste, Trieste, Italy

    Eugenio G. Omodeo

Bibliographic Information

  • Book Title: Computational Logic and Set Theory

  • Book Subtitle: Applying Formalized Logic to Analysis

  • Authors: Jacob T. Schwartz, Domenico Cantone, Eugenio G. Omodeo

  • DOI: https://doi.org/10.1007/978-0-85729-808-9

  • Publisher: Springer London

  • eBook Packages: Computer Science, Computer Science (R0)

  • Copyright Information: Springer-Verlag London Limited 2011

  • Hardcover ISBN: 978-0-85729-807-2

  • Softcover ISBN: 978-1-4471-6018-2

  • eBook ISBN: 978-0-85729-808-9

  • Edition Number: 1

  • Number of Pages: XVII, 416

  • Topics: Computer Science, Theory of Computation, Formal Languages and Automata Theory

Buying options

eBook USD 69.99
Price excludes VAT (USA)
  • ISBN: 978-0-85729-808-9
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 89.95
Price excludes VAT (USA)
Hardcover Book USD 89.95
Price excludes VAT (USA)