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Computational Logic and Set Theory

Applying Formalized Logic to Analysis

  • Textbook
  • © 2011

Overview

Authors:
  1. Jacob T. Schwartz

    1. New York University, New York, USA

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  2. Domenico Cantone

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

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  3. Eugenio G. Omodeo

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

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  • 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

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Table of contents (7 chapters)

  1. Front Matter

    Pages I-XVII
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  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
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Keywords

About this book

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. Topics and features: 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 in large-scale software systems; 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.

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: 978-0-85729-807-2Published: 16 July 2011

  • Softcover ISBN: 978-1-4471-6018-2Published: 06 September 2014

  • eBook ISBN: 978-0-85729-808-9Published: 16 July 2011

  • Edition Number: 1

  • Number of Pages: XVII, 416

  • Topics: Computer Science, general, Computation by Abstract Devices, Mathematical Logic and Formal Languages

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