Computational Logic and Set Theory

Applying Formalized Logic to Analysis

By Jacob T. Schwartz , Domenico Cantone , Eugenio G. Omodeo , Martin Davis

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This must-read text presents the late Professor Jacob T. Schwartz's work on computational logic and set theory and its application to proof verification techniques. Covers the ÆtnaNova system, a program built to verify the correctness of mathematical proofs.

Full Description

  • ISBN13: 978-0-8572-9807-2
  • 433 Pages
  • User Level: Students
  • Publication Date: July 16, 2011
  • Available eBook Formats: PDF
  • eBook Price: $89.95
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Full Description
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.
Table of Contents

Table of Contents

  1. Introduction.
  2. Propositional and Predicate
  3. Calculus Preliminaries.
  4. A Survey of Inference Mechanisms.
  5. More on the Structure of the Verifier System.
  6. A Closer Examination of the Sequence of Definitions and Theorems Presented in this Book.
  7. Undecidability and Unsolvability.
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