Computational Logic and Set Theory

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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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.

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

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)

• 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

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