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Lecture Notes in Logic, 23
Logicism Renewed, Logical Foundations for Mathematics and Computer Science

Paul C. Gilmore

 

Logicism, as put forward by Bertrand Russell, was predicated on a belief that all of mathematics can be deduced from a very small number of fundamental logical principles. In Logicism Renewed, the author revisits this concept in light of advances in mathematical logic and the need for languages that can be understood by both humans and computers that require distinguishing between the intension and extension of predicates.

Using Intensional Type Theory (ITT) the author provides a unified foundation for mathematics and computer science, yielding a much simpler foundation for recursion theory and the semantics of computer programs than that currently provided by category theory.

Year: 2005
Price:$39.00
ISBN: 1-56881-276-0
250 pages. Paperback.
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Year: 2005
Price:$69.00 ISBN:1-56881-275-2
250 pages. Hardcover.

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Table of Contents

Preface

Chapter 1. - Elementary Logic
Chapter 2. - Type Theory
Chapter 3. - An Intensional Type Theory
Chapter 4. - Recursions
Chapter 5. - Choice and Function Terms
Chapter 6. - Intuitionist Logic
Chapter 7. - Logic and Mathematics
Chapter 8. - Logic and Computer Science


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