Logicism Renewed: Logical Foundations for Mathematics and Computer Science (Lecture Notes in Logic #23)...

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Paul C. Gilmore

Logicism Renewed

Logical Foundations for Mathematics and Computer Science (Lecture Notes in Logic #23)

Paul C. Gilmore

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English

A K Peters
18 November 2005

Mathematical logic

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.

By: Paul C. Gilmore
Imprint: A K Peters
Country of Publication: United States
Volume: 23
Dimensions: Height: 229mm, Width: 152mm,
Weight: 498g
ISBN: 9781568812755
ISBN 10: 1568812752
Pages: 252
Publication Date: 18 November 2005
Audience: College/higher education , Professional and scholarly , Further / Higher Education , Undergraduate
Format: Hardback
Publisher's Status: Active

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, References, Index

Paul Gilmore is professor emeritus in the Computer Science department at the University of British Columbia. His research interests include Logical Foundations of Mathematics and Computer Science, Applications of Logic in Computer Science, and Databases.