Gilmore Logicism Renewed

Logical Foundations for Mathematics and Computer Science
Erscheinungsjahr 2020
ISBN: 978-1-108-67693-9
Verlag: Cambridge University Press
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, Band 23, 0 Seiten

Reihe: Lecture Notes in Logic

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. 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 this volume, the twenty-third publication in the Lecture Notes in Logic series, Paul C. Gilmore revisits logicism in light of recent advances in mathematical logic and theoretical computer science. Gilmore addresses the need for languages which can be understood by both humans and computers and, using Intensional Type Theory (ITT), provides a unified basis for mathematics and computer science. This yields much simpler foundations for recursion theory and the semantics of computer programs than those currently provided by category theory.

Autoren/Hrsg.

Gilmore, Paul C.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Philosophie der Mathematik
• Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik
• Geisteswissenschaften Philosophie Philosophie der Mathematik, Philosophie der Physik
• Geisteswissenschaften Philosophie Philosophische Logik, Argumentationstheorie
• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker

Inhaltsverzeichnis

Preface; 1. Elementary logic; 2. Type theory; 3. An intensional type theory; 4. Recursions; 5. choice and function terms; 6. Intuitionist logic; 7. Logic and mathematics; 8. Logic and computer science.

Über Autor(innen)

Gilmore, Paul C.
Paul C. Gilmore is Professor Emeritus in the Computer Science Department at the University of British Columbia, Vancouver. His research interests include logical foundations of mathematics and computer science, applications of logic in computer science, and databases.