Introduction to Higher-Order Categorical Logic: 7 (Cambridge Studies in Advanced Mathematics, Series Number 7) - Softcover

J. Lambek , P. J. Scott

Softcover

ISBN 10: 0521356539 ISBN 13: 9780521356534

Publisher: Cambridge University Press, 1988

Synopsis

In this book the authors reconcile two different viewpoints of the foundations of mathematics, namely mathematical logic and category theory. In Part I, they show that typed lambda-calculi, a formulation of higher order logic, and cartesian closed categories are essentially the same. In Part II, it is demonstrated that another formulation of higher order logic (intuitionistic type theories) is closely related to topos theory. Part III is devoted to recursive functions. Numerous applications of the close relationship between traditional logic and the algebraic language of category theory are given. The authors have included an introduction to category theory and develop the necessary logic as required, making the book essentially self-contained. Detailed historical references are provided throughout, and each section concludes with a set of exercises. Thus it is well-suited for graduate courses and research in mathematics and logic. Researchers in theoretical computer science, artificial intelligence and mathematical linguistics will also find this an accessible introduction to a subject of increasing application to these disciplines.

About this title

Review

'A readable and timely account of important results, most of which were not previously available in book form.' Bulletin of the London Mathematical Society

Book Description

In this book the authors reconcile two different viewpoints of the foundations of mathematics, namely mathematical logic and category theory. Numerous applications of the close relationship between traditional logic and the algebraic language of category theory are given. Detailed references are provided and each section concludes with exercises.

Edition details

• Publisher: Cambridge University Press
• Publication date: 1988
• Language: English
• ISBN 10: 0521356539
• ISBN 13: 9780521356534
• Binding: Paperback
• Number of pages: 304