Introduction to Higher-Order Categorical Logic

J. Lambek, P. J. Scott

ISBN 10: 0521356539 / ISBN 13: 9780521356534

Published by Cambridge University Press, GB, 1988

About this Item

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 Detailed historical references are provided throughout, and each section concludes with a set of exercises.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.

Seller Inventory # LU-9780521356534

Bibliographic Details

• Title: Introduction to Higher-Order Categorical Logic
• Publisher: Cambridge University Press, GB
• Publication Date: 1988
• Language: English
• ISBN 10: 0521356539
• ISBN 13: 9780521356534
• Binding: Paperback
• Edition: Illustrated.
• Condition: New
• Dimensions: 15.88W x 1.91H x 22.86D centimeters 15.88 centimeters width by 1.91 centimeters height by 22.86 centimeters depth
• Weight: 500 grams

About this title

Synopsis

In this volume, Lambek and Scott 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. Part II demonstrates 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 concludeds with a set of exercises.

Book Description

Part I indicates that typed-calculi are a formulation of higher-order logic, and cartesian closed categories are essentially the same. Part II demonstrates that another formulation of higher-order logic is closely related to topos theory.