Description: 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 Detailed historical references are provided throughout, and each section concludes with a set of exercises.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.
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EAN: 9780521356534
UPC: 9780521356534
ISBN: 9780521356534
MPN: N/A
Item Length: 23.4 cm
Book Title: Introduction to Higher-Order Categorical Logic
Item Height: 234mm
Item Width: 155mm
Author: J. Lambek, P. J. Scott
Format: Paperback
Language: English
Topic: Popular Philosophy, Mathematics
Publisher: Cambridge University Press
Publication Year: 1988
Type: Textbook
Item Weight: 450 g
Number of Pages: 304 Pages
