Wow! eBook
Higher-Order Logic and Type Theory New Edition
Author(s): John L. Bell (Author)
- Publisher: Cambridge University Press
- Publication Date: March 31, 2022
- Edition: New
- Language: English
- Print length: 88 pages
- ISBN-10: 1108986900
- ISBN-13: 9781108986908
Book Description
This Element is an exposition of second- and higher-order logic and type theory. It begins with a presentation of the syntax and semantics of classical second-order logic, pointing up the contrasts with first-order logic. This leads to a discussion of higher-order logic based on the concept of a type. The second Section contains an account of the origins and nature of type theory, and its relationship to set theory. Section 3 introduces Local Set Theory (also known as higher-order intuitionistic logic), an important form of type theory based on intuitionistic logic. In Section 4 number of contemporary forms of type theory are described, all of which are based on the so-called ‘doctrine of propositions as types’. We conclude with an Appendix in which the semantics for Local Set Theory – based on category theory – is outlined.
Editorial Reviews
Book Description
The Element provides a wide-ranging, but unified account of higher-order logic and contemporary type theory.
