Higher-Order Logic and Type Theory (Elements in Philosophy and Logic)

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.

• | Author: John L. Bell
• | Publisher: Cambridge University Press
• | Publication Date: Mar 31, 2022
• | Number of Pages: 88 pages
• | Language: English
• | Binding: Paperback
• | ISBN-10: 1108986900
• | ISBN-13: 9781108986908