Higher-Order Logic and Type Theory

John L. Bell (University of Western Ontario)

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English

Cambridge University Press
31 March 2022

Philosophy; Philosophy: logic; Set theory

Series: 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.

By: John L. Bell (University of Western Ontario)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Edition: New edition
Dimensions: Height: 228mm, Width: 152mm, Spine: 5mm
Weight: 140g
ISBN: 9781108986908
ISBN 10: 1108986900
Series: Elements in Philosophy and Logic
Pages: 75
Publication Date: 31 March 2022
Audience: General/trade , ELT Advanced
Format: Paperback
Publisher's Status: Active

1. Second- Order Logic and Higher-Order Logic; 2. Type Theory and its Origins; 3. Local set theory; 4. Newer Forms of Type Theory Based on the Doctrine of 'Propositions as Types'; Appendix; The Semantics of Local Set Theory/Intuitionistic Higher-Order Logic.