Higher-Order Logic and Type Theory
Published on 16. March 2022
978-1-108-99195-7 (ISBN)
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.
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Series
Language
English
Place of publication
Cambridge
United Kingdom
Illustrations
Worked examples or Exercises
File size
1,90 MB
ISBN-13
978-1-108-99195-7 (9781108991957)
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Other editions
Additional editions
John L. Bell
Higher-Order Logic and Type Theory
Book
03/2022
Cambridge University Press
€26.70
Shipment within 15-20 days
Person
Content
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.
