Higher-Order Logic and Type Theory by John L Bell

Higher-Order Logic and Type Theory by John L Bell

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.

SKU	Unavailable
ISBN 13	9781108986908
ISBN 10	1108986900
Title	Higher-Order Logic and Type Theory
Author	John L Bell
Series	Elements In Philosophy And Logic
Condition	Unavailable
Binding Type	Paperback
Publisher	Cambridge University Press
Year published	2022-03-31
Number of pages	75
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.