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.

The Element provides a wide-ranging, but unified account of higher-order logic and contemporary type theory.

Book Information
ISBN 9781108986908
Author John L. Bell
Format Paperback
Page Count 75
Imprint Cambridge University Press
Publisher Cambridge University Press
Weight(grams) 140g
Dimensions(mm) 228mm * 152mm * 5mm