Higher-Order Logic and Type Theory

By: John L. Bell

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Paperback | 31 March 2022

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88 Pages

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New edition

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15.2 x 22.8 x 0.8

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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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