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Higher-Order Logic and Type Theory

Higher-Order Logic and Type Theory - Cambridge Elements. Elements in Philosophy and Logic

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Publisher's Synopsis

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.

About the Publisher

Cambridge University Press

Cambridge University Press dates from 1534 and is part of the University of Cambridge. We further the University's mission by disseminating knowledge in the pursuit of education, learning and research at the highest international levels of excellence.

Book information

ISBN: 9781108986908
Publisher: Cambridge University Press
Imprint: Cambridge University Press
Pub date:
DEWEY: 511.3
DEWEY edition: 23
Language: English
Number of pages: 79
Weight: 148g
Height: 152mm
Width: 228mm
Spine width: 8mm