Higher-Order Logic and Type Theory
by
John L. Bell
Book Details
Format
Paperback / Softback
Book Series
Elements in Philosophy and Logic
ISBN-10
1108986900
ISBN-13
9781108986908
Publisher
Cambridge University Press
Imprint
Cambridge University Press
Country of Manufacture
GB
Country of Publication
GB
Publication Date
Mar 31st, 2022
Print length
75 Pages
Weight
148 grams
Dimensions
15.20 x 22.80 x 0.80 cms
Product Classification:
PhilosophyPhilosophy: logicSet theory
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An exposition of second- and higher-order logic and type theory. It includes the syntax and semantics of classical second-order logic and a discussion of higher-order logic based on the concept of a type. Also explored are origins and nature of type theory, its relationship to set theory, and descriptions of contemporary forms of type theory.
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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