Element contents
Series: Elements in Philosophy and Logic
Higher-Order Logic and Type Theory
Published online by Cambridge University Press: 10 March 2022
Summary
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.
Keywords
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- Type
- Element
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- Series: Elements in Philosophy and LogicOnline ISBN: 9781108981804Publisher: Cambridge University PressPrint publication: 31 March 2022
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