Higher-order logic and type theory / John L. Bell.

Format:

• Book

Author/Creator:

• Bell, J. L. (John Lane), author.

Series:

• Cambridge elements. Elements in philosophy and logic 2516-418X

Language:

English

Subjects (All):

• Logic, Symbolic and mathematical.
• Type theory.
• Set theory.

Physical Description:

1 online resource (79 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 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.

Notes:

Title from publisher's bibliographic system (viewed on 21 Mar 2022).

Other Format:

Print version:

ISBN:

9781108981804 (ebook)

Access Restriction:

Restricted for use by site license.