Higher-Order Logic and Type Theory

This Element covers second- and higher-order logic and type theory, discussing classical second-order logic, higher-order logic based on types, Local Set Theory, and contemporary forms of type theory. It concludes with an Appendix outlining the semantics for Local Set Theory.

Format: Paperback / softback
Length: 75 pages
Publication date: 31 March 2022
Publisher: Cambridge University Press

This Element is a comprehensive exposition of second- and higher-order logic and type theory. It begins with a detailed presentation of the syntax and semantics of classical second-order logic, highlighting the contrasts with first-order logic. This foundation is then built upon to explore higher-order logic, which is based on the concept of types.

The second section delves into the origins and nature of type theory, exploring its relationship to set theory. In Section 3, Local Set Theory (also known as higher-order intuitionistic logic) is introduced, an important form of type theory rooted in intuitionistic logic.

Section 4 presents a range of contemporary forms of type theory, all of which are based on the doctrine of propositions as types. These forms encompass various approaches, including category theory, homotopy type theory, and dependent type theory.

To conclude, an Appendix outlines the semantics for Local Set Theory, which is based on category theory. This appendix provides a deeper understanding of the theoretical foundations and applications of type theory in computer science and mathematics.

Overall, this Element offers a thorough and accessible introduction to second- and higher-order logic and type theory, providing students and researchers with the necessary tools to explore these complex areas of mathematics and computer science.

Weight: 142g
Dimension: 152 x 228 x 8 (mm)
ISBN-13: 9781108986908
Edition number: New ed