Description
| Product ID: | 9781108986908 |
| Product Form: | Paperback / softback |
| Country of Manufacture: | GB |
| Series: | Elements in Philosophy and Logic |
| Title: | Higher-Order Logic and Type Theory |
| Authors: | Author: John L. Bell |
| Page Count: | 75 |
| Subjects: | Philosophy, Philosophy, Philosophy: logic, Set theory, Philosophy: logic, Set theory |
| Description: | 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. |
| Imprint Name: | Cambridge University Press |
| Publisher Name: | Cambridge University Press |
| Country of Publication: | GB |
| Publishing Date: | 2022-03-31 |
