Higher-Order Logic And Type Theory
- Editore:
Cambridge University Press
- Collana:
- Elements In Philosophy And Logic
- EAN:
9781108986908
- ISBN:
1108986900
- Pagine:
- 75
- Formato:
- Paperback
- Lingua:
- Inglese
Descrizione Higher-Order Logic And 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.