Higher-Order Logic and Type Theory
Seiten
2022
Cambridge University Press (Verlag)
978-1-108-98690-8 (ISBN)
Cambridge University Press (Verlag)
978-1-108-98690-8 (ISBN)
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.
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.
1. Second- Order Logic and Higher-Order Logic; 2. Type Theory and its Origins; 3. Local set theory; 4. Newer Forms of Type Theory Based on the Doctrine of 'Propositions as Types'; Appendix; The Semantics of Local Set Theory/Intuitionistic Higher-Order Logic.
| Erscheinungsdatum | 21.03.2022 |
|---|---|
| Reihe/Serie | Elements in Philosophy and Logic |
| Zusatzinfo | Worked examples or Exercises |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 152 x 228 mm |
| Gewicht | 140 g |
| Themenwelt | Geisteswissenschaften ► Philosophie ► Logik |
| Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre | |
| ISBN-10 | 1-108-98690-0 / 1108986900 |
| ISBN-13 | 978-1-108-98690-8 / 9781108986908 |
| Zustand | Neuware |
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