TY - BOOK ID - 101210628 TI - Higher-order logic and type theory PY - 2022 SN - 1108981801 1108986900 1108991955 PB - Cambridge : Cambridge University Press, DB - UniCat KW - Logic, Symbolic and mathematical. KW - Type theory. KW - Set theory. KW - Logic, Symbolic and mathematical KW - Mathematics KW - Algebra, Abstract KW - Metamathematics KW - Set theory KW - Syllogism KW - Algebra of logic KW - Logic, Universal KW - Mathematical logic KW - Symbolic and mathematical logic KW - Symbolic logic KW - Aggregates KW - Classes (Mathematics) KW - Ensembles (Mathematics) KW - Mathematical sets KW - Sets (Mathematics) KW - Theory of sets UR - https://www.unicat.be/uniCat?func=search&query=sysid:101210628 AB - 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. ER -