000			a
999			_c32211 _d32211
008			231011b xxu||||| |||| 00| 0 eng d
020			_a9781108986908
082			_a511.3 _bBEL
100			_aBell, John L.
245			_aHigher-order logic and type theory
260			_bCambridge University Press, _c2022 _aCambridge :
300			_a79 p. ; _bill., _c23 cm
365			_b17.00 _cGBP _d109.80
490			_aCambridge elements. Elements in philosophy and logic
504			_aIncludes bibliographical references.
520			_aThis 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.
650			_aLogic
650			_aSymbolic and mathematical
650			_aSet theory
650			_aType theory
942			_2ddc _cBK