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02001aam a2200325 i 4500 001 8A485C2272D911EDA0B05B7C49ECA4DB 003 SILO 005 20221203010154 008 220119t20222022enka b 000 0 eng d 020 $a 1108986900 020 $a 9781108986908 035 $a (OCoLC)1292591483 040 $a YDX $b eng $e rda $c YDX $d UKMGB $d OCLCO $d OCLCF $d TJC $d YDX $d SILO 050 4 $a QA9 B45 2022 100 1 $a Bell, J. L. $q (John Lane), $e author. 245 10 $a Higher-order logic and type theory / $c John L. Bell. 264 1 $a Cambridge : $b Cambridge University Press, $c 2022. 300 $a 79 pages : $b illustrations ; $c 23 cm. 490 1 $a Cambridge elements. Elements in philosophy and logic. 520 $a 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. 504 $a Includes bibliographical references (pages 75-79) 650 0 $a Logic, Symbolic and mathematical. 650 0 $a Type theory. 650 0 $a Set theory. 776 08 $i ebook version : $z 9781108981804 830 0 $a Cambridge elements. $p Elements in philosophy and logic. 941 $a 1 952 $l USUX851 $d 20240403014014.0 956 $a http://locator.silo.lib.ia.us/search.cgi?index_0=id&term_0=8A485C2272D911EDA0B05B7C49ECA4DB 994 $a C0 $b IWAInitiate Another SILO Locator Search