{"id":"https://openalex.org/W2092575189","doi":"https://doi.org/10.2307/2267329","title":"Practical forms of type theory","display_name":"Practical forms of type theory","publication_year":1948,"publication_date":"1948-06-09","ids":{"openalex":"https://openalex.org/W2092575189","doi":"https://doi.org/10.2307/2267329","mag":"2092575189"},"language":"en","primary_location":{"id":"doi:10.2307/2267329","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2267329","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066565862","display_name":"Alan Turing","orcid":null},"institutions":[{"id":"https://openalex.org/I134421475","display_name":"National Physical Laboratory","ror":"https://ror.org/015w2mp89","country_code":"GB","type":"facility","lineage":["https://openalex.org/I134421475"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"A. M. Turing","raw_affiliation_strings":["National Physical Laboratory, Teddington","NATIONAL PHYSICAL LABORATORY"],"affiliations":[{"raw_affiliation_string":"National Physical Laboratory, Teddington","institution_ids":["https://openalex.org/I134421475"]},{"raw_affiliation_string":"NATIONAL PHYSICAL LABORATORY","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5066565862"],"corresponding_institution_ids":["https://openalex.org/I134421475"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.0489463,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"13","issue":"2","first_page":"80","last_page":"94"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9919999837875366,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10258","display_name":"Philosophy and Theoretical Science","score":0.980400025844574,"subfield":{"id":"https://openalex.org/subfields/3205","display_name":"Experimental and Cognitive Psychology"},"field":{"id":"https://openalex.org/fields/32","display_name":"Psychology"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.831270158290863},{"id":"https://openalex.org/keywords/type-theory","display_name":"Type theory","score":0.7644885182380676},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.7568972110748291},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.619055986404419},{"id":"https://openalex.org/keywords/argument","display_name":"Argument (complex analysis)","score":0.5699124932289124},{"id":"https://openalex.org/keywords/logical-framework","display_name":"Logical framework","score":0.5661473870277405},{"id":"https://openalex.org/keywords/foundation","display_name":"Foundation (evidence)","score":0.5305566787719727},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5161439180374146},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.4592980444431305},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.45740652084350586},{"id":"https://openalex.org/keywords/doctrine","display_name":"Doctrine","score":0.41922739148139954},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3800315856933594},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.27828747034072876},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.199383944272995},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.10896289348602295}],"concepts":[{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.831270158290863},{"id":"https://openalex.org/C93682546","wikidata":"https://www.wikidata.org/wiki/Q1056428","display_name":"Type theory","level":3,"score":0.7644885182380676},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.7568972110748291},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.619055986404419},{"id":"https://openalex.org/C98184364","wikidata":"https://www.wikidata.org/wiki/Q1780131","display_name":"Argument (complex analysis)","level":2,"score":0.5699124932289124},{"id":"https://openalex.org/C20693621","wikidata":"https://www.wikidata.org/wiki/Q6667502","display_name":"Logical framework","level":2,"score":0.5661473870277405},{"id":"https://openalex.org/C2780966255","wikidata":"https://www.wikidata.org/wiki/Q5474306","display_name":"Foundation (evidence)","level":2,"score":0.5305566787719727},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5161439180374146},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.4592980444431305},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.45740652084350586},{"id":"https://openalex.org/C2776211767","wikidata":"https://www.wikidata.org/wiki/Q117850","display_name":"Doctrine","level":2,"score":0.41922739148139954},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3800315856933594},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.27828747034072876},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.199383944272995},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.10896289348602295},{"id":"https://openalex.org/C27206212","wikidata":"https://www.wikidata.org/wiki/Q34178","display_name":"Theology","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2267329","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2267329","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1183410407","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183410407","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/4","display_name":"Quality Education","score":0.4099999964237213}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":3,"referenced_works":["https://openalex.org/W1996404651","https://openalex.org/W4251196936","https://openalex.org/W6649247312"],"related_works":["https://openalex.org/W1976278597","https://openalex.org/W2985557298","https://openalex.org/W2125274893","https://openalex.org/W1483170865","https://openalex.org/W3043607029","https://openalex.org/W1974190112","https://openalex.org/W2750688286","https://openalex.org/W3006935326","https://openalex.org/W3171769836","https://openalex.org/W4287126609"],"abstract_inverted_index":{"Russell's":[0],"theory":[1,30,80],"of":[2,18,31],"types,":[3],"though":[4],"probably":[5],"not":[6,90],"providing":[7],"the":[8,16,29,37,59,68],"soundest":[9],"possible":[10],"foundation":[11],"for":[12],"mathematics,":[13],"follows":[14],"closely":[15],"outlook":[17],"most":[19],"mathematicians.":[20],"The":[21],"present":[22,28],"paper":[23],"is":[24,65],"an":[25],"attempt":[26],"to":[27,77,93,99],"types":[32,38],"in":[33,35,49,71,81,86],"forms":[34],"which":[36],"themselves":[39],"only":[40],"play":[41],"a":[42,95],"rather":[43],"small":[44],"part,":[45],"as":[46,83,85],"they":[47],"do":[48,100],"ordinary":[50],"mathematical":[51],"argument.":[52],"Two":[53],"logical":[54,97],"systems":[55,73],"are":[56],"described":[57],"(called":[58],"\u201cnested-type\u201d":[60],"and":[61],"\u201cconcealed-type\u201d":[62],"systems).":[63],"It":[64,88],"hoped":[66],"that":[67],"ideas":[69],"involved":[70],"these":[72],"may":[74],"help":[75],"mathematicians":[76],"observe":[78],"type":[79],"proofs":[82],"well":[84],"doctrine.":[87],"will":[89],"be":[91],"necessary":[92],"adopt":[94],"formal":[96],"notation":[98],"so.":[101]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
