{"id":"https://openalex.org/W2143121603","doi":"https://doi.org/10.2307/2274910","title":"Normalization theorems for full first order classical natural deduction","display_name":"Normalization theorems for full first order classical natural deduction","publication_year":1991,"publication_date":"1991-03-01","ids":{"openalex":"https://openalex.org/W2143121603","doi":"https://doi.org/10.2307/2274910","mag":"2143121603"},"language":"en","primary_location":{"id":"doi:10.2307/2274910","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2274910","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/A5069086225","display_name":"Gunnar St\u00e5lmarck","orcid":null},"institutions":[{"id":"https://openalex.org/I161593684","display_name":"Stockholm University","ror":"https://ror.org/05f0yaq80","country_code":"SE","type":"education","lineage":["https://openalex.org/I161593684"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"Gunnar St\u00e5lmarck","raw_affiliation_strings":["Department of Philosophy, University of Stockholm, Stockholm, Sweden","University of Stockholm"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Philosophy, University of Stockholm, Stockholm, Sweden","institution_ids":["https://openalex.org/I161593684"]},{"raw_affiliation_string":"University of Stockholm","institution_ids":["https://openalex.org/I161593684"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5069086225"],"corresponding_institution_ids":["https://openalex.org/I161593684"],"apc_list":null,"apc_paid":null,"fwci":0.5395,"has_fulltext":false,"cited_by_count":77,"citation_normalized_percentile":{"value":0.75646697,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"56","issue":"1","first_page":"129","last_page":"149"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9988999962806702,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/normalization","display_name":"Normalization (sociology)","score":0.8111052513122559},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.6104196310043335},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5711427927017212},{"id":"https://openalex.org/keywords/first-order-logic","display_name":"First-order logic","score":0.525770902633667},{"id":"https://openalex.org/keywords/natural-deduction","display_name":"Natural deduction","score":0.5038051009178162},{"id":"https://openalex.org/keywords/automated-theorem-proving","display_name":"Automated theorem proving","score":0.467172235250473},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44858691096305847},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.42651355266571045},{"id":"https://openalex.org/keywords/first-order","display_name":"First order","score":0.4169132709503174},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3290979266166687},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.15775570273399353},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.10080555081367493}],"concepts":[{"id":"https://openalex.org/C136886441","wikidata":"https://www.wikidata.org/wiki/Q926129","display_name":"Normalization (sociology)","level":2,"score":0.8111052513122559},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.6104196310043335},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5711427927017212},{"id":"https://openalex.org/C100481476","wikidata":"https://www.wikidata.org/wiki/Q4055684","display_name":"First-order logic","level":2,"score":0.525770902633667},{"id":"https://openalex.org/C62073222","wikidata":"https://www.wikidata.org/wiki/Q1572108","display_name":"Natural deduction","level":2,"score":0.5038051009178162},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.467172235250473},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44858691096305847},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.42651355266571045},{"id":"https://openalex.org/C2987642246","wikidata":"https://www.wikidata.org/wiki/Q5452196","display_name":"First order","level":2,"score":0.4169132709503174},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3290979266166687},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.15775570273399353},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.10080555081367493},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"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/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C19165224","wikidata":"https://www.wikidata.org/wiki/Q23404","display_name":"Anthropology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2274910","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2274910","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/1183743557","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183743557","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W566558991","https://openalex.org/W1557413548","https://openalex.org/W2054162580","https://openalex.org/W2085516474","https://openalex.org/W2744169538"],"related_works":["https://openalex.org/W613892192","https://openalex.org/W179453746","https://openalex.org/W4390542336","https://openalex.org/W3100311625","https://openalex.org/W4232650499","https://openalex.org/W2155990634","https://openalex.org/W2162672092","https://openalex.org/W4232291640","https://openalex.org/W197813433","https://openalex.org/W1499822848"],"abstract_inverted_index":{"In":[0,222],"this":[1,151],"paper":[2,152],"we":[3],"prove":[4,184],"the":[5,18,35,43,58,74,111,130,137,145,168,185,203,225,231,246,258,266,271,281,285,288,295,301,305],"strong":[6,99,146,186,267],"normalization":[7,41,100,117,147,187,268,302],"theorem":[8,38,47,101,114,118,132,148,188,269,303],"for":[9,42,77,90,96,133,136,189,270,290,304],"full":[10,68,204,306],"first":[11,61,69,194,275],"order":[12,70,92,195,276],"classical":[13,71,196,277],"N.D.":[14,72,226,278],"(natural":[15],"deduction)\u2014full":[16],"in":[17,57,64,87,120,150,167,230,294],"sense":[19,232],"that":[20,157,233],"all":[21,165],"logical":[22,242,260],"constants":[23],"are":[24,237],"taken":[25],"as":[26,123,240],"primitive.":[27],"We":[28],"also":[29],"give":[30],"a":[31,88,98,127,158,190],"syntactic":[32],"proof":[33,62,109,128,143],"of":[34,110,126,129,144,161,193,274,287],"normal":[36,112],"form":[37,113],"and":[39,53,79,115,198,219,235,244,292],"(weak)":[40,116],"same":[44,131],"system.":[45,205,307],"The":[46,60,142,171],"has":[48],"been":[49,211],"stated":[50],"several":[51],"times,":[52],"some":[54],"proofs":[55],"appear":[56],"literature.":[59],"occurs":[63,119],"Statman":[65],"[1],":[66],"where":[67,179],"(with":[73],"elimination":[75],"rules":[76,289],"\u2228":[78,234,291],"\u2203":[80,236,293],"restricted":[81,191,229,272,296],"to":[82,164,183,201,208,252,257],"atomic":[83],"conclusions)":[84],"is":[85,102,153,174,181,199,228],"embedded":[86],"system":[89,169,227,297],"second":[91],"(propositional)":[93],"intuitionistic":[94],"N.D.,":[95,197],"which":[97],"proved":[103],"using":[104],"strongly":[105],"impredicative":[106],"methods.":[107],"A":[108],"Seldin":[121],"[1]":[122],"an":[124,134],"extension":[125],"N.D.-system":[135],"intermediate":[138],"logic":[139],"called":[140],"MH.":[141],"presented":[149],"obtained":[154],"by":[155,214],"proving":[156],"certain":[159],"kind":[160],"validity":[162],"applies":[163],"derivations":[166],"considered.":[170],"notion":[172],"\u201cvalidity\u201d":[173,209],"adopted":[175],"from":[176],"Prawitz":[177,223],"[2],":[178],"it":[180,264],"used":[182,212],"version":[192,273],"extended":[200],"cover":[202],"Notions":[206],"similar":[207],"have":[210],"earlier":[213],"Tait":[215],"(convertability),":[216],"Girard":[217],"(r\u00e9ducibilit\u00e9)":[218],"Martin-L\u00f6f":[220],"(computability).":[221],"[2]":[224],"not":[238,299],"treated":[239],"primitive":[241],"constants,":[243],"hence":[245],"deductions":[247],"can":[248],"only":[249],"be":[250,253],"seen":[251],"\u201cnatural\u201d":[254],"with":[255,280],"respect":[256],"other":[259],"constants.":[261],"To":[262],"spell":[263],"out,":[265],"together":[279],"well-known":[282],"results":[283],"on":[284],"definability":[286],"does":[298],"imply":[300]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":20},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":5}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
