{"id":"https://openalex.org/W2016129710","doi":"https://doi.org/10.1305/ndjfl/1093635158","title":"The completeness of provable realizability.","display_name":"The completeness of provable realizability.","publication_year":1989,"publication_date":"1989-06-01","ids":{"openalex":"https://openalex.org/W2016129710","doi":"https://doi.org/10.1305/ndjfl/1093635158","mag":"2016129710"},"language":"en","primary_location":{"id":"doi:10.1305/ndjfl/1093635158","is_oa":false,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093635158","pdf_url":null,"source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal 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/A5055210751","display_name":"G. E. Mints","orcid":"https://orcid.org/0000-0002-3013-2608"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"G. E. Mints","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5055210751"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9636,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.79867074,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"30","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.987500011920929,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.987500011920929,"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/T10215","display_name":"Semantic Web and Ontologies","score":0.9733999967575073,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9682000279426575,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/realizability","display_name":"Realizability","score":0.6928311586380005},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6664547920227051},{"id":"https://openalex.org/keywords/predicate","display_name":"Predicate (mathematical logic)","score":0.627371072769165},{"id":"https://openalex.org/keywords/conjunction","display_name":"Conjunction (astronomy)","score":0.5897922515869141},{"id":"https://openalex.org/keywords/completeness","display_name":"Completeness (order theory)","score":0.5876787900924683},{"id":"https://openalex.org/keywords/propositional-calculus","display_name":"Propositional calculus","score":0.5439131855964661},{"id":"https://openalex.org/keywords/intuitionistic-logic","display_name":"Intuitionistic logic","score":0.5302029848098755},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4648076295852661},{"id":"https://openalex.org/keywords/predicate-variable","display_name":"Predicate variable","score":0.42608416080474854},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.41051095724105835},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.40432482957839966},{"id":"https://openalex.org/keywords/zeroth-order-logic","display_name":"Zeroth-order logic","score":0.2893950343132019},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17659059166908264},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.15511858463287354},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.13546264171600342},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.058978915214538574}],"concepts":[{"id":"https://openalex.org/C2776378722","wikidata":"https://www.wikidata.org/wiki/Q3454417","display_name":"Realizability","level":2,"score":0.6928311586380005},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6664547920227051},{"id":"https://openalex.org/C140146324","wikidata":"https://www.wikidata.org/wiki/Q1144319","display_name":"Predicate (mathematical logic)","level":2,"score":0.627371072769165},{"id":"https://openalex.org/C59656382","wikidata":"https://www.wikidata.org/wiki/Q191536","display_name":"Conjunction (astronomy)","level":2,"score":0.5897922515869141},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.5876787900924683},{"id":"https://openalex.org/C69562738","wikidata":"https://www.wikidata.org/wiki/Q200694","display_name":"Propositional calculus","level":2,"score":0.5439131855964661},{"id":"https://openalex.org/C178421362","wikidata":"https://www.wikidata.org/wiki/Q176786","display_name":"Intuitionistic logic","level":3,"score":0.5302029848098755},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4648076295852661},{"id":"https://openalex.org/C73314972","wikidata":"https://www.wikidata.org/wiki/Q10531432","display_name":"Predicate variable","level":5,"score":0.42608416080474854},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.41051095724105835},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.40432482957839966},{"id":"https://openalex.org/C110039528","wikidata":"https://www.wikidata.org/wiki/Q8069651","display_name":"Zeroth-order logic","level":4,"score":0.2893950343132019},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17659059166908264},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.15511858463287354},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.13546264171600342},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.058978915214538574},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C203659156","wikidata":"https://www.wikidata.org/wiki/Q6934805","display_name":"Multimodal logic","level":3,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1305/ndjfl/1093635158","is_oa":false,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093635158","pdf_url":null,"source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.ndjfl/1093635158","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.ndjfl/1093635158","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":[{"score":0.49000000953674316,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W1483568252","https://openalex.org/W1838665644","https://openalex.org/W2009862785","https://openalex.org/W2051685387","https://openalex.org/W2313175711"],"related_works":["https://openalex.org/W206382595","https://openalex.org/W2010884894","https://openalex.org/W2092876471","https://openalex.org/W4313156797","https://openalex.org/W1555566156","https://openalex.org/W4253721198","https://openalex.org/W1571826459","https://openalex.org/W2140640825","https://openalex.org/W2051829567","https://openalex.org/W4236400184"],"abstract_inverted_index":{"Let":[0],"A":[1,8,39,43,132,158,221],"be":[2,64,75,111],"a":[3,30,205],"propositional":[4,136,235],"formula":[5,131,156,175,195,219,256],"and":[6,49,96,102,124,143,223,242],"r":[7,26,157,220],"[x]":[9],"express":[10],"in":[11,44,100,121,133,161,184,238,252,273],"the":[12,15,22,35,41,45,54,78,87,127,130,134,151,155,162,165,168,174,186,190,193,214,218,224,227,234,249,255,268,274],"predicate":[13,166],"logic":[14],"statement":[16,225],"\"x":[17],"realizes":[18,173],"A\".We":[19],"prove":[20],"that":[21,126],"classical":[23,152],"derivability":[24,37],"of":[25,38,105,113,116,129,154,164,179,217,226],"\u0386":[27],"[t]":[28,222],"for":[29,40,240],"lambda":[31],"term":[32,269],"t":[33,172],"implies":[34],"intuitionistic":[36,135],"formulas":[42],"languges":[46],"(D,\u039b,":[47],"-I)":[48],"(D,&),":[50],"where":[51],"&":[52,146,210,263],"is":[53,84,92,200,211,245,265],"so-called":[55],"strong":[56,144,243],"conjunction.Intuitionistic":[57],"logical":[58],"connectives":[59],"are":[60,229],"often":[61],"supposed":[62],"to":[63,94,248],"determined":[65,76,212],"by":[66,197,204,213,267],"semantical":[67],"constructions.For":[68],"every":[69],"such":[70],"(binary)":[71],"connective":[72,188],"Cit":[73],"should":[74],"how":[77],"construction":[79],"proving":[80],"(or":[81],"justifying)":[82],"C(A,B)":[83],"composed":[85],"from":[86,232],"ones":[88],"justifying":[89],"A,B.This":[90],"approach":[91],"traceable":[93],"Brouwer":[95],"was":[97],"clearly":[98],"formulated":[99,237],"[2]":[101],"[6].Various":[103],"notions":[104],"realizability":[106],"beginning":[107],"with":[108,138,150],"[4]":[109],"can":[110],"thought":[112],"as":[114],"formalizations":[115],"these":[117],"ideas.We":[118],"follow":[119],"[7]":[120,239],"formalizing":[122],"further":[123],"show":[125],"provability":[128,153],"calculus":[137,167,236,275],"implication,":[139],"negation,":[140],"conjunction":[141,145,209,244],"\u039b,":[142],"(see":[147,276],"below)":[148],"coincides":[149],"[t],":[159],"expressing":[160],"language":[163],"statement:":[169],"\"the":[170],"\u03bb-term":[171],"A\".The":[176],"main":[177],"results":[178],"this":[180],"paper":[181],"were":[182],"announced":[183],"[8].Adding":[185],"disjunction":[187],"changes":[189],"situation":[191],"drastically:":[192],"familiar":[194],"constructed":[196],"G.":[198],"Rose":[199],"unprovable":[201,272],"but":[202,271],"realizable":[203,266],"suitable":[206],"if-then-else":[207],"term.Strong":[208],"stipulation:The":[215],"definition":[216],"problem":[228],"taken":[230],"essentially":[231],"[7].Nevertheless,":[233],"implication":[241],"incomplete,":[246],"contrary":[247],"conjecture":[250],"made":[251],"[7]:":[253],"consider":[254],"((A":[257],"D":[258],"B)":[259],"&D)D":[260],"(((A":[261],"&C)DB)":[262],"D).It":[264],"\u03bbx.x":[270],"[7]).":[277]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}