{"id":"https://openalex.org/W2030678653","doi":"https://doi.org/10.2307/2586717","title":"Completeness of the propositions-as-types interpretation of intuitionistic logic into illative combinatory logic","display_name":"Completeness of the propositions-as-types interpretation of intuitionistic logic into illative combinatory logic","publication_year":1998,"publication_date":"1998-09-01","ids":{"openalex":"https://openalex.org/W2030678653","doi":"https://doi.org/10.2307/2586717","mag":"2030678653"},"language":"en","primary_location":{"id":"doi:10.2307/2586717","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2586717","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":true,"oa_status":"green","oa_url":"http://hdl.handle.net/2066/17260","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112030792","display_name":"Wil Dekkers","orcid":null},"institutions":[{"id":"https://openalex.org/I84470341","display_name":"Catholic University of America","ror":"https://ror.org/047yk3s18","country_code":"US","type":"education","lineage":["https://openalex.org/I84470341"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Wil Dekkers","raw_affiliation_strings":["Faculty of Mathematics and Computer Science, Catholic University, Nijmegen, The Netherlands E-mail:"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, Catholic University, Nijmegen, The Netherlands E-mail:","institution_ids":["https://openalex.org/I84470341"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038043998","display_name":"M. W. Bunder","orcid":null},"institutions":[{"id":"https://openalex.org/I204824540","display_name":"University of Wollongong","ror":"https://ror.org/00jtmb277","country_code":"AU","type":"education","lineage":["https://openalex.org/I204824540"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Martin Bunder","raw_affiliation_strings":["Faculty of Informatics, Department of Mathematics, University of Wollonoong, Nsw Australia E-mail:"],"affiliations":[{"raw_affiliation_string":"Faculty of Informatics, Department of Mathematics, University of Wollonoong, Nsw Australia E-mail:","institution_ids":["https://openalex.org/I204824540"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016150987","display_name":"Henk Barendregt","orcid":"https://orcid.org/0000-0002-3735-4078"},"institutions":[{"id":"https://openalex.org/I84470341","display_name":"Catholic University of America","ror":"https://ror.org/047yk3s18","country_code":"US","type":"education","lineage":["https://openalex.org/I84470341"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Henk Barendregt","raw_affiliation_strings":["Faculty of Mathematics and Computer Science, Catholic University, Nijmegen, The Netherlands E-mail:"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, Catholic University, Nijmegen, The Netherlands E-mail:","institution_ids":["https://openalex.org/I84470341"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5112030792"],"corresponding_institution_ids":["https://openalex.org/I84470341"],"apc_list":null,"apc_paid":null,"fwci":1.0985,"has_fulltext":true,"cited_by_count":18,"citation_normalized_percentile":{"value":0.82413804,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"63","issue":"3","first_page":"869","last_page":"890"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9994999766349792,"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":0.9994999766349792,"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":0.9994000196456909,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9970999956130981,"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/combinatory-logic","display_name":"Combinatory logic","score":0.9296965599060059},{"id":"https://openalex.org/keywords/predicate-logic","display_name":"Predicate logic","score":0.6625728607177734},{"id":"https://openalex.org/keywords/predicate-variable","display_name":"Predicate variable","score":0.6211388111114502},{"id":"https://openalex.org/keywords/intuitionistic-logic","display_name":"Intuitionistic logic","score":0.592094361782074},{"id":"https://openalex.org/keywords/curry\u2013howard-correspondence","display_name":"Curry\u2013Howard correspondence","score":0.5286847949028015},{"id":"https://openalex.org/keywords/zeroth-order-logic","display_name":"Zeroth-order logic","score":0.5229626297950745},{"id":"https://openalex.org/keywords/logical-equivalence","display_name":"Logical equivalence","score":0.5229600071907043},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5111520886421204},{"id":"https://openalex.org/keywords/completeness","display_name":"Completeness (order theory)","score":0.5110862851142883},{"id":"https://openalex.org/keywords/second-order-logic","display_name":"Second-order logic","score":0.4965065121650696},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.4928321838378906},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.4910757541656494},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.4874408543109894},{"id":"https://openalex.org/keywords/autoepistemic-logic","display_name":"Autoepistemic logic","score":0.48673275113105774},{"id":"https://openalex.org/keywords/predicate-functor-logic","display_name":"Predicate functor logic","score":0.4733063280582428},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4682416021823883},{"id":"https://openalex.org/keywords/propositional-calculus","display_name":"Propositional calculus","score":0.43309056758880615},{"id":"https://openalex.org/keywords/higher-order-logic","display_name":"Higher-order logic","score":0.4327126741409302},{"id":"https://openalex.org/keywords/many-valued-logic","display_name":"Many-valued logic","score":0.42698949575424194},{"id":"https://openalex.org/keywords/interpretation","display_name":"Interpretation (philosophy)","score":0.4243260324001312},{"id":"https://openalex.org/keywords/natural-deduction","display_name":"Natural deduction","score":0.38895753026008606},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37735021114349365},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33473384380340576},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.2955685555934906},{"id":"https://openalex.org/keywords/multimodal-logic","display_name":"Multimodal logic","score":0.21858137845993042},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.20103377103805542},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.19913727045059204},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.13531196117401123}],"concepts":[{"id":"https://openalex.org/C79678938","wikidata":"https://www.wikidata.org/wiki/Q1481571","display_name":"Combinatory logic","level":2,"score":0.9296965599060059},{"id":"https://openalex.org/C19689857","wikidata":"https://www.wikidata.org/wiki/Q4055684","display_name":"Predicate logic","level":3,"score":0.6625728607177734},{"id":"https://openalex.org/C73314972","wikidata":"https://www.wikidata.org/wiki/Q10531432","display_name":"Predicate variable","level":5,"score":0.6211388111114502},{"id":"https://openalex.org/C178421362","wikidata":"https://www.wikidata.org/wiki/Q176786","display_name":"Intuitionistic logic","level":3,"score":0.592094361782074},{"id":"https://openalex.org/C85343465","wikidata":"https://www.wikidata.org/wiki/Q975734","display_name":"Curry\u2013Howard correspondence","level":3,"score":0.5286847949028015},{"id":"https://openalex.org/C110039528","wikidata":"https://www.wikidata.org/wiki/Q8069651","display_name":"Zeroth-order logic","level":4,"score":0.5229626297950745},{"id":"https://openalex.org/C70846408","wikidata":"https://www.wikidata.org/wiki/Q220433","display_name":"Logical equivalence","level":3,"score":0.5229600071907043},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5111520886421204},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.5110862851142883},{"id":"https://openalex.org/C144791301","wikidata":"https://www.wikidata.org/wiki/Q1548746","display_name":"Second-order logic","level":4,"score":0.4965065121650696},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.4928321838378906},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.4910757541656494},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.4874408543109894},{"id":"https://openalex.org/C3845977","wikidata":"https://www.wikidata.org/wiki/Q4826262","display_name":"Autoepistemic logic","level":4,"score":0.48673275113105774},{"id":"https://openalex.org/C2039508","wikidata":"https://www.wikidata.org/wiki/Q7239631","display_name":"Predicate functor logic","level":5,"score":0.4733063280582428},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4682416021823883},{"id":"https://openalex.org/C69562738","wikidata":"https://www.wikidata.org/wiki/Q200694","display_name":"Propositional calculus","level":2,"score":0.43309056758880615},{"id":"https://openalex.org/C169896238","wikidata":"https://www.wikidata.org/wiki/Q1644136","display_name":"Higher-order logic","level":3,"score":0.4327126741409302},{"id":"https://openalex.org/C150889026","wikidata":"https://www.wikidata.org/wiki/Q185502","display_name":"Many-valued logic","level":3,"score":0.42698949575424194},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.4243260324001312},{"id":"https://openalex.org/C62073222","wikidata":"https://www.wikidata.org/wiki/Q1572108","display_name":"Natural deduction","level":2,"score":0.38895753026008606},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37735021114349365},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33473384380340576},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.2955685555934906},{"id":"https://openalex.org/C203659156","wikidata":"https://www.wikidata.org/wiki/Q6934805","display_name":"Multimodal logic","level":3,"score":0.21858137845993042},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.20103377103805542},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.19913727045059204},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.13531196117401123},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.2307/2586717","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2586717","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:ru:oai:repository.ubn.ru.nl:2066/17260","is_oa":true,"landing_page_url":"http://hdl.handle.net/2066/17260","pdf_url":"http://hdl.handle.net/2066/17260","source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Symbolic Logic, 63, 869 - 890","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:ro.uow.edu.au:eispapers-2892","is_oa":false,"landing_page_url":"https://ro.uow.edu.au/eispapers/1883","pdf_url":null,"source":{"id":"https://openalex.org/S4306400510","display_name":"Research Online (University of Wollongong)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I204824540","host_organization_name":"University of Wollongong","host_organization_lineage":["https://openalex.org/I204824540"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty of Engineering and Information Sciences - Papers: Part A","raw_type":"article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1183745571","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183745571","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"},{"id":"pmh:oai:figshare.com:article/27710454","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"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"},{"id":"pmh:oai:repository.ubn.ru.nl:2066/161695","is_oa":false,"landing_page_url":"http://hdl.handle.net/2066/161695","pdf_url":null,"source":{"id":"https://openalex.org/S4306401067","display_name":"Radboud Repository (Radboud University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I145872427","host_organization_name":"Radboud University Nijmegen","host_organization_lineage":["https://openalex.org/I145872427"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article / Letter to editor"},{"id":"pmh:oai:repository.ubn.ru.nl:2066/298292","is_oa":false,"landing_page_url":"https://repository.ubn.ru.nl/handle/2066/298292","pdf_url":null,"source":{"id":"https://openalex.org/S4306401067","display_name":"Radboud Repository (Radboud University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I145872427","host_organization_name":"Radboud University Nijmegen","host_organization_lineage":["https://openalex.org/I145872427"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article / Letter to editor"}],"best_oa_location":{"id":"pmh:ru:oai:repository.ubn.ru.nl:2066/17260","is_oa":true,"landing_page_url":"http://hdl.handle.net/2066/17260","pdf_url":"http://hdl.handle.net/2066/17260","source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Symbolic Logic, 63, 869 - 890","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2030678653.pdf","grobid_xml":"https://content.openalex.org/works/W2030678653.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W2044758536","https://openalex.org/W2112160811","https://openalex.org/W2159511425","https://openalex.org/W4250879870","https://openalex.org/W4388299483"],"related_works":["https://openalex.org/W4389618767","https://openalex.org/W2479875366","https://openalex.org/W4147469","https://openalex.org/W2506419265","https://openalex.org/W4388397425","https://openalex.org/W1522769018","https://openalex.org/W2071436802","https://openalex.org/W4378499270","https://openalex.org/W2030678653","https://openalex.org/W1484845602"],"abstract_inverted_index":{"Abstract":[0],"Illative":[1],"combinatory":[2,37],"logic":[3,38,54],"consists":[4],"of":[5,8,35,102,157],"the":[6,56,66,96,103,108,115,136,144,148,158],"theory":[7],"combinators":[9],"or":[10,74],"lambda":[11],"calculus":[12,165],"extended":[13],"by":[14,133],"extra":[15],"constants":[16],"(and":[17],"corresponding":[18,138],"axioms":[19],"and":[20,47],"rules)":[21],"intended":[22],"to":[23],"capture":[24],"inference.":[25],"In":[26,95,107],"a":[27,76,92],"preceding":[28],"paper,":[29],"[2],":[30],"we":[31,99,111,130,152],"considered":[32],"4":[33],"systems":[34,58,140,146,159],"illative":[36,57,139],"that":[39,113,135,155],"are":[40,83,88,119,123,141],"sound":[41],"for":[42,147,163],"first":[43],"order":[44],"intuitionistic":[45],"propositional":[46],"predicate":[48,164],"logic.":[49],"The":[50],"interpretation":[51],"from":[52],"ordinary":[53],"into":[55],"can":[59],"be":[60],"done":[61],"in":[62,69,75,80,91,126],"two":[63,104,116,137,145],"ways:":[64],"following":[65],"propositions-as-types":[67],"paradigm,":[68],"which":[70,81],"derivations":[71,82],"become":[72],"combinators,":[73],"more":[77],"direct":[78,105,124,149],"way,":[79],"not":[84],"translated.":[85],"Both":[86],"translations":[87,118],"closely":[89],"related":[90],"canonical":[93],"way.":[94],"cited":[97],"paper":[98,110],"proved":[100,131],"completeness":[101,132],"translations.":[106,150],"present":[109],"prove":[112,154],"also":[114,161],"indirect":[117],"complete.":[120],"These":[121],"proofs":[122],"whereas":[125],"another":[127],"version,":[128],"[3],":[129],"showing":[134],"conservative":[142],"over":[143],"Moreover":[151],"shall":[153],"one":[156],"is":[160],"complete":[162],"with":[166],"higher":[167],"type":[168],"functions.":[169]},"counts_by_year":[{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":4}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}