{"id":"https://openalex.org/W2112160811","doi":"https://doi.org/10.2307/2275096","title":"Systems of illative combinatory logic complete for first-order propositional and predicate calculus","display_name":"Systems of illative combinatory logic complete for first-order propositional and predicate calculus","publication_year":1993,"publication_date":"1993-09-01","ids":{"openalex":"https://openalex.org/W2112160811","doi":"https://doi.org/10.2307/2275096","mag":"2112160811"},"language":"en","primary_location":{"id":"doi:10.2307/2275096","is_oa":true,"landing_page_url":"https://doi.org/10.2307/2275096","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/721B390070A46E2ADC11511EDC52B3DC/S0022481200020880a.pdf/div-class-title-systems-of-illative-combinatory-logic-complete-for-first-order-propositional-and-predicate-calculus-div.pdf","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":"bronze","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/721B390070A46E2ADC11511EDC52B3DC/S0022481200020880a.pdf/div-class-title-systems-of-illative-combinatory-logic-complete-for-first-order-propositional-and-predicate-calculus-div.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","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"]},{"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","US"],"is_corresponding":true,"raw_author_name":"Henk Barendregt","raw_affiliation_strings":["Faculty of Mathematics and Computer Science, Catholic University, Nijmegen, The Netherlands, E-mail:","University of Wollongong"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, Catholic University, Nijmegen, The Netherlands, E-mail:","institution_ids":["https://openalex.org/I84470341"]},{"raw_affiliation_string":"University of Wollongong","institution_ids":["https://openalex.org/I204824540"]}]},{"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 Wollongong, NSW Australia, E-mail:","University of Wollongong"],"affiliations":[{"raw_affiliation_string":"Faculty of Informatics, Department of Mathematics, University of Wollongong, NSW Australia, E-mail:","institution_ids":["https://openalex.org/I204824540"]},{"raw_affiliation_string":"University of Wollongong","institution_ids":["https://openalex.org/I204824540"]}]},{"author_position":"last","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":false,"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"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5016150987"],"corresponding_institution_ids":["https://openalex.org/I204824540","https://openalex.org/I84470341"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":21,"citation_normalized_percentile":{"value":0.18566412,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"58","issue":"3","first_page":"769","last_page":"788"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9836000204086304,"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":0.9836000204086304,"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":0.9731000065803528,"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"}},{"id":"https://openalex.org/T10215","display_name":"Semantic Web and Ontologies","score":0.9728000164031982,"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/combinatory-logic","display_name":"Combinatory logic","score":0.9655568599700928},{"id":"https://openalex.org/keywords/predicate-logic","display_name":"Predicate logic","score":0.6887044310569763},{"id":"https://openalex.org/keywords/zeroth-order-logic","display_name":"Zeroth-order logic","score":0.5553163290023804},{"id":"https://openalex.org/keywords/propositional-calculus","display_name":"Propositional calculus","score":0.5417104959487915},{"id":"https://openalex.org/keywords/predicate-variable","display_name":"Predicate variable","score":0.5357142686843872},{"id":"https://openalex.org/keywords/curry\u2013howard-correspondence","display_name":"Curry\u2013Howard correspondence","score":0.5148257613182068},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.5054724216461182},{"id":"https://openalex.org/keywords/logical-equivalence","display_name":"Logical equivalence","score":0.4978315830230713},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.4627881348133087},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4579777121543884},{"id":"https://openalex.org/keywords/rule-of-inference","display_name":"Rule of inference","score":0.4563170373439789},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4385881721973419},{"id":"https://openalex.org/keywords/autoepistemic-logic","display_name":"Autoepistemic logic","score":0.4288235902786255},{"id":"https://openalex.org/keywords/well-formed-formula","display_name":"Well-formed formula","score":0.42876169085502625},{"id":"https://openalex.org/keywords/interpretation","display_name":"Interpretation (philosophy)","score":0.4136834740638733},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.41268038749694824},{"id":"https://openalex.org/keywords/predicate","display_name":"Predicate (mathematical logic)","score":0.41062888503074646},{"id":"https://openalex.org/keywords/natural-deduction","display_name":"Natural deduction","score":0.38821569085121155},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.3144508898258209},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2649281620979309},{"id":"https://openalex.org/keywords/multimodal-logic","display_name":"Multimodal logic","score":0.16892659664154053},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.16496002674102783},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.12379127740859985},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.09521231055259705}],"concepts":[{"id":"https://openalex.org/C79678938","wikidata":"https://www.wikidata.org/wiki/Q1481571","display_name":"Combinatory logic","level":2,"score":0.9655568599700928},{"id":"https://openalex.org/C19689857","wikidata":"https://www.wikidata.org/wiki/Q4055684","display_name":"Predicate logic","level":3,"score":0.6887044310569763},{"id":"https://openalex.org/C110039528","wikidata":"https://www.wikidata.org/wiki/Q8069651","display_name":"Zeroth-order logic","level":4,"score":0.5553163290023804},{"id":"https://openalex.org/C69562738","wikidata":"https://www.wikidata.org/wiki/Q200694","display_name":"Propositional calculus","level":2,"score":0.5417104959487915},{"id":"https://openalex.org/C73314972","wikidata":"https://www.wikidata.org/wiki/Q10531432","display_name":"Predicate variable","level":5,"score":0.5357142686843872},{"id":"https://openalex.org/C85343465","wikidata":"https://www.wikidata.org/wiki/Q975734","display_name":"Curry\u2013Howard correspondence","level":3,"score":0.5148257613182068},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.5054724216461182},{"id":"https://openalex.org/C70846408","wikidata":"https://www.wikidata.org/wiki/Q220433","display_name":"Logical equivalence","level":3,"score":0.4978315830230713},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.4627881348133087},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4579777121543884},{"id":"https://openalex.org/C3746660","wikidata":"https://www.wikidata.org/wiki/Q1068763","display_name":"Rule of inference","level":2,"score":0.4563170373439789},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4385881721973419},{"id":"https://openalex.org/C3845977","wikidata":"https://www.wikidata.org/wiki/Q4826262","display_name":"Autoepistemic logic","level":4,"score":0.4288235902786255},{"id":"https://openalex.org/C191222856","wikidata":"https://www.wikidata.org/wiki/Q655328","display_name":"Well-formed formula","level":5,"score":0.42876169085502625},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.4136834740638733},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.41268038749694824},{"id":"https://openalex.org/C140146324","wikidata":"https://www.wikidata.org/wiki/Q1144319","display_name":"Predicate (mathematical logic)","level":2,"score":0.41062888503074646},{"id":"https://openalex.org/C62073222","wikidata":"https://www.wikidata.org/wiki/Q1572108","display_name":"Natural deduction","level":2,"score":0.38821569085121155},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.3144508898258209},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2649281620979309},{"id":"https://openalex.org/C203659156","wikidata":"https://www.wikidata.org/wiki/Q6934805","display_name":"Multimodal logic","level":3,"score":0.16892659664154053},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.16496002674102783},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.12379127740859985},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.09521231055259705},{"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:10.2307/2275096","is_oa":true,"landing_page_url":"https://doi.org/10.2307/2275096","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/721B390070A46E2ADC11511EDC52B3DC/S0022481200020880a.pdf/div-class-title-systems-of-illative-combinatory-logic-complete-for-first-order-propositional-and-predicate-calculus-div.pdf","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:ro.uow.edu.au:eispapers-2968","is_oa":false,"landing_page_url":"https://ro.uow.edu.au/eispapers/1959","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/1183744297","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183744297","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:CiteSeerX.psu:10.1.1.47.640","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.47.640","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://ftp.cs.kun.nl/pub/CompMath.Found/ICL1.ps.Z","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.877.4339","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.877.4339","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://ro.uow.edu.au/cgi/viewcontent.cgi?article%3D2968%26context%3Deispapers","raw_type":"text"},{"id":"pmh:oai:figshare.com:article/27710670","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:2066/17259","is_oa":false,"landing_page_url":"http://hdl.handle.net/2066/17259","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":"doi:10.2307/2275096","is_oa":true,"landing_page_url":"https://doi.org/10.2307/2275096","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/721B390070A46E2ADC11511EDC52B3DC/S0022481200020880a.pdf/div-class-title-systems-of-illative-combinatory-logic-complete-for-first-order-propositional-and-predicate-calculus-div.pdf","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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2112160811.pdf","grobid_xml":"https://content.openalex.org/works/W2112160811.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W123923308","https://openalex.org/W1570195473","https://openalex.org/W1594912681","https://openalex.org/W1971830381","https://openalex.org/W1973312452","https://openalex.org/W1979324125","https://openalex.org/W2008406112","https://openalex.org/W2028227692","https://openalex.org/W2029902469","https://openalex.org/W2041887887","https://openalex.org/W2063377490","https://openalex.org/W2071926437","https://openalex.org/W2132425970","https://openalex.org/W2154273644","https://openalex.org/W2159676458","https://openalex.org/W2319210160","https://openalex.org/W2321172684","https://openalex.org/W2323724534","https://openalex.org/W2323803659","https://openalex.org/W2326394178","https://openalex.org/W2326697462","https://openalex.org/W2334571683","https://openalex.org/W2519425411","https://openalex.org/W4234418851","https://openalex.org/W6726801172"],"related_works":["https://openalex.org/W2006341276","https://openalex.org/W44725458","https://openalex.org/W2811159399","https://openalex.org/W2170952169","https://openalex.org/W2030678653","https://openalex.org/W2014841514","https://openalex.org/W1595549069","https://openalex.org/W2112160811","https://openalex.org/W2074282135","https://openalex.org/W1981178597"],"abstract_inverted_index":{"Abstract":[0],"Illative":[1],"combinatory":[2,32],"logic":[3,33,47,111],"consists":[4],"of":[5,8,30,102,116,127],"the":[6,49,59,100],"theory":[7],"combinators":[9,66],"or":[10,118,138],"lambda":[11],"calculus":[12],"extended":[13],"by":[14],"extra":[15],"constants":[16],"(and":[17],"corresponding":[18],"axioms":[19],"and":[20,40,106],"rules)":[21],"intended":[22],"to":[23,94,109],"capture":[24],"inference.":[25],"The":[26,43,88,97],"paper":[27,98],"considers":[28],"systems":[29,51,126],"illative":[31,50],"that":[34],"are":[35,76,81],"sound":[36,136],"for":[37],"first-order":[38],"propositional":[39],"predicate":[41],"calculus.":[42],"interpretation":[44],"from":[45],"ordinary":[46],"into":[48],"can":[52],"be":[53,95],"done":[54],"in":[55,62,68,73,84],"two":[56,89],"ways:":[57],"following":[58],"propositions-as-types":[60],"paradigm,":[61],"which":[63,74],"derivations":[64,75],"become":[65],"or,":[67],"a":[69,85,113,135],"more":[70],"direct":[71,90],"way,":[72],"not":[77],"translated.":[78],"Both":[79],"translations":[80,91],"closely":[82],"related":[83],"canonical":[86],"way.":[87],"turn":[92],"out":[93],"complete.":[96],"fulfills":[99],"program":[101,122],"Church":[103],"[1932],":[104],"[1933]":[105],"Curry":[107],"[1930]":[108],"base":[110],"on":[112],"consistent":[114],"system":[115],"\u03bb-terms":[117],"combinators.":[119],"Hitherto":[120],"this":[121],"had":[123],"failed":[124],"because":[125],"ICL":[128],"were":[129],"either":[130],"too":[131,139],"weak":[132],"(to":[133],"provide":[134],"interpretation)":[137],"strong":[140],"(sometimes":[141],"even":[142],"inconsistent).":[143]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}