{"id":"https://openalex.org/W2579853059","doi":"https://doi.org/10.2307/2271943","title":"On the inconsistency of systems similar to","display_name":"On the inconsistency of systems similar to","publication_year":1978,"publication_date":"1978-03-01","ids":{"openalex":"https://openalex.org/W2579853059","doi":"https://doi.org/10.2307/2271943","mag":"2579853059"},"language":"en","primary_location":{"id":"doi:10.2307/2271943","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2271943","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/A5038043998","display_name":"M. W. Bunder","orcid":null},"institutions":[{"id":"https://openalex.org/I4210120676","display_name":"Mathematical Institute of the Slovak Academy of Sciences","ror":"https://ror.org/02fhy7464","country_code":"SK","type":"facility","lineage":["https://openalex.org/I207624831","https://openalex.org/I4210120676"]}],"countries":["SK"],"is_corresponding":true,"raw_author_name":"M. W. Bunder","raw_affiliation_strings":["Mathematics Institute, Oxford, England"],"affiliations":[{"raw_affiliation_string":"Mathematics Institute, Oxford, England","institution_ids":["https://openalex.org/I4210120676"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089471037","display_name":"R. Meyer","orcid":"https://orcid.org/0000-0003-0106-7066"},"institutions":[{"id":"https://openalex.org/I4210120676","display_name":"Mathematical Institute of the Slovak Academy of Sciences","ror":"https://ror.org/02fhy7464","country_code":"SK","type":"facility","lineage":["https://openalex.org/I207624831","https://openalex.org/I4210120676"]}],"countries":["SK"],"is_corresponding":false,"raw_author_name":"R. K. Meyer","raw_affiliation_strings":["Mathematics Institute, Oxford, England"],"affiliations":[{"raw_affiliation_string":"Mathematics Institute, Oxford, England","institution_ids":["https://openalex.org/I4210120676"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5038043998"],"corresponding_institution_ids":["https://openalex.org/I4210120676"],"apc_list":null,"apc_paid":null,"fwci":5.2716,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.95582714,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"43","issue":"1","first_page":"1","last_page":"2"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9987000226974487,"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":0.9987000226974487,"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":0.9973000288009644,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9860000014305115,"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/modus-ponens","display_name":"Modus ponens","score":0.941258430480957},{"id":"https://openalex.org/keywords/combinatory-logic","display_name":"Combinatory logic","score":0.8230357766151428},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.6499933004379272},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5773084759712219},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3849450945854187},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3759145140647888},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3659462630748749},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21219408512115479},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.07642397284507751}],"concepts":[{"id":"https://openalex.org/C193885149","wikidata":"https://www.wikidata.org/wiki/Q655742","display_name":"Modus ponens","level":3,"score":0.941258430480957},{"id":"https://openalex.org/C79678938","wikidata":"https://www.wikidata.org/wiki/Q1481571","display_name":"Combinatory logic","level":2,"score":0.8230357766151428},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.6499933004379272},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5773084759712219},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3849450945854187},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3759145140647888},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3659462630748749},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21219408512115479},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.07642397284507751},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2307/2271943","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2271943","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2026765907","https://openalex.org/W4307413753","https://openalex.org/W2029563506","https://openalex.org/W1588067599","https://openalex.org/W2040259072","https://openalex.org/W1992256554","https://openalex.org/W2579853059","https://openalex.org/W1988686825","https://openalex.org/W2288082802","https://openalex.org/W2579272254"],"abstract_inverted_index":{"This":[0],"note":[1],"shows":[2],"that":[3,44],"the":[4,8,25,36,42,45,50,58,61,84,139],"inconsistency":[5,27,62],"proof":[6],"of":[7,10,28,35,49],"system":[9],"illative":[11],"combinatory":[12],"logic":[13],"given":[14],"in":[15,38,41],"[1]":[16,39],"can":[17],"be":[18],"simplified":[19],"as":[20,22,65,68],"well":[21],"extended":[23],"to":[24,57],"absolute":[26],"a":[29],"more":[30,85],"general":[31,86],"system.":[32],"One":[33],"extension":[34],"result":[37],"lies":[40],"fact":[43],"following":[46],"weakened":[47],"form":[48],"deduction":[51],"theorem":[52],"for":[53,67,71,76,100],"implication":[54],"will":[55,82],"lead":[56],"inconsistency:":[59],"Also":[60],"follows":[63],"almost":[64],"easily":[66],"it":[69],"does":[70],"\u22a2":[72],"H":[73,112,119],"2":[74,120],"X":[75,78,143,148,153,155],"arbitrary":[77],",":[79,130,147,156],"so":[80],"we":[81,91],"consider":[83],"case.":[87],"The":[88],"only":[89],"properties":[90],"require":[92],"other":[93],"than":[94],"(DT),":[95],"(1)":[96],"and":[97,105,142],"Rule":[98],"Eq":[99],"equality":[101],"are":[102],"modus":[103],"ponens,":[104],"Let":[106],"G":[107,146],"=":[108,144,149],"[":[109],"x":[110,115,121,124,127],"]":[111],"n":[113],"\u22121":[114],"\u2283:":[116],".":[117,126,151],"\u2026":[118],"\u2283":[122,125,128],":H":[123],"A":[129,132],"where":[131],"is":[133,138],"arbitrary.":[134],"Then":[135],"if":[136],"Y":[137,145],"paradoxical":[140],"combinator":[141],"GX":[150],"Now":[152],"\u2282":[154],"i.e.,":[157]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
