{"id":"https://openalex.org/W2083210279","doi":"https://doi.org/10.1305/ndjfl/1093890904","title":"A note on transitivity.","display_name":"A note on transitivity.","publication_year":1973,"publication_date":"1973-02-01","ids":{"openalex":"https://openalex.org/W2083210279","doi":"https://doi.org/10.1305/ndjfl/1093890904","mag":"2083210279"},"language":"en","primary_location":{"id":"doi:10.1305/ndjfl/1093890904","is_oa":false,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093890904","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/A5015219005","display_name":"John R. Chidgey","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"John R. Chidgey","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5015219005"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.24323264,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"14","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.4846999943256378,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.4846999943256378,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.4747999906539917,"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/transitive-relation","display_name":"Transitive relation","score":0.8901442289352417},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47891342639923096},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.32954639196395874},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2233160436153412}],"concepts":[{"id":"https://openalex.org/C191399111","wikidata":"https://www.wikidata.org/wiki/Q64861","display_name":"Transitive relation","level":2,"score":0.8901442289352417},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47891342639923096},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.32954639196395874},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2233160436153412}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1305/ndjfl/1093890904","is_oa":false,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093890904","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/1093890904","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.ndjfl/1093890904","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":3,"referenced_works":["https://openalex.org/W2077798500","https://openalex.org/W2083488768","https://openalex.org/W2921632628"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W4312527695","https://openalex.org/W2361167282","https://openalex.org/W1528932152","https://openalex.org/W2091342995","https://openalex.org/W1677394555","https://openalex.org/W3007067598","https://openalex.org/W1963504579","https://openalex.org/W2359420171","https://openalex.org/W2271118953"],"abstract_inverted_index":{"Prefixing":[0],"CCpqCCrpCrq":[1],"1":[2],"(T":[3,8,119,170],"pre)":[4],"and":[5,31,43,62,178,250,273],"suffixing":[6],"CCpqCCqrCpr":[7],"suf)":[9],"are":[10,65,80,130,135],"usually":[11],"taken":[12,224],"to":[13,57,72,103],"be":[14,70,127,223],"the":[15,24,27,36,85,105,125,139,164,195,203,241,246,266],"two":[16],"theorem":[17],"forms":[18,83],"of":[19,26,29,39,47,84,107,141,166,175,217,220,229,248,270],"transitivity,":[20],"chiefly":[21],"because":[22],"in":[23,75,132,138,163,190,194,205],"presence":[25,140,165],"rules":[28,247],"substitution":[30,249],"detachment,":[32],"they":[33,79,134],"both":[34],"yield":[35],"derived":[37],"rule":[38],"transitivity":[40],"\"From,":[41],"Cpq":[42],"Cqr":[44],"infer":[45,145,154],"Cpr.\"Because":[46],"this,":[48],"even":[49,92,115],"though":[50],"Sobocinski":[51,161],"[4]":[52],"reports":[53],"a":[54,212],"result":[55],"attributed":[56],"Lukasiewicz":[58],"that":[59,74,182],"T":[60,63,108,111,176,179,191,206,209],"pre":[61,109,177],"suf":[64,180,210],"mutually":[66],"independent,":[67],"one":[68,234],"might":[69,89],"tempted":[71],"suppose":[73,90],"any":[76],"reasonable":[77],"context":[78],"equivalent":[81],"(interreplaceable)":[82],"same":[86],"basic":[87],"idea-transitivity.One":[88],"this":[91,221],"given":[93],"Soboci\u03aeski's":[94],"proof":[95],"2":[96,269],"for":[97],"matrix":[98],"K,":[99],"which":[100,133,200],"he":[101],"uses":[102],"show":[104],"independence":[106],"from":[110,225],"suf,":[112,192],"does":[113],"not":[114,124,202],"satisfy":[116],"identity":[117],"Cpp":[118],"identity);":[120],"but":[121],"such":[122],"is":[123,184,201,211,264],"case.To":[126],"sure,":[128],"there":[129,183],"contexts":[131],"interreplaceable,":[136],"e.g.,":[137],"permutation":[142,151,187],"\"From":[143,152],"CpCqr":[144],"CqCpr\"":[146],"(DR":[147,156],"perm),":[148,158],"or":[149,159],"restricted":[150],"CpCCqrs":[153],"CCqrCps\"":[155],"rest":[157],"as":[160],"shows":[162],"unrestricted":[167],"assertion":[168],"CpCCpqq":[169],"assertion).":[171],"3A":[172],"closer":[173],"inspection":[174],"reveals":[181],"indeed":[185],"some":[186],"already":[188],"present":[189],"i.e.,":[193],"consequent":[196],"q":[197],"precedes":[198],"p,":[199],"case":[204],"pre.This":[207],"suggests":[208],"more":[213],"powerful":[214],"(useful)":[215],"form":[216],"transitivity.An":[218],"example":[219],"may":[222],"Anderson's":[226],"pure":[227],"calculus":[228],"entailment":[230],"Ei":[231],"[l]":[232],"where":[233],"formulation":[235,263,267],"(here":[236],"denoted":[237],"by":[238],"Eil)":[239],"has":[240],"following":[242],"axioms":[243],"together":[244],"with":[245],"detachment:":[251],"E\u03cal":[252],"Axl.CCCppqq":[253],"\u0388.":[254],"\u03bb":[255],"l":[256,260],"Ax2.CCpqCCqrCpr":[257],"\u0388":[258],"\u03b3":[259],"Ax3.CCpCpqCpq":[261],"This":[262],"essentially":[265],"I":[268],"Anderson,":[271],"Belnap":[272],"1.":[274]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}