{"id":"https://openalex.org/W1983295338","doi":"https://doi.org/10.1305/ndjfl/1093887646","title":"On a modal system of R. A. Bull's","display_name":"On a modal system of R. A. Bull's","publication_year":1976,"publication_date":"1976-07-01","ids":{"openalex":"https://openalex.org/W1983295338","doi":"https://doi.org/10.1305/ndjfl/1093887646","mag":"1983295338"},"language":"en","primary_location":{"id":"doi:10.1305/ndjfl/1093887646","is_oa":false,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093887646","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/A5006732059","display_name":"Dolph Ulrich","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Dolph Ulrich","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5006732059"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.18116752,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"17","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11394","display_name":"Dynamics and Control of Mechanical Systems","score":0.5073999762535095,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11394","display_name":"Dynamics and Control of Mechanical Systems","score":0.5073999762535095,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/modal","display_name":"Modal","score":0.6315032839775085},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46585947275161743},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3727337419986725},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.32920533418655396},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.1262754499912262},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.08623254299163818},{"id":"https://openalex.org/keywords/composite-material","display_name":"Composite material","score":0.048788219690322876}],"concepts":[{"id":"https://openalex.org/C71139939","wikidata":"https://www.wikidata.org/wiki/Q910194","display_name":"Modal","level":2,"score":0.6315032839775085},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46585947275161743},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3727337419986725},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.32920533418655396},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.1262754499912262},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.08623254299163818},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.048788219690322876},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1305/ndjfl/1093887646","is_oa":false,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093887646","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/1093887646","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.ndjfl/1093887646","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":1,"referenced_works":["https://openalex.org/W2005922990"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644"],"abstract_inverted_index":{"Bull":[0],"[1]":[1],"mentions,":[2],"in":[3,34,46,125,130,146],"passing,":[4],"having":[5],"discovered":[6],"the":[7,32,68,142,147,200],"weakest":[8],"extension":[9],"of":[10,40,153],"S4":[11,21,41,131,154],"that":[12,58,75,90,171,209,225,235],"both":[13],"contains":[14],"S4.3":[15],"and":[16,60,82,95,112,168,176,181,185,199,212,230,240],"is":[17,44,128,137,203,245],"obtainable":[18],"by":[19,97],"extending":[20],"with":[22,164],"an":[23],"axiom":[24,33],"involving":[25],"a":[26],"single":[27],"sentential":[28],"variable.I":[29],"shall":[30],"call":[31],"question":[35],"F3CMLpALCpLpLCLCpLpLpLemma":[36],"1":[37,81,94,111,228],"Each":[38,122],"theorem":[39],"+":[42,132,155],"F3":[43],"valid":[45,124],"every":[47],"SAF-model.(3)":[48],"V(LCLCpLpLp,":[49],"x)":[50,116],"=":[51,64,80,85,93,110,117],"0.By":[52],"(1)":[53],"there":[54,71,157],"exists":[55,72],"zeW":[56],"such":[57,74,224],"xRz":[59],"(4)":[61,89],"V(Lp,":[62],"z)":[63,92],"1.By":[65],"(3),":[66],"on":[67],"other":[69],"hand,":[70],"yeW":[73],"xRy,":[76,165],"(5)":[77,105],"V(LCpLp,":[78,115],"y)":[79,109],"(6)":[83],"V{Lp,y)":[84],"0.It":[86],"follows":[87],"from":[88,104,141],"V(LLp,":[91],"so,":[96],"(6),":[98],"zfty.According":[99],"to":[100],"(F),":[101],"then,":[102,189,208],"yRx.But":[103],"I":[106],"have":[107],"V(LLCpLp,":[108],"so":[113,170,186,197,217,234,241],"now":[114],"1,":[118],"contradicting":[119],"(2).Lemma":[120],"2":[121],"formula":[123],"all":[126],"S4F-models":[127],"provable":[129],"F3.I":[133],"prove":[134],"only":[135],"what":[136],"not":[138],"already":[139],"familiar":[140],"literature:":[143],"(F)":[144],"holds":[145],"canonical":[148],"model":[149],"(W,":[150],"R,":[151],"V)":[152],"F3.Otherwise,":[156],"exist":[158,221],"x,":[159],"y,":[160],"z":[161],"e":[162],"W":[163,223],"xRz,":[166],"zfly,":[167],"yj\u03afx":[169],"for":[172],"some":[173],"formulas":[174],"q":[175],"r,":[177],"Lrez,":[178,183],"rj\u03ady,":[179],"Lqey,":[180],"q\u00a3x.Since":[182],"LCqLrez":[184],"MLCqLrex.By":[187],"F3,":[188],"LCCqLrLCqLrex":[190],"or":[191],"LCLCCqLrLCqLrLCqLrex.CqLrex":[192],"since":[193],"qj\u03afx-,":[194],"CqLrj\u03afy,":[195],"however,":[196],"LCqLrj\u03afx":[198],"first":[201],"alternative":[202],"impossible:":[204],"LCCqLrLCqLrex.It":[205],"must":[206,219],"be,":[207],"LCLCCqLrLCqLrLCqLr":[210],"ex,":[211],"CLCCqLrLCqLrLCqLr":[213],"ey.As":[214],"before,":[215],"LCqLrj\u03afy,":[216],"LCCqLrLCqLr^y.There":[218],"then":[220],"y'e":[222],"yRy\\":[226],"CqLrey":[227],",":[229],"LCqLr\u03afy\\":[231],"However,":[232],"Lqey":[233],"qey'.Hence":[236],"Lr":[237],"ey":[238],"r":[239],"LCqLr":[242],"ey\\":[243],"which":[244],"also":[246],"impossible.":[247]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
