{"id":"https://openalex.org/W2032691586","doi":"https://doi.org/10.1215/00294527-1722773","title":"Minimally Congruential Contexts: Observations and Questions on Embedding E in K","display_name":"Minimally Congruential Contexts: Observations and Questions on Embedding E in K","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2032691586","doi":"https://doi.org/10.1215/00294527-1722773","mag":"2032691586"},"language":"en","primary_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.1215/00294527-1722773","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/P4310315572","https://openalex.org/P4310315698"],"host_organization_lineage_names":["Duke University","Duke University Press"],"type":"journal"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true},"type":"article","type_crossref":"journal-article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1215/00294527-1722773","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066338069","display_name":"Lloyd Humberstone","orcid":"https://orcid.org/0000-0003-4932-1027"},"institutions":[{"id":"https://openalex.org/I56590836","display_name":"Monash University","ror":"https://ror.org/02bfwt286","country_code":"AU","type":"education","lineage":["https://openalex.org/I56590836"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Lloyd Humberstone","raw_affiliation_strings":["Department of Philosophy School of Philosophical, Historical and International Studies","Monash University Clayton, Victoria 3800 Australia"],"affiliations":[{"raw_affiliation_string":"Department of Philosophy School of Philosophical, Historical and International Studies","institution_ids":[]},{"raw_affiliation_string":"Monash University Clayton, Victoria 3800 Australia","institution_ids":["https://openalex.org/I56590836"]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5066338069"],"corresponding_institution_ids":["https://openalex.org/I56590836"],"apc_list":null,"apc_paid":null,"fwci":0.361,"has_fulltext":true,"fulltext_origin":"pdf","cited_by_count":1,"citation_normalized_percentile":{"value":0.5499,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":64,"max":72},"biblio":{"volume":"53","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9995,"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":0.9995,"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":0.9989,"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":0.9973,"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/undecidable-problem","display_name":"Undecidable problem","score":0.41846135}],"concepts":[{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.6935765},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.61297005},{"id":"https://openalex.org/C27508121","wikidata":"https://www.wikidata.org/wiki/Q210841","display_name":"Modal logic","level":3,"score":0.51289725},{"id":"https://openalex.org/C149364088","wikidata":"https://www.wikidata.org/wiki/Q185917","display_name":"Translation (biology)","level":4,"score":0.5115396},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5095568},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.47575706},{"id":"https://openalex.org/C192034797","wikidata":"https://www.wikidata.org/wiki/Q3502995","display_name":"Undecidable problem","level":3,"score":0.41846135},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40288758},{"id":"https://openalex.org/C71139939","wikidata":"https://www.wikidata.org/wiki/Q910194","display_name":"Modal","level":2,"score":0.39639008},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3428381},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32851785},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.21079901},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.13226709},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C105580179","wikidata":"https://www.wikidata.org/wiki/Q188928","display_name":"Messenger RNA","level":3,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C188027245","wikidata":"https://www.wikidata.org/wiki/Q750446","display_name":"Polymer chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"is_oa":true,"landing_page_url":"https://doi.org/10.1215/00294527-1722773","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/P4310315572","https://openalex.org/P4310315698"],"host_organization_lineage_names":["Duke University","Duke University Press"],"type":"journal"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true},{"is_oa":true,"landing_page_url":"http://projecteuclid.org/euclid.ndjfl/1352383234","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-53/issue-4/Minimally-Congruential-Contexts--Observations-and-Questions-on-Embedding-E/10.1215/00294527-1722773.pdf","source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":["Cornell University"],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.1215/00294527-1722773","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/P4310315572","https://openalex.org/P4310315698"],"host_organization_lineage_names":["Duke University","Duke University Press"],"type":"journal"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true},"sustainable_development_goals":[{"display_name":"Peace, justice, and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.49}],"grants":[],"datasets":[],"versions":[],"referenced_works_count":18,"referenced_works":["https://openalex.org/W1490829364","https://openalex.org/W1517992131","https://openalex.org/W1541365419","https://openalex.org/W1545118076","https://openalex.org/W1584744137","https://openalex.org/W1596067335","https://openalex.org/W1963857568","https://openalex.org/W1967192042","https://openalex.org/W2006861379","https://openalex.org/W2009762006","https://openalex.org/W2010897591","https://openalex.org/W2038242523","https://openalex.org/W2076644510","https://openalex.org/W2095704391","https://openalex.org/W2275071415","https://openalex.org/W2335099172","https://openalex.org/W4242309855","https://openalex.org/W582134418"],"related_works":["https://openalex.org/W4287814874","https://openalex.org/W3016746667","https://openalex.org/W2962420748","https://openalex.org/W2125797022","https://openalex.org/W2120230527","https://openalex.org/W2028144918","https://openalex.org/W1587059467","https://openalex.org/W1536365843","https://openalex.org/W1498755214","https://openalex.org/W119381390"],"abstract_inverted_index":{"Recently,":[0],"an":[1],"improvement":[2],"in":[3,23,126,133,141,149],"respect":[4],"of":[5,37,52,58,73,144,146,172],"simplicity":[6],"was":[7,65],"found":[8],"by":[9],"Rohan":[10],"French":[11],"over":[12],"extant":[13],"translations":[14],"faithfully":[15,125],"embedding":[16,123],"the":[17,24,35,40,71,110],"smallest":[18,25],"congruential":[19,76,95,132],"modal":[20,27],"logic":[21,28],"(E)":[22],"normal":[26],"(K).":[29],"After":[30],"some":[31,143],"preliminaries,":[32],"we":[33],"explore":[34],"possibility":[36],"further":[38],"simplifying":[39],"translation,":[41],"with":[42,169],"various":[43],"negative":[44],"findings":[45],"(but":[46],"no":[47,86],"positive":[48],"solution).":[49],"This":[50,78],"line":[51],"inquiry":[53],"leads,":[54],"via":[55],"a":[56,74,83,118,121,170],"consideration":[57],"one":[59],"candidate":[60],"simpler":[61],"translation":[62,122],"whose":[63],"status":[64],"left":[66],"open":[67,173],"earlier,":[68],"to":[69,82],"isolating":[70],"concept":[72],"minimally":[75,131],"context.":[77],"amounts,":[79],"roughly":[80],"speaking,":[81],"context":[84,119],"exhibiting":[85],"logical":[87],"properties":[88],"beyond":[89],"those":[90],"following":[91],"from":[92,97],"its":[93,98],"being":[94],"(i.e.,":[96],"yielding":[99],"provably":[100,104],"equivalent":[101,105],"results":[102],"when":[103],"formulas":[106],"are":[107,139],"inserted":[108],"into":[109],"context).":[111],"On":[112],"investigation,":[113],"it":[114,165,167],"turns":[115],"out":[116],"that":[117],"inducing":[120],"E":[124],"K":[127],"need":[128],"not":[129],"be":[130],"K.":[134],"Several":[135],"related":[136],"minimality":[137],"conditions":[138],"noted":[140],"passing,":[142],"them":[145],"considerable":[147],"interest":[148],"their":[150],"own":[151],"right":[152],"(in":[153],"particular,":[154],"minimal":[155],"normality).":[156],"The":[157],"paper":[158],"is":[159],"exploratory,":[160],"raising":[161],"more":[162],"questions":[163],"than":[164],"settles;":[166],"ends":[168],"list":[171],"problems.":[174]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2032691586","counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2024-12-08T23:30:10.695328","created_date":"2016-06-24"}