{"id":"https://openalex.org/W2135933448","doi":"https://doi.org/10.2307/2266508","title":"On ternary logic","display_name":"On ternary logic","publication_year":1949,"publication_date":"1949-06-23","ids":{"openalex":"https://openalex.org/W2135933448","doi":"https://doi.org/10.2307/2266508","mag":"2135933448"},"language":"en","primary_location":{"id":"doi:10.2307/2266508","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2266508","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/A5078492480","display_name":"Paul Dienes","orcid":null},"institutions":[{"id":"https://openalex.org/I98259816","display_name":"Birkbeck, University of London","ror":"https://ror.org/02mb95055","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I98259816"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Paul Dienes","raw_affiliation_strings":["Birkbeck College, University of London","Birkbeck College"],"affiliations":[{"raw_affiliation_string":"Birkbeck College, University of London","institution_ids":["https://openalex.org/I98259816"]},{"raw_affiliation_string":"Birkbeck College","institution_ids":["https://openalex.org/I98259816"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5078492480"],"corresponding_institution_ids":["https://openalex.org/I98259816"],"apc_list":null,"apc_paid":null,"fwci":1.6143,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.83898305,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"2","first_page":"85","last_page":"94"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9896000027656555,"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"}},"topics":[{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9896000027656555,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9259999990463257,"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/mathematical-proof","display_name":"Mathematical proof","score":0.6424585580825806},{"id":"https://openalex.org/keywords/ternary-operation","display_name":"Ternary operation","score":0.5662312507629395},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5517690181732178},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5116057991981506},{"id":"https://openalex.org/keywords/intuitionistic-logic","display_name":"Intuitionistic logic","score":0.5049598813056946},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4686049222946167},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.4199680685997009},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.3871389925479889},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36770564317703247},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3404042720794678},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3210012912750244},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2905181646347046},{"id":"https://openalex.org/keywords/propositional-calculus","display_name":"Propositional calculus","score":0.22497734427452087},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.1830178201198578},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.057376712560653687}],"concepts":[{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.6424585580825806},{"id":"https://openalex.org/C64452783","wikidata":"https://www.wikidata.org/wiki/Q1524945","display_name":"Ternary operation","level":2,"score":0.5662312507629395},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5517690181732178},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5116057991981506},{"id":"https://openalex.org/C178421362","wikidata":"https://www.wikidata.org/wiki/Q176786","display_name":"Intuitionistic logic","level":3,"score":0.5049598813056946},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4686049222946167},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.4199680685997009},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3871389925479889},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36770564317703247},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3404042720794678},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3210012912750244},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2905181646347046},{"id":"https://openalex.org/C69562738","wikidata":"https://www.wikidata.org/wiki/Q200694","display_name":"Propositional calculus","level":2,"score":0.22497734427452087},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.1830178201198578},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.057376712560653687},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"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/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2307/2266508","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2266508","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":[{"score":0.6499999761581421,"display_name":"Decent work and economic growth","id":"https://metadata.un.org/sdg/8"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":3,"referenced_works":["https://openalex.org/W1960494084","https://openalex.org/W2157476045","https://openalex.org/W4300474804"],"related_works":["https://openalex.org/W2808944898","https://openalex.org/W3196207352","https://openalex.org/W2951724202","https://openalex.org/W3084261076","https://openalex.org/W1996614773","https://openalex.org/W4387820098","https://openalex.org/W2576399385","https://openalex.org/W2963408011","https://openalex.org/W4236324517","https://openalex.org/W1586813864"],"abstract_inverted_index":{"1.":[0],"The":[1,36,68],"problem":[2],"In":[3],"this":[4],"paper":[5],"we":[6,58],"give":[7],"the":[8,12,39],"complete":[9],"list":[10],"of":[11,14,19,24,30,38,45],"functions":[13,25],"one":[15],"variable":[16],"with":[17],"some":[18],"their":[20],"properties,":[21],"and":[22,34,62],"lists":[23],"corresponding":[26],"to":[27],"various":[28],"properties":[29],"sum,":[31],"product,":[32],"implication,":[33],"equivalence.":[35],"range":[37],"variables":[40],"as":[41,43,73],"well":[42],"that":[44],"functional":[46],"values":[47],"will":[48,79],"be":[49,80],"\u043e":[50],"(false),":[51],"\u00bd,":[52],"1":[53],"(true).":[54],"As":[55],"an":[56],"application":[57],"consider":[59],"Frege's,":[60],"Russell's":[61],"Heyting's":[63],"systems":[64],"in":[65],"ternary":[66],"logic.":[67],"proofs":[69],"are":[70],"mostly":[71],"omitted":[72],"obvious":[74],"if":[75],"sometimes":[76],"laborious.":[77],"Functions":[78],"denned":[81],"by":[82],"matrices:":[83],"e.g.":[84],"F(p,":[85],"q)":[86]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}
