{"id":"https://openalex.org/W4285326919","doi":"https://doi.org/10.2478/forma-2021-0015","title":"Automatization of Ternary Boolean Algebras","display_name":"Automatization of Ternary Boolean Algebras","publication_year":2021,"publication_date":"2021-12-01","ids":{"openalex":"https://openalex.org/W4285326919","doi":"https://doi.org/10.2478/forma-2021-0015"},"language":"en","primary_location":{"id":"doi:10.2478/forma-2021-0015","is_oa":true,"landing_page_url":"https://doi.org/10.2478/forma-2021-0015","pdf_url":"https://www.sciendo.com/pdf/10.2478/forma-2021-0015","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.sciendo.com/pdf/10.2478/forma-2021-0015","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016610781","display_name":"Wojciech Ku\u015bmierowski","orcid":null},"institutions":[{"id":"https://openalex.org/I4210087266","display_name":"Institute of Computer Science","ror":"https://ror.org/003fvp964","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210087266","https://openalex.org/I99542240"]},{"id":"https://openalex.org/I245364917","display_name":"University of Bia\u0142ystok","ror":"https://ror.org/01qaqcf60","country_code":"PL","type":"education","lineage":["https://openalex.org/I245364917"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Wojciech Ku\u015bmierowski","raw_affiliation_strings":["Institute of Computer Science , University of Bia\u0142ystok , Cio\u0142kowskiego 1M, 15-245 Bia\u0142ystok , Poland"],"affiliations":[{"raw_affiliation_string":"Institute of Computer Science , University of Bia\u0142ystok , Cio\u0142kowskiego 1M, 15-245 Bia\u0142ystok , Poland","institution_ids":["https://openalex.org/I245364917","https://openalex.org/I4210087266"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073856205","display_name":"Adam Grabowski","orcid":"https://orcid.org/0000-0001-5026-3990"},"institutions":[{"id":"https://openalex.org/I4210087266","display_name":"Institute of Computer Science","ror":"https://ror.org/003fvp964","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210087266","https://openalex.org/I99542240"]},{"id":"https://openalex.org/I245364917","display_name":"University of Bia\u0142ystok","ror":"https://ror.org/01qaqcf60","country_code":"PL","type":"education","lineage":["https://openalex.org/I245364917"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Adam Grabowski","raw_affiliation_strings":["Institute of Computer Science , University of Bia\u0142ystok , Cio\u0142kowskiego 1M, 15-245 Bia\u0142ystok , Poland"],"affiliations":[{"raw_affiliation_string":"Institute of Computer Science , University of Bia\u0142ystok , Cio\u0142kowskiego 1M, 15-245 Bia\u0142ystok , Poland","institution_ids":["https://openalex.org/I245364917","https://openalex.org/I4210087266"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5016610781"],"corresponding_institution_ids":["https://openalex.org/I245364917","https://openalex.org/I4210087266"],"apc_list":null,"apc_paid":null,"fwci":0.1508,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.56788051,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"29","issue":"4","first_page":"153","last_page":"159"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9993000030517578,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9948999881744385,"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":0.6390702724456787},{"id":"https://openalex.org/keywords/two-element-boolean-algebra","display_name":"Two-element Boolean algebra","score":0.6096600890159607},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6004677414894104},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.5978183746337891},{"id":"https://openalex.org/keywords/boolean-algebra","display_name":"Boolean algebra","score":0.5963968634605408},{"id":"https://openalex.org/keywords/complete-boolean-algebra","display_name":"Complete Boolean algebra","score":0.5890800356864929},{"id":"https://openalex.org/keywords/stones-representation-theorem-for-boolean-algebras","display_name":"Stone's representation theorem for Boolean algebras","score":0.544762134552002},{"id":"https://openalex.org/keywords/boolean-algebras-canonically-defined","display_name":"Boolean algebras canonically defined","score":0.5201866626739502},{"id":"https://openalex.org/keywords/ternary-operation","display_name":"Ternary operation","score":0.5120430588722229},{"id":"https://openalex.org/keywords/free-boolean-algebra","display_name":"Free Boolean algebra","score":0.5113186836242676},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5071771144866943},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.44457608461380005},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4368094801902771},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.42778468132019043},{"id":"https://openalex.org/keywords/boolean-expression","display_name":"Boolean expression","score":0.4181172251701355},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.3967093527317047},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.31388169527053833},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.21675601601600647},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.139333575963974},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08442118763923645},{"id":"https://openalex.org/keywords/algebra-representation","display_name":"Algebra representation","score":0.0687083899974823}],"concepts":[{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.6390702724456787},{"id":"https://openalex.org/C207764348","wikidata":"https://www.wikidata.org/wiki/Q7858706","display_name":"Two-element Boolean algebra","level":4,"score":0.6096600890159607},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6004677414894104},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.5978183746337891},{"id":"https://openalex.org/C39685927","wikidata":"https://www.wikidata.org/wiki/Q173183","display_name":"Boolean algebra","level":2,"score":0.5963968634605408},{"id":"https://openalex.org/C81518389","wikidata":"https://www.wikidata.org/wiki/Q5156447","display_name":"Complete Boolean algebra","level":5,"score":0.5890800356864929},{"id":"https://openalex.org/C10021369","wikidata":"https://www.wikidata.org/wiki/Q1166774","display_name":"Stone's representation theorem for Boolean algebras","level":5,"score":0.544762134552002},{"id":"https://openalex.org/C45503250","wikidata":"https://www.wikidata.org/wiki/Q4943350","display_name":"Boolean algebras canonically defined","level":5,"score":0.5201866626739502},{"id":"https://openalex.org/C64452783","wikidata":"https://www.wikidata.org/wiki/Q1524945","display_name":"Ternary operation","level":2,"score":0.5120430588722229},{"id":"https://openalex.org/C188159880","wikidata":"https://www.wikidata.org/wiki/Q5499761","display_name":"Free Boolean algebra","level":5,"score":0.5113186836242676},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5071771144866943},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.44457608461380005},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4368094801902771},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.42778468132019043},{"id":"https://openalex.org/C158465420","wikidata":"https://www.wikidata.org/wiki/Q1979515","display_name":"Boolean expression","level":3,"score":0.4181172251701355},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.3967093527317047},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31388169527053833},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.21675601601600647},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.139333575963974},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08442118763923645},{"id":"https://openalex.org/C14394260","wikidata":"https://www.wikidata.org/wiki/Q4723980","display_name":"Algebra representation","level":3,"score":0.0687083899974823},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2478/forma-2021-0015","is_oa":true,"landing_page_url":"https://doi.org/10.2478/forma-2021-0015","pdf_url":"https://www.sciendo.com/pdf/10.2478/forma-2021-0015","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:repozytorium.uwb.edu.pl:11320/13651","is_oa":true,"landing_page_url":"http://hdl.handle.net/11320/13651","pdf_url":null,"source":{"id":"https://openalex.org/S4306400933","display_name":"The Repository of University in Bialystok (University in Bialystok)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210094198","host_organization_name":"University Clinical Hospital In Bialystok","host_organization_lineage":["https://openalex.org/I4210094198"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.2478/forma-2021-0015","is_oa":true,"landing_page_url":"https://doi.org/10.2478/forma-2021-0015","pdf_url":"https://www.sciendo.com/pdf/10.2478/forma-2021-0015","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4285326919.pdf","grobid_xml":"https://content.openalex.org/works/W4285326919.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1976520413","https://openalex.org/W2026094806","https://openalex.org/W2082915738","https://openalex.org/W2093397547","https://openalex.org/W2128085487","https://openalex.org/W2295728669","https://openalex.org/W2770430340","https://openalex.org/W3145098521","https://openalex.org/W4205529794","https://openalex.org/W4206606501","https://openalex.org/W4211016048","https://openalex.org/W4300748666"],"related_works":["https://openalex.org/W1974935489","https://openalex.org/W2094060015","https://openalex.org/W2143150930","https://openalex.org/W2349635818","https://openalex.org/W2357249222","https://openalex.org/W1507532953","https://openalex.org/W2148363933","https://openalex.org/W1496446432","https://openalex.org/W2138251320","https://openalex.org/W2134580212"],"abstract_inverted_index":{"Summary":[0],"The":[1,63,118],"main":[2,64],"aim":[3],"of":[4,17,31,46,56,73,80,88,96,107,114,140,143,150,162],"this":[5,47,71],"article":[6],"is":[7,51,66,77,131],"to":[8,23,84,180],"introduce":[9],"formally":[10],"ternary":[11,20],"Boolean":[12,33,60,89],"algebras":[13],"(TBAs)":[14],"in":[15,37,94,104,112,126,133,137,155],"terms":[16,95,113],"an":[18],"abstract":[19],"operation,":[21],"and":[22,100,128,146],"show":[24],"their":[25],"connection":[26],"with":[27,159],"the":[28,38,44,54,67,78,81,97,101,105,108,138,151,156,160],"ordinary":[29],"notion":[30],"a":[32],"algebra,":[34],"already":[35],"present":[36],"Mizar":[39,48,157],"Mathematical":[40],"Library":[41],"[2].":[42],"Essentially,":[43],"core":[45],"[1]":[49],"formalization":[50,106,130],"based":[52],"on":[53],"paper":[55],"A.A.":[57],"Grau":[58],"\u201cTernary":[59],"Algebras\u201d":[61],"[7].":[62],"result":[65],"single":[68],"axiom":[69],"for":[70,177],"class":[72],"lattices":[74],"[12].":[75],"This":[76],"continuation":[79],"articles":[82],"devoted":[83],"various":[85],"equivalent":[86],"axiomatizations":[87],"algebras:":[90],"following":[91],"Huntington":[92],"[8]":[93],"binary":[98],"sum":[99],"complementation":[102],"useful":[103],"Robbins":[109],"problem":[110],"[5],":[111],"Sheffer":[115],"stroke":[116],"[9].":[117],"classical":[119],"definition":[120],"([6],":[121],"[3])":[122],"can":[123,174],"be":[124,175],"found":[125],"[15]":[127],"its":[129],"described":[132],"[4].":[134],"Similarly":[135],"as":[136],"case":[139],"recent":[141],"formalizations":[142],"WA-lattices":[144],"[14]":[145],"quasilattices":[147],"[10],":[148],"some":[149],"results":[152],"were":[153],"proven":[154],"system":[158],"help":[161],"Prover9":[163],"[13],":[164],"[11]":[165],"proof":[166],"assistant,":[167],"so":[168],"proofs":[169],"are":[170],"quite":[171],"lengthy.":[172],"They":[173],"subject":[176],"subsequent":[178],"revisions":[179],"make":[181],"them":[182],"more":[183],"compact.":[184]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}