{"id":"https://openalex.org/W2091634131","doi":"https://doi.org/10.1080/00207169908804810","title":"Boolean embedding from a partially ordered structure to a boolean algebra","display_name":"Boolean embedding from a partially ordered structure to a boolean algebra","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W2091634131","doi":"https://doi.org/10.1080/00207169908804810","mag":"2091634131"},"language":"en","primary_location":{"id":"doi:10.1080/00207169908804810","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169908804810","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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/A5015005709","display_name":"Jinsei Yamaguchi","orcid":null},"institutions":[{"id":"https://openalex.org/I41802502","display_name":"Kanagawa University","ror":"https://ror.org/02j6c0d67","country_code":"JP","type":"education","lineage":["https://openalex.org/I41802502"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Jinsei Yamaguchi","raw_affiliation_strings":["\n Department of Information and Computer Sciences, Kanagawa University, Hiratsuka, Kanagawa, 259\u20131293, Japan","Department of Information and Computer Sciences, Kanagawa University, Hiratsuka, Kanagawa, 259\u20131293, Japan"],"affiliations":[{"raw_affiliation_string":"\n Department of Information and Computer Sciences, Kanagawa University, Hiratsuka, Kanagawa, 259\u20131293, Japan","institution_ids":["https://openalex.org/I41802502"]},{"raw_affiliation_string":"Department of Information and Computer Sciences, Kanagawa University, Hiratsuka, Kanagawa, 259\u20131293, Japan","institution_ids":["https://openalex.org/I41802502"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5015005709"],"corresponding_institution_ids":["https://openalex.org/I41802502"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.21702668,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"71","issue":"3","first_page":"301","last_page":"317"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9948999881744385,"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":0.9948999881744385,"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/T11072","display_name":"Peroxisome Proliferator-Activated Receptors","score":0.9387999773025513,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9211000204086304,"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/mathematics","display_name":"Mathematics","score":0.8224406838417053},{"id":"https://openalex.org/keywords/complete-boolean-algebra","display_name":"Complete Boolean algebra","score":0.7148401737213135},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.6815758943557739},{"id":"https://openalex.org/keywords/stones-representation-theorem-for-boolean-algebras","display_name":"Stone's representation theorem for Boolean algebras","score":0.630605161190033},{"id":"https://openalex.org/keywords/boolean-algebra","display_name":"Boolean algebra","score":0.5744430422782898},{"id":"https://openalex.org/keywords/two-element-boolean-algebra","display_name":"Two-element Boolean algebra","score":0.5487972497940063},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.543209969997406},{"id":"https://openalex.org/keywords/free-boolean-algebra","display_name":"Free Boolean algebra","score":0.5420390963554382},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5157065987586975},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.4703308045864105},{"id":"https://openalex.org/keywords/boolean-algebras-canonically-defined","display_name":"Boolean algebras canonically defined","score":0.4700191020965576},{"id":"https://openalex.org/keywords/natural-number","display_name":"Natural number","score":0.4591732323169708},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.43174025416374207},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.42296427488327026},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.26047414541244507},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.24280565977096558},{"id":"https://openalex.org/keywords/algebra-representation","display_name":"Algebra representation","score":0.07765510678291321},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.05994457006454468}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8224406838417053},{"id":"https://openalex.org/C81518389","wikidata":"https://www.wikidata.org/wiki/Q5156447","display_name":"Complete Boolean algebra","level":5,"score":0.7148401737213135},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.6815758943557739},{"id":"https://openalex.org/C10021369","wikidata":"https://www.wikidata.org/wiki/Q1166774","display_name":"Stone's representation theorem for Boolean algebras","level":5,"score":0.630605161190033},{"id":"https://openalex.org/C39685927","wikidata":"https://www.wikidata.org/wiki/Q173183","display_name":"Boolean algebra","level":2,"score":0.5744430422782898},{"id":"https://openalex.org/C207764348","wikidata":"https://www.wikidata.org/wiki/Q7858706","display_name":"Two-element Boolean algebra","level":4,"score":0.5487972497940063},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.543209969997406},{"id":"https://openalex.org/C188159880","wikidata":"https://www.wikidata.org/wiki/Q5499761","display_name":"Free Boolean algebra","level":5,"score":0.5420390963554382},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5157065987586975},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.4703308045864105},{"id":"https://openalex.org/C45503250","wikidata":"https://www.wikidata.org/wiki/Q4943350","display_name":"Boolean algebras canonically defined","level":5,"score":0.4700191020965576},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.4591732323169708},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.43174025416374207},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.42296427488327026},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.26047414541244507},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.24280565977096558},{"id":"https://openalex.org/C14394260","wikidata":"https://www.wikidata.org/wiki/Q4723980","display_name":"Algebra representation","level":3,"score":0.07765510678291321},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.05994457006454468},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/00207169908804810","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169908804810","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.632.2352","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.632.2352","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.int2.info/papers/Boolean Embedding.pdf","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/W1553920270"],"related_works":["https://openalex.org/W2940617399","https://openalex.org/W2037090414","https://openalex.org/W2369221237","https://openalex.org/W4256012180","https://openalex.org/W2064028328","https://openalex.org/W2377493875","https://openalex.org/W2377302330","https://openalex.org/W2349635818","https://openalex.org/W176883546","https://openalex.org/W4243997191"],"abstract_inverted_index":{"We":[0],"prove":[1],"the":[2,46,104,108,116,132],"following":[3],"theorem.":[4],"Theorem":[5],"Let\uff08\uff30,\u2266\uff09be":[6],"an":[7,97,112],"arbitrary":[8],"partially":[9,121],"ordered":[10,122],"structure.":[11],"Then,":[12],"there":[13],"is":[14,25,52,55,60],"a":[15,26,80,85],"canonical":[16],"embedding":[17,105],"(1:1,":[18],"order-preserving":[19],"map)":[20],"\uff45\uff1a\uff08\uff30,\u2266\uff09\u2192":[21],"such":[22],"that":[23,115],"(i).":[24],"complete":[27],"Boolean":[28],"algebra.":[29],"(ii).":[30],"(\u2200p,q\u2208\uff30)(p":[31],"and":[32,137],"q":[33],"are":[34,139],"compatible":[35],"\u2192\uff45(p)\u2227\uff45(q)":[36],"\u2260)":[37],"(iii).":[38],"{\uff45(p)\uff5cp\u2208\uff30}":[39],"satisfies":[40],"\u201ca":[41],"small":[42],"property":[43],"\u201d":[44],"in":[45,68,81,88],"sense":[47],"that;":[48],"(a)":[49],"If":[50,58],"\uff30":[51,59],"finite,":[53,94],"then":[54,62],"finite.":[56],"(b)":[57],"infinite,":[61],"for":[63,76],"any":[64,77],"infinite":[65],"branch":[66],"l":[67],"\uff0d":[69,89],"{},":[70],"(":[71],"\u2200":[72],"\u2208l)(\u2203q\u2208\uff30)(\uff45(q)":[73],"\u2266).":[74],"(c)":[75],"minimal":[78,86],"element":[79,87],"\uff30,":[82],"\uff45(a)":[83],"becomes":[84],"{}.":[90],"\u25a1":[91],"Especially,":[92],"when\uff08\uff30,\u2266\uff09is":[93],"we":[95,110],"give":[96],"algorithm":[98],"called":[99],"\u201cthe":[100],"Normal":[101],"Separativization\u201dwhich":[102],"realize":[103],"\uff45.":[106],"As":[107],"byproduct,":[109],"obtain":[111],"interesting":[113],"insight":[114],"set":[117],"of":[118,131],"all":[119],"finite":[120],"structures":[123],"can":[124],"be":[125],"classified":[126],"to":[127],"categories":[128],"called\u201cBoolean":[129],"complexity":[130],"type":[133],"(n,m)\u201d,":[134],"where":[135],"n":[136],"m":[138],"natural":[140],"numbers.":[141]},"counts_by_year":[],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
