{"id":"https://openalex.org/W1974513041","doi":"https://doi.org/10.1142/s0218196704001785","title":"INVOLUTED SEMILATTICES AND UNCERTAINTY IN TERNARY ALGEBRAS","display_name":"INVOLUTED SEMILATTICES AND UNCERTAINTY IN TERNARY ALGEBRAS","publication_year":2004,"publication_date":"2004-06-01","ids":{"openalex":"https://openalex.org/W1974513041","doi":"https://doi.org/10.1142/s0218196704001785","mag":"1974513041"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196704001785","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196704001785","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","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/A5016883956","display_name":"Janusz Brzozowski","orcid":"https://orcid.org/0000-0003-3390-2767"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"J. A. BRZOZOWSKI","raw_affiliation_strings":["School of Computer Science, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1, Canada","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5016883956"],"corresponding_institution_ids":["https://openalex.org/I151746483"],"apc_list":null,"apc_paid":null,"fwci":0.3459,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.59405834,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"14","issue":"03","first_page":"295","last_page":"310"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9983000159263611,"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":0.9983000159263611,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.9843999743461609,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.9383999705314636,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/semilattice","display_name":"Semilattice","score":0.9897440671920776},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8716505765914917},{"id":"https://openalex.org/keywords/ternary-operation","display_name":"Ternary operation","score":0.677543580532074},{"id":"https://openalex.org/keywords/involution","display_name":"Involution (esoterism)","score":0.6299671530723572},{"id":"https://openalex.org/keywords/binary-operation","display_name":"Binary operation","score":0.4884306490421295},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4703916311264038},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.44697296619415283},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41678181290626526},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.37754517793655396},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.1617056131362915},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.05718308687210083}],"concepts":[{"id":"https://openalex.org/C132170107","wikidata":"https://www.wikidata.org/wiki/Q834585","display_name":"Semilattice","level":3,"score":0.9897440671920776},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8716505765914917},{"id":"https://openalex.org/C64452783","wikidata":"https://www.wikidata.org/wiki/Q1524945","display_name":"Ternary operation","level":2,"score":0.677543580532074},{"id":"https://openalex.org/C2781409172","wikidata":"https://www.wikidata.org/wiki/Q17056802","display_name":"Involution (esoterism)","level":3,"score":0.6299671530723572},{"id":"https://openalex.org/C185529760","wikidata":"https://www.wikidata.org/wiki/Q164307","display_name":"Binary operation","level":2,"score":0.4884306490421295},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4703916311264038},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.44697296619415283},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41678181290626526},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.37754517793655396},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.1617056131362915},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.05718308687210083},{"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/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218196704001785","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196704001785","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1975547774","https://openalex.org/W2049090131","https://openalex.org/W2049911511","https://openalex.org/W2086655170","https://openalex.org/W2789396085","https://openalex.org/W4235222319","https://openalex.org/W6607083367"],"related_works":["https://openalex.org/W755468446","https://openalex.org/W2111407784","https://openalex.org/W2963481928","https://openalex.org/W4210408227","https://openalex.org/W2275539153","https://openalex.org/W2044825552","https://openalex.org/W2072782595","https://openalex.org/W1974513041","https://openalex.org/W2102413253","https://openalex.org/W4226315300"],"abstract_inverted_index":{"An":[0,55],"involuted":[1,43,56],"semilattice":[2,8,57],"<S,\u2228,":[3,17,58],"-":[4,13,18,59,95,127],">":[5,19],"is":[6,65,97,129],"a":[7,53,98,103,116,130],"<S,\u2228>":[9],"with":[10,61,102],"an":[11],"involution":[12],":":[14],"S\u2192S,":[15],"i.e.,":[16],"satisfies":[20,72],"[Formula:":[21,25,108],"see":[22,26,109],"text],":[23,110],"and":[24,111],"text].":[27],"In":[28,38],"this":[29],"paper":[30],"we":[31,40,114],"study":[32],"the":[33],"properties":[34],"of":[35,47,50,52],"such":[36],"semilattices.":[37,79],"particular,":[39],"characterize":[41,76],"free":[42,77],"semilattices":[44,85],"in":[45],"terms":[46],"ordered":[48],"pairs":[49],"subsets":[51],"set.":[54],",1>":[60],"greatest":[62],"element":[63],"1":[64],"said":[66],"to":[67,88],"be":[68],"complemented":[69,78,84,131],"if":[70],"it":[71],"a\u2228\u0101=1.":[73],"We":[74,80],"also":[75],"next":[81],"show":[82],"that":[83],"are":[86],"related":[87],"ternary":[89,92],"algebras.":[90],"A":[91],"algebra":[93,101],"<T,+,*,":[94],",0,\u03d5,1>":[96],"de":[99],"Morgan":[100],"third":[104,117],"constant":[105],"\u03d5":[106],"satisfying":[107],"(a+\u0101)+\u03d5=a+\u0101.":[112],"If":[113],"define":[115],"binary":[118],"operation":[119],"\u2228":[120],"on":[121],"T":[122],"as":[123],"a\u2228b=a*b+(a+b)*\u03d5,":[124],"then":[125],"<T,\u2228,":[126],",\u03d5>":[128],"semilattice.":[132]},"counts_by_year":[{"year":2016,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}