{"id":"https://openalex.org/W2526342011","doi":"https://doi.org/10.15439/2016f520","title":"On algebraic hierarchies in mathematical repository of Mizar","display_name":"On algebraic hierarchies in mathematical repository of Mizar","publication_year":2016,"publication_date":"2016-10-02","ids":{"openalex":"https://openalex.org/W2526342011","doi":"https://doi.org/10.15439/2016f520","mag":"2526342011"},"language":"en","primary_location":{"id":"doi:10.15439/2016f520","is_oa":true,"landing_page_url":"https://doi.org/10.15439/2016f520","pdf_url":"https://annals-csis.org/proceedings/2016/pliks/520.pdf","source":{"id":"https://openalex.org/S4220651875","display_name":"Annals of Computer Science and Information Systems","issn_l":"2300-5963","issn":["2300-5963"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":"https://openalex.org/P4310317484","host_organization_name":"Polskie Towarzystwo Informatyczne","host_organization_lineage":["https://openalex.org/P4310317484"],"host_organization_lineage_names":["Polskie Towarzystwo Informatyczne"],"type":"conference"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Computer Science and Information Systems","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://annals-csis.org/proceedings/2016/pliks/520.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073856205","display_name":"Adam Grabowski","orcid":"https://orcid.org/0000-0001-5026-3990"},"institutions":[{"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 Informatics University of Biaystok ul. Ciokowskiego 1 M, 15-245 Biaystok, Poland","Institute of Informatics University of Bia\u0142ystok ul. Cio\u0142kowskiego 1 M, 15-245 Bia\u0142ystok, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Informatics University of Biaystok ul. Ciokowskiego 1 M, 15-245 Biaystok, Poland","institution_ids":["https://openalex.org/I245364917"]},{"raw_affiliation_string":"Institute of Informatics University of Bia\u0142ystok ul. Cio\u0142kowskiego 1 M, 15-245 Bia\u0142ystok, Poland","institution_ids":["https://openalex.org/I245364917"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090121372","display_name":"Artur Korni\u0142owicz","orcid":"https://orcid.org/0000-0002-4565-9082"},"institutions":[{"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":"Artur Kornilowicz","raw_affiliation_strings":["Institute of Informatics University of Bia\u0142ystok ul. Cio\u0142kowskiego 1 M, 15-245 Bia\u0142ystok, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Informatics University of Bia\u0142ystok ul. Cio\u0142kowskiego 1 M, 15-245 Bia\u0142ystok, Poland","institution_ids":["https://openalex.org/I245364917"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048465549","display_name":"Christoph Schwarzweller","orcid":"https://orcid.org/0000-0001-9587-8737"},"institutions":[{"id":"https://openalex.org/I40413290","display_name":"University of Gda\u0144sk","ror":"https://ror.org/011dv8m48","country_code":"PL","type":"education","lineage":["https://openalex.org/I40413290"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Christoph Schwarzweller","raw_affiliation_strings":["Department of Computer Science University of Gdask Wita Stwosza 57, 80-952 Gdask, Poland","Department of Computer Science University of Gda\u0144sk Wita Stwosza 57, 80-952 Gda\u0144sk, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science University of Gdask Wita Stwosza 57, 80-952 Gdask, Poland","institution_ids":["https://openalex.org/I40413290"]},{"raw_affiliation_string":"Department of Computer Science University of Gda\u0144sk Wita Stwosza 57, 80-952 Gda\u0144sk, Poland","institution_ids":["https://openalex.org/I40413290"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5090121372"],"corresponding_institution_ids":["https://openalex.org/I245364917"],"apc_list":null,"apc_paid":null,"fwci":5.0405,"has_fulltext":true,"cited_by_count":40,"citation_normalized_percentile":{"value":0.96213877,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"8","issue":null,"first_page":"363","last_page":"371"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9973999857902527,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9973999857902527,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9959999918937683,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9749000072479248,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6884125471115112},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.6505331993103027},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.6114567518234253},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.45719611644744873},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4392518997192383},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.23691722750663757},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.15211692452430725}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6884125471115112},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.6505331993103027},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.6114567518234253},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.45719611644744873},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4392518997192383},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.23691722750663757},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.15211692452430725},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.15439/2016f520","is_oa":true,"landing_page_url":"https://doi.org/10.15439/2016f520","pdf_url":"https://annals-csis.org/proceedings/2016/pliks/520.pdf","source":{"id":"https://openalex.org/S4220651875","display_name":"Annals of Computer Science and Information Systems","issn_l":"2300-5963","issn":["2300-5963"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":"https://openalex.org/P4310317484","host_organization_name":"Polskie Towarzystwo Informatyczne","host_organization_lineage":["https://openalex.org/P4310317484"],"host_organization_lineage_names":["Polskie Towarzystwo Informatyczne"],"type":"conference"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Computer Science and Information Systems","raw_type":"proceedings-article"},{"id":"pmh:oai:doaj.org/article:93bcc28f10c04c50a695d661bdd30c63","is_oa":true,"landing_page_url":"https://doaj.org/article/93bcc28f10c04c50a695d661bdd30c63","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"Annals of computer science and information systems, Vol 8, Pp 363-371 (2016)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.15439/2016f520","is_oa":true,"landing_page_url":"https://doi.org/10.15439/2016f520","pdf_url":"https://annals-csis.org/proceedings/2016/pliks/520.pdf","source":{"id":"https://openalex.org/S4220651875","display_name":"Annals of Computer Science and Information Systems","issn_l":"2300-5963","issn":["2300-5963"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":"https://openalex.org/P4310317484","host_organization_name":"Polskie Towarzystwo Informatyczne","host_organization_lineage":["https://openalex.org/P4310317484"],"host_organization_lineage_names":["Polskie Towarzystwo Informatyczne"],"type":"conference"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Computer Science and Information Systems","raw_type":"proceedings-article"},"sustainable_development_goals":[{"score":0.5699999928474426,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2526342011.pdf","grobid_xml":"https://content.openalex.org/works/W2526342011.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W826005707","https://openalex.org/W959889677","https://openalex.org/W1245804045","https://openalex.org/W1486157587","https://openalex.org/W1532290481","https://openalex.org/W1768814311","https://openalex.org/W1778672286","https://openalex.org/W1789208025","https://openalex.org/W1924950049","https://openalex.org/W1938825438","https://openalex.org/W1945317924","https://openalex.org/W1963457827","https://openalex.org/W1968315351","https://openalex.org/W1999680561","https://openalex.org/W2013140497","https://openalex.org/W2053634551","https://openalex.org/W2060832326","https://openalex.org/W2062563895","https://openalex.org/W2128085487","https://openalex.org/W2130628061","https://openalex.org/W2146945204","https://openalex.org/W2147609833","https://openalex.org/W2165764163","https://openalex.org/W2184838578","https://openalex.org/W2293507108","https://openalex.org/W2295728669","https://openalex.org/W2326370346","https://openalex.org/W2588251761","https://openalex.org/W3104322198","https://openalex.org/W4231714022","https://openalex.org/W4238623226","https://openalex.org/W6959456255"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278","https://openalex.org/W2350741829","https://openalex.org/W2530322880","https://openalex.org/W1596801655","https://openalex.org/W2359140296"],"abstract_inverted_index":{"Mathematics,":[0],"especially":[1],"algebra,":[2],"uses":[3],"plenty":[4],"of":[5,18,24,55,90],"structures:":[6],"groups,":[7],"rings,":[8],"integral":[9],"domains,":[10],"fields,":[11],"vector":[12],"spaces":[13],"to":[14,34],"name":[15],"a":[16,52,77],"few":[17],"the":[19,63,67,91],"most":[20],"basic":[21],"ones.":[22],"Classes":[23],"structures":[25],"are":[26],"closely":[27],"connected":[28],"-usually":[29],"by":[30],"inclusion":[31],"-naturally":[32],"leading":[33],"hierarchies":[35,59],"that":[36,81],"has":[37,82],"been":[38,83],"reproduced":[39],"in":[40,43,66,85],"different":[41,44],"forms":[42],"mathematical":[45,111],"repositories.":[46],"In":[47,73],"this":[48],"paper":[49],"we":[50,75,103],"give":[51],"brief":[53],"overview":[54],"some":[56],"existing":[57],"algebraic":[58,79],"and":[60,87],"report":[61],"on":[62],"latest":[64],"developments":[65],"Mizar":[68,86],"computerized":[69],"proof":[70],"assistant":[71],"system.":[72],"particular":[74],"present":[76],"detailed":[78],"hierarchy":[80,92],"defined":[84],"discuss":[88],"extensions":[89],"towards":[93],"more":[94],"involved":[95],"domains.":[96],"Taking":[97],"fully":[98],"formal":[99],"approach":[100],"into":[101],"account":[102],"meet":[104],"new":[105],"difficulties":[106],"comparing":[107],"with":[108],"its":[109],"informal":[110],"framework.":[112]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":10}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
