{"id":"https://openalex.org/W2554707563","doi":"https://doi.org/10.3233/fi-2016-1406","title":"Lattice Theory for Rough Sets \u2013 A Case Study with Mizar","display_name":"Lattice Theory for Rough Sets \u2013 A Case Study with Mizar","publication_year":2016,"publication_date":"2016-11-17","ids":{"openalex":"https://openalex.org/W2554707563","doi":"https://doi.org/10.3233/fi-2016-1406","mag":"2554707563"},"language":"en","primary_location":{"id":"doi:10.3233/fi-2016-1406","is_oa":false,"landing_page_url":"https://doi.org/10.3233/fi-2016-1406","pdf_url":null,"source":{"id":"https://openalex.org/S39012697","display_name":"Fundamenta Informaticae","issn_l":"0169-2968","issn":["0169-2968","1875-8681"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fundamenta Informaticae","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/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":true,"raw_author_name":"Adam Grabowski","raw_affiliation_strings":["Institute of Informatics, University of Bia\u0142ystok, Konstantego Cio\u0142kowskiego 1M, 15-245 Bia\u0142ystok, Poland"],"affiliations":[{"raw_affiliation_string":"Institute of Informatics, University of Bia\u0142ystok, Konstantego Cio\u0142kowskiego 1M, 15-245 Bia\u0142ystok, Poland","institution_ids":["https://openalex.org/I245364917"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5073856205"],"corresponding_institution_ids":["https://openalex.org/I245364917"],"apc_list":null,"apc_paid":null,"fwci":4.5301,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.9499538,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"147","issue":"2-3","first_page":"223","last_page":"240"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9993000030517578,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9993000030517578,"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/T10215","display_name":"Semantic Web and Ontologies","score":0.9922999739646912,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.973800003528595,"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/rough-set","display_name":"Rough set","score":0.81297767162323},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6374143958091736},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5465840697288513},{"id":"https://openalex.org/keywords/binary-relation","display_name":"Binary relation","score":0.534775972366333},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.533725917339325},{"id":"https://openalex.org/keywords/proof-assistant","display_name":"Proof assistant","score":0.5102138519287109},{"id":"https://openalex.org/keywords/complete-lattice","display_name":"Complete lattice","score":0.4320947527885437},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4036892354488373},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3508254885673523},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.32244014739990234},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.29967010021209717},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.28797250986099243},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.19274285435676575}],"concepts":[{"id":"https://openalex.org/C111012933","wikidata":"https://www.wikidata.org/wiki/Q3137210","display_name":"Rough set","level":2,"score":0.81297767162323},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6374143958091736},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5465840697288513},{"id":"https://openalex.org/C65180967","wikidata":"https://www.wikidata.org/wiki/Q130901","display_name":"Binary relation","level":2,"score":0.534775972366333},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.533725917339325},{"id":"https://openalex.org/C203265346","wikidata":"https://www.wikidata.org/wiki/Q11387554","display_name":"Proof assistant","level":3,"score":0.5102138519287109},{"id":"https://openalex.org/C201640847","wikidata":"https://www.wikidata.org/wiki/Q2362924","display_name":"Complete lattice","level":3,"score":0.4320947527885437},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4036892354488373},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3508254885673523},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.32244014739990234},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.29967010021209717},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.28797250986099243},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.19274285435676575},{"id":"https://openalex.org/C183992945","wikidata":"https://www.wikidata.org/wiki/Q2495574","display_name":"Universality (dynamical systems)","level":2,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/fi-2016-1406","is_oa":false,"landing_page_url":"https://doi.org/10.3233/fi-2016-1406","pdf_url":null,"source":{"id":"https://openalex.org/S39012697","display_name":"Fundamenta Informaticae","issn_l":"0169-2968","issn":["0169-2968","1875-8681"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fundamenta Informaticae","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W139714950","https://openalex.org/W826005707","https://openalex.org/W1150633565","https://openalex.org/W1494553505","https://openalex.org/W1510333080","https://openalex.org/W1530333737","https://openalex.org/W1535538569","https://openalex.org/W1556028890","https://openalex.org/W1557923305","https://openalex.org/W1589305208","https://openalex.org/W1602202955","https://openalex.org/W1789208025","https://openalex.org/W1855754411","https://openalex.org/W1933950199","https://openalex.org/W1938825438","https://openalex.org/W1983426508","https://openalex.org/W2045864901","https://openalex.org/W2055266411","https://openalex.org/W2060832326","https://openalex.org/W2089727912","https://openalex.org/W2103898608","https://openalex.org/W2128085487","https://openalex.org/W2161332902","https://openalex.org/W2247065077","https://openalex.org/W2295728669","https://openalex.org/W2912565176","https://openalex.org/W3100298706","https://openalex.org/W3101484944","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W4247436880","https://openalex.org/W2064989302","https://openalex.org/W1880323254","https://openalex.org/W4366967255","https://openalex.org/W2042475680","https://openalex.org/W1985759900","https://openalex.org/W1695035718","https://openalex.org/W2041596646","https://openalex.org/W2167108569","https://openalex.org/W2100155797"],"abstract_inverted_index":{"Rough":[0],"sets":[1,68,132],"offer":[2],"a":[3,103,111,116,142,147,168],"well-known":[4],"approach":[5,37],"to":[6,58,69,84,101,145],"incomplete":[7],"or":[8,79],"imprecise":[9],"data.":[10],"In":[11],"the":[12,28,33,71,93,119,150,172,179],"paper":[13,113],"I":[14,61,99],"briefly":[15],"report":[16],"how":[17],"this":[18],"framework":[19],"was":[20,140,165],"successfully":[21],"encoded":[22],"by":[23,115,133],"means":[24],"of":[25,27,49,66,73,95,154,157,178,182],"one":[26,177],"leading":[29],"computer":[30],"proof-assistants":[31],"in":[32,92,176],"world.":[34],"The":[35],"general":[36],"is":[38],"essentially":[39],"based":[40],"on":[41,63],"binary":[42],"relations,":[43],"and":[44,156],"all":[45,171],"natural":[46],"pro":[47],"perties":[48],"approximation":[50],"operators":[51],"can":[52],"be":[53,146],"obtained":[54],"via":[55],"adjectives":[56],"added":[57],"underlying":[59],"relations.":[60],"focus":[62],"lattice-theoretical":[64],"aspects":[65],"rough":[67,131,158],"enable":[70],"application":[72],"external":[74],"theorem":[75],"provers":[76],"like":[77],"EQP":[78],"Prover9":[80],"as":[81,83,110,167],"well":[82],"translate":[85],"them":[86],"into":[87],"TPTP":[88],"format":[89],"widely":[90],"recognized":[91],"world":[94],"automated":[96],"proof":[97],"search.":[98],"wanted":[100],"have":[102],"clearly":[104],"written,":[105],"possibly":[106],"formal,":[107],"although":[108],"informal":[109],"rule,":[112],"authored":[114],"specialist":[117],"from":[118],"discipline":[120],"another":[121],"than":[122],"lattice":[123],"theory.":[124],"It":[125],"appeared":[126],"that":[127],"Lattice":[128],"theory":[129],"for":[130,138,149],"Jouni":[134],"J\u00e4rvinen":[135],"(called":[136],"LTRS":[137],"short)":[139],"quite":[141],"reasonable":[143],"choice":[144],"testbed":[148],"current":[151],"formalisation":[152],"both":[153],"lattices":[155],"sets.":[159],"A":[160],"popular":[161],"computerised":[162],"proof-assistant":[163],"Mizar":[164,187],"used":[166],"tool,":[169],"hence":[170],"efforts":[173],"are":[174],"available":[175],"largest":[180],"repositories":[181],"computer-checked":[183],"mathematical":[184],"knowledge,":[185],"called":[186],"Mathematical":[188],"Library.":[189]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":8}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}