{"id":"https://openalex.org/W3122440787","doi":"https://doi.org/10.1093/comjnl/bxab030","title":"Proof Automation in the Theory of Finite Sets and Finite Set Relation Algebra","display_name":"Proof Automation in the Theory of Finite Sets and Finite Set Relation Algebra","publication_year":2021,"publication_date":"2021-03-17","ids":{"openalex":"https://openalex.org/W3122440787","doi":"https://doi.org/10.1093/comjnl/bxab030","mag":"3122440787"},"language":"en","primary_location":{"id":"doi:10.1093/comjnl/bxab030","is_oa":false,"landing_page_url":"https://doi.org/10.1093/comjnl/bxab030","pdf_url":null,"source":{"id":"https://openalex.org/S44643521","display_name":"The Computer Journal","issn_l":"0010-4620","issn":["0010-4620","1460-2067"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Computer Journal","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2101.07700","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032325980","display_name":"Maximiliano Cristi\u00e1","orcid":"https://orcid.org/0000-0001-9163-2609"},"institutions":[{"id":"https://openalex.org/I4210109384","display_name":"Centro Internacional Franco-Argentino de Ciencias de la Informaci\u00f3n y de Sistemas","ror":"https://ror.org/02m19wv39","country_code":"AR","type":"facility","lineage":["https://openalex.org/I151201029","https://openalex.org/I21491767","https://openalex.org/I4141589","https://openalex.org/I4210107757","https://openalex.org/I4210109384","https://openalex.org/I4210123736","https://openalex.org/I4387155568"]},{"id":"https://openalex.org/I4141589","display_name":"National University of Rosario","ror":"https://ror.org/02tphfq59","country_code":"AR","type":"education","lineage":["https://openalex.org/I4141589"]}],"countries":["AR"],"is_corresponding":true,"raw_author_name":"Maximiliano Cristi\u00e1","raw_affiliation_strings":["Universidad Nacional de Rosario and CIFASIS , Pellegrini 250 - (2000) Rosario, Argentina","Universidad Nacional de Rosario and CIFASIS, Pellegrini 250 - (2000) Rosario, Argentina"],"affiliations":[{"raw_affiliation_string":"Universidad Nacional de Rosario and CIFASIS , Pellegrini 250 - (2000) Rosario, Argentina","institution_ids":["https://openalex.org/I4141589","https://openalex.org/I4210109384"]},{"raw_affiliation_string":"Universidad Nacional de Rosario and CIFASIS, Pellegrini 250 - (2000) Rosario, Argentina","institution_ids":["https://openalex.org/I4141589","https://openalex.org/I4210109384"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016418405","display_name":"Ricardo D. Katz","orcid":"https://orcid.org/0000-0002-6750-2692"},"institutions":[{"id":"https://openalex.org/I4210107757","display_name":"Centro Cient\u00edfico Tecn\u00f3logico - Rosario","ror":"https://ror.org/01qkxb782","country_code":"AR","type":"facility","lineage":["https://openalex.org/I151201029","https://openalex.org/I4210107757","https://openalex.org/I4210123736","https://openalex.org/I4387155568"]},{"id":"https://openalex.org/I4210109384","display_name":"Centro Internacional Franco-Argentino de Ciencias de la Informaci\u00f3n y de Sistemas","ror":"https://ror.org/02m19wv39","country_code":"AR","type":"facility","lineage":["https://openalex.org/I151201029","https://openalex.org/I21491767","https://openalex.org/I4141589","https://openalex.org/I4210107757","https://openalex.org/I4210109384","https://openalex.org/I4210123736","https://openalex.org/I4387155568"]}],"countries":["AR"],"is_corresponding":false,"raw_author_name":"Ricardo D Katz","raw_affiliation_strings":["CIFASIS-CONICET , Bv. 27 de febrero 210 bis - (2000) Rosario, Argentina","CIFASIS-CONICET, Bv.\u00a027 de febrero 210 bis, 2000 Rosario, Argentina"],"affiliations":[{"raw_affiliation_string":"CIFASIS-CONICET , Bv. 27 de febrero 210 bis - (2000) Rosario, Argentina","institution_ids":["https://openalex.org/I4210107757","https://openalex.org/I4210109384"]},{"raw_affiliation_string":"CIFASIS-CONICET, Bv.\u00a027 de febrero 210 bis, 2000 Rosario, Argentina","institution_ids":["https://openalex.org/I4210107757","https://openalex.org/I4210109384"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062894556","display_name":"Gianfranco Rossi","orcid":"https://orcid.org/0000-0002-6970-8790"},"institutions":[{"id":"https://openalex.org/I124601658","display_name":"University of Parma","ror":"https://ror.org/02k7wn190","country_code":"IT","type":"education","lineage":["https://openalex.org/I124601658"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Gianfranco Rossi","raw_affiliation_strings":["Universit\u00e0 di Parma , Parco Area delle Scienze, 53/A - 43100 PARMA, Italy","University of Parma"],"affiliations":[{"raw_affiliation_string":"Universit\u00e0 di Parma , Parco Area delle Scienze, 53/A - 43100 PARMA, Italy","institution_ids":["https://openalex.org/I124601658"]},{"raw_affiliation_string":"University of Parma","institution_ids":["https://openalex.org/I124601658"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5032325980"],"corresponding_institution_ids":["https://openalex.org/I4141589","https://openalex.org/I4210109384"],"apc_list":{"value":2635,"currency":"GBP","value_usd":3232},"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01548101,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"65","issue":"7","first_page":"1891","last_page":"1903"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9998000264167786,"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":0.9998000264167786,"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/T10142","display_name":"Formal Methods in Verification","score":0.9994999766349792,"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":0.9994000196456909,"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":0.7301644086837769},{"id":"https://openalex.org/keywords/automated-theorem-proving","display_name":"Automated theorem proving","score":0.7087152004241943},{"id":"https://openalex.org/keywords/proof-assistant","display_name":"Proof assistant","score":0.652743935585022},{"id":"https://openalex.org/keywords/relation-algebra","display_name":"Relation algebra","score":0.5869554877281189},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.551283597946167},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.5488118529319763},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5097596049308777},{"id":"https://openalex.org/keywords/satisfiability","display_name":"Satisfiability","score":0.5034579634666443},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.48752257227897644},{"id":"https://openalex.org/keywords/boolean-satisfiability-problem","display_name":"Boolean satisfiability problem","score":0.48702841997146606},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.4522441625595093},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.441048264503479},{"id":"https://openalex.org/keywords/automation","display_name":"Automation","score":0.43032407760620117},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.42939993739128113},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41517066955566406},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.31568944454193115},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.25526154041290283},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.15251386165618896},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10248318314552307}],"concepts":[{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.7301644086837769},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.7087152004241943},{"id":"https://openalex.org/C203265346","wikidata":"https://www.wikidata.org/wiki/Q11387554","display_name":"Proof assistant","level":3,"score":0.652743935585022},{"id":"https://openalex.org/C10282146","wikidata":"https://www.wikidata.org/wiki/Q5965969","display_name":"Relation algebra","level":5,"score":0.5869554877281189},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.551283597946167},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.5488118529319763},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5097596049308777},{"id":"https://openalex.org/C168773769","wikidata":"https://www.wikidata.org/wiki/Q1350299","display_name":"Satisfiability","level":2,"score":0.5034579634666443},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48752257227897644},{"id":"https://openalex.org/C6943359","wikidata":"https://www.wikidata.org/wiki/Q875276","display_name":"Boolean satisfiability problem","level":2,"score":0.48702841997146606},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.4522441625595093},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.441048264503479},{"id":"https://openalex.org/C115901376","wikidata":"https://www.wikidata.org/wiki/Q184199","display_name":"Automation","level":2,"score":0.43032407760620117},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.42939993739128113},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41517066955566406},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.31568944454193115},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.25526154041290283},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.15251386165618896},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10248318314552307},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C100899422","wikidata":"https://www.wikidata.org/wiki/Q5058347","display_name":"Cellular algebra","level":4,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C14394260","wikidata":"https://www.wikidata.org/wiki/Q4723980","display_name":"Algebra representation","level":3,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1093/comjnl/bxab030","is_oa":false,"landing_page_url":"https://doi.org/10.1093/comjnl/bxab030","pdf_url":null,"source":{"id":"https://openalex.org/S44643521","display_name":"The Computer Journal","issn_l":"0010-4620","issn":["0010-4620","1460-2067"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Computer Journal","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2101.07700","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2101.07700","pdf_url":"https://arxiv.org/pdf/2101.07700","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:ri.conicet.gov.ar:11336/182878","is_oa":true,"landing_page_url":"http://hdl.handle.net/11336/182878","pdf_url":null,"source":{"id":"https://openalex.org/S4306401400","display_name":"Conicet","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210104196","host_organization_name":"Centro Cient\u00edfico Tecnol\u00f3gico - Nordeste","host_organization_lineage":["https://openalex.org/I4210104196"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.2101.07700","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2101.07700","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"},{"id":"mag:3122440787","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2101.07700","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2101.07700","pdf_url":"https://arxiv.org/pdf/2101.07700","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W3122440787.pdf"},"referenced_works_count":45,"referenced_works":["https://openalex.org/W62808609","https://openalex.org/W177306140","https://openalex.org/W836255558","https://openalex.org/W1497011154","https://openalex.org/W1497965065","https://openalex.org/W1553511155","https://openalex.org/W1559870885","https://openalex.org/W1561838277","https://openalex.org/W1573992413","https://openalex.org/W1780472831","https://openalex.org/W1807555267","https://openalex.org/W1895387792","https://openalex.org/W1900292471","https://openalex.org/W2022589543","https://openalex.org/W2022846948","https://openalex.org/W2027319813","https://openalex.org/W2064441356","https://openalex.org/W2106192381","https://openalex.org/W2144973245","https://openalex.org/W2172550627","https://openalex.org/W2497399989","https://openalex.org/W2549482841","https://openalex.org/W2587613907","https://openalex.org/W2735882127","https://openalex.org/W2792493843","https://openalex.org/W2801704253","https://openalex.org/W2893343347","https://openalex.org/W2895766200","https://openalex.org/W2939708371","https://openalex.org/W3003901859","https://openalex.org/W3046152566","https://openalex.org/W3082413280","https://openalex.org/W3208325358","https://openalex.org/W4254354208","https://openalex.org/W6607122937","https://openalex.org/W6623458269","https://openalex.org/W6629521785","https://openalex.org/W6631438910","https://openalex.org/W6637837010","https://openalex.org/W6638306832","https://openalex.org/W6639770882","https://openalex.org/W6685162135","https://openalex.org/W6741128425","https://openalex.org/W6751114381","https://openalex.org/W6754916089"],"related_works":["https://openalex.org/W260563712","https://openalex.org/W1600661924","https://openalex.org/W3183065824","https://openalex.org/W1516832052","https://openalex.org/W2152128484","https://openalex.org/W2073911647","https://openalex.org/W2038861555","https://openalex.org/W109827950","https://openalex.org/W2387368775","https://openalex.org/W1752849388","https://openalex.org/W1598448873","https://openalex.org/W1836725053","https://openalex.org/W1967592514","https://openalex.org/W1987466669","https://openalex.org/W117725373","https://openalex.org/W2229132677","https://openalex.org/W2075268055","https://openalex.org/W2013572173","https://openalex.org/W2008288068","https://openalex.org/W2778694581"],"abstract_inverted_index":{"Abstract":[0],"$\\{log\\}$":[1,35,59,97],"(\u2018setlog\u2019)":[2],"is":[3,36,79],"a":[4,41,67,82,93,103,126],"satisfiability":[5],"solver":[6],"for":[7,32],"formulas":[8],"of":[9,12,43,49,76,96,106,134],"the":[10,119,130,135],"theory":[11],"finite":[13,16],"sets":[14],"and":[15,121,132],"set":[17],"relation":[18],"algebra":[19],"(FS&amp;RA).":[20],"As":[21],"such,":[22],"it":[23],"can":[24,63,101],"be":[25,64],"used":[26],"as":[27],"an":[28],"automated":[29],"theorem":[30,85],"prover":[31,86],"this":[33,77],"theory.":[34],"able":[37],"to":[38,80,139],"automatically":[39,61,70],"prove":[40,62],"number":[42],"FS&amp;RA":[44],"theorems,":[45],"but":[46],"not":[47],"all":[48],"them.":[50],"Nevertheless,":[51],"we":[52],"have":[53],"observed":[54],"that":[55,58,92],"many":[56],"theorems":[57,117],"cannot":[60],"divided":[65],"into":[66,98],"few":[68],"subgoals":[69],"dischargeable":[71],"by":[72],"$\\{log\\}$.":[73],"The":[74],"purpose":[75],"work":[78],"present":[81],"prototype":[83],"interactive":[84],"(ITP),":[87],"called":[88],"$\\{log\\}$-ITP,":[89],"providing":[90],"evidence":[91],"proper":[94],"integration":[95],"world-class":[99],"ITP\u2019s":[100],"deliver":[102],"great":[104],"deal":[105],"proof":[107],"automation":[108],"concerning":[109],"FS&amp;RA.":[110],"An":[111],"empirical":[112],"evaluation":[113],"based":[114],"on":[115],"210":[116],"from":[118],"TPTP":[120],"Coq\u2019s":[122],"SSReflect":[123],"libraries":[124],"shows":[125],"noticeable":[127],"reduction":[128],"in":[129],"size":[131],"complexity":[133],"proofs":[136],"with":[137],"respect":[138],"Coq.":[140]},"counts_by_year":[],"updated_date":"2026-03-21T08:13:44.787528","created_date":"2022-07-25T00:00:00"}
