{"id":"https://openalex.org/W3092732582","doi":"https://doi.org/10.1145/3404889","title":"Non-well-founded Proof Theory of Transitive Closure Logic","display_name":"Non-well-founded Proof Theory of Transitive Closure Logic","publication_year":2020,"publication_date":"2020-08-11","ids":{"openalex":"https://openalex.org/W3092732582","doi":"https://doi.org/10.1145/3404889","mag":"3092732582"},"language":"en","primary_location":{"id":"doi:10.1145/3404889","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3404889","pdf_url":null,"source":{"id":"https://openalex.org/S117153874","display_name":"ACM Transactions on Computational Logic","issn_l":"1529-3785","issn":["1529-3785","1557-945X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Computational Logic","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":null,"display_name":"Liron Cohen","orcid":"https://orcid.org/0000-0002-4271-9078"},"institutions":[{"id":"https://openalex.org/I124227911","display_name":"Ben-Gurion University of the Negev","ror":"https://ror.org/05tkyf982","country_code":"IL","type":"education","lineage":["https://openalex.org/I124227911"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Liron Cohen","raw_affiliation_strings":["Ben-Gurion University, Israel"],"raw_orcid":"https://orcid.org/0000-0002-4271-9078","affiliations":[{"raw_affiliation_string":"Ben-Gurion University, Israel","institution_ids":["https://openalex.org/I124227911"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056648657","display_name":"Reuben N. S. Rowe","orcid":"https://orcid.org/0000-0002-4271-9078"},"institutions":[{"id":"https://openalex.org/I184558857","display_name":"Royal Holloway University of London","ror":"https://ror.org/04g2vpn86","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I184558857"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Reuben N. S. Rowe","raw_affiliation_strings":["Royal Holloway, University of London, Egham, TW, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Royal Holloway, University of London, Egham, TW, UK","institution_ids":["https://openalex.org/I184558857"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9126,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.80786229,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"21","issue":"4","first_page":"1","last_page":"31"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":1.0,"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":1.0,"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":0.9998000264167786,"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":0.9993000030517578,"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/transitive-closure","display_name":"Transitive closure","score":0.8698998689651489},{"id":"https://openalex.org/keywords/finitary","display_name":"Finitary","score":0.6248255372047424},{"id":"https://openalex.org/keywords/higher-order-logic","display_name":"Higher-order logic","score":0.5401408076286316},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5316693782806396},{"id":"https://openalex.org/keywords/proof-theory","display_name":"Proof theory","score":0.5277676582336426},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.5247723460197449},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.5175772905349731},{"id":"https://openalex.org/keywords/first-order-logic","display_name":"First-order logic","score":0.45092839002609253},{"id":"https://openalex.org/keywords/transitive-relation","display_name":"Transitive relation","score":0.4406326115131378},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41282764077186584},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36941593885421753},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.36837488412857056},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.34144675731658936},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.34059226512908936},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.19286823272705078},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1916690468788147},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.08620354533195496}],"concepts":[{"id":"https://openalex.org/C128896722","wikidata":"https://www.wikidata.org/wiki/Q1501387","display_name":"Transitive closure","level":2,"score":0.8698998689651489},{"id":"https://openalex.org/C2778003309","wikidata":"https://www.wikidata.org/wiki/Q5450381","display_name":"Finitary","level":2,"score":0.6248255372047424},{"id":"https://openalex.org/C169896238","wikidata":"https://www.wikidata.org/wiki/Q1644136","display_name":"Higher-order logic","level":3,"score":0.5401408076286316},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5316693782806396},{"id":"https://openalex.org/C2318724","wikidata":"https://www.wikidata.org/wiki/Q852732","display_name":"Proof theory","level":3,"score":0.5277676582336426},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.5247723460197449},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.5175772905349731},{"id":"https://openalex.org/C100481476","wikidata":"https://www.wikidata.org/wiki/Q4055684","display_name":"First-order logic","level":2,"score":0.45092839002609253},{"id":"https://openalex.org/C191399111","wikidata":"https://www.wikidata.org/wiki/Q64861","display_name":"Transitive relation","level":2,"score":0.4406326115131378},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41282764077186584},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36941593885421753},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.36837488412857056},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.34144675731658936},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34059226512908936},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.19286823272705078},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1916690468788147},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.08620354533195496},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3404889","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3404889","pdf_url":null,"source":{"id":"https://openalex.org/S117153874","display_name":"ACM Transactions on Computational Logic","issn_l":"1529-3785","issn":["1529-3785","1557-945X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Computational Logic","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":24,"referenced_works":["https://openalex.org/W657401719","https://openalex.org/W1196275239","https://openalex.org/W1575501012","https://openalex.org/W1983496086","https://openalex.org/W1988083342","https://openalex.org/W1988449272","https://openalex.org/W1999823887","https://openalex.org/W2023808162","https://openalex.org/W2039977878","https://openalex.org/W2054834413","https://openalex.org/W2081739832","https://openalex.org/W2123056643","https://openalex.org/W2160331299","https://openalex.org/W2561675875","https://openalex.org/W2611853323","https://openalex.org/W2611879577","https://openalex.org/W2726021294","https://openalex.org/W2735988056","https://openalex.org/W2744665143","https://openalex.org/W2745268854","https://openalex.org/W2753717632","https://openalex.org/W2953665898","https://openalex.org/W3104826616","https://openalex.org/W4212983671"],"related_works":["https://openalex.org/W67269200","https://openalex.org/W2113317244","https://openalex.org/W2168681835","https://openalex.org/W56017028","https://openalex.org/W34477560","https://openalex.org/W1970719697","https://openalex.org/W3022749099","https://openalex.org/W1550770522","https://openalex.org/W2153439064","https://openalex.org/W31250260"],"abstract_inverted_index":{"Supporting":[0],"inductive":[1,50,60,78,172],"reasoning":[2,84],"is":[3,7,30,38,100,122],"an":[4,93,101,167],"essential":[5],"component":[6],"any":[8],"framework":[9,20],"of":[10,24,34,46,59,64,73,136],"use":[11],"in":[12],"computer":[13],"science.":[14],"To":[15,80],"do":[16],"so,":[17],"the":[18,62,71,83,107,114,119,125,130,134,137,154,164],"logical":[19],"must":[21],"extend":[22],"that":[23,37,118],"first-order":[25,35,47],"logic.":[26,115],"Transitive":[27],"closure":[28,68,88,139],"logic":[29,36,48],"a":[31,53,57,65],"known":[32],"extension":[33],"particularly":[39],"straightforward":[40],"to":[41,106,146,156],"automate.":[42],"While":[43],"other":[44],"extensions":[45],"with":[49],"definitions":[51],"are":[52],"priori":[54],"parametrized":[55],"by":[56],"set":[58],"definitions,":[61],"addition":[63],"single":[66],"transitive":[67,87,138],"operator":[69,140],"has":[70],"advantage":[72],"uniformly":[74],"capturing":[75],"all":[76],"finitary":[77],"definitions.":[79],"further":[81],"improve":[82],"techniques":[85],"for":[86,97,113,124,166,170],"logic,":[89],"we":[90],"here":[91],"present":[92],"infinitary":[94,120,158],"proof":[95,111],"system":[96,112,121,169],"it,":[98],"which":[99],"infinite":[102],"descent":[103],"\u2013style":[104],"counterpart":[105],"existing":[108],"(explicit":[109],"induction)":[110],"We":[116],"show":[117],"complete":[123,144],"standard":[126],"semantics":[127],"and":[128],"subsumes":[129],"explicit":[131],"system.":[132],"Moreover,":[133],"uniformity":[135],"allows":[141],"semantically":[142],"meaningful":[143],"restrictions":[145],"be":[147],"defined":[148],"using":[149],"simple":[150],"syntactic":[151],"criteria.":[152],"Consequently,":[153],"restriction":[155],"regular":[157],"(i.e.,":[159],"cyclic":[160],")":[161],"proofs":[162],"provides":[163],"basis":[165],"effective":[168],"automating":[171],"reasoning.":[173]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
