{"id":"https://openalex.org/W2010924417","doi":"https://doi.org/10.1016/s1571-0661(05)80265-8","title":"From Set-theoretic Coinduction to Coalgebraic Coinduction: some results, some problems","display_name":"From Set-theoretic Coinduction to Coalgebraic Coinduction: some results, some problems","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W2010924417","doi":"https://doi.org/10.1016/s1571-0661(05)80265-8","mag":"2010924417"},"language":"en","primary_location":{"id":"doi:10.1016/s1571-0661(05)80265-8","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s1571-0661(05)80265-8","pdf_url":null,"source":{"id":"https://openalex.org/S50368787","display_name":"Electronic Notes in Theoretical Computer Science","issn_l":"1571-0661","issn":["1571-0661"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Notes in Theoretical Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.1016/s1571-0661(05)80265-8","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111459665","display_name":"Marina Lenisa","orcid":null},"institutions":[{"id":"https://openalex.org/I98677209","display_name":"University of Edinburgh","ror":"https://ror.org/01nrxwf90","country_code":"GB","type":"education","lineage":["https://openalex.org/I98677209"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Marina Lenisa","raw_affiliation_strings":["Laboratory for the Foundations of Computer Science University of Edinburgh, Scotland","Laboratory for the Foundations of Computer Science, University of Edinburgh, Scotland"],"affiliations":[{"raw_affiliation_string":"Laboratory for the Foundations of Computer Science University of Edinburgh, Scotland","institution_ids":[]},{"raw_affiliation_string":"Laboratory for the Foundations of Computer Science, University of Edinburgh, Scotland","institution_ids":["https://openalex.org/I98677209"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5111459665"],"corresponding_institution_ids":["https://openalex.org/I98677209"],"apc_list":null,"apc_paid":null,"fwci":1.0389,"has_fulltext":false,"cited_by_count":33,"citation_normalized_percentile":{"value":0.8147098,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"19","issue":null,"first_page":"2","last_page":"22"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9990000128746033,"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":0.9990000128746033,"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":0.9916999936103821,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9837999939918518,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/coinduction","display_name":"Coinduction","score":0.8167277574539185},{"id":"https://openalex.org/keywords/coalgebra","display_name":"Coalgebra","score":0.8062341809272766},{"id":"https://openalex.org/keywords/bisimulation","display_name":"Bisimulation","score":0.6817520260810852},{"id":"https://openalex.org/keywords/categorical-variable","display_name":"Categorical variable","score":0.6210068464279175},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6115161180496216},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5765340328216553},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4932085871696472},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.4904892146587372},{"id":"https://openalex.org/keywords/morphism","display_name":"Morphism","score":0.43650686740875244},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3911551833152771},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32899391651153564},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.28432098031044006},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.19706106185913086},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.1261424720287323},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.0595325231552124}],"concepts":[{"id":"https://openalex.org/C40220748","wikidata":"https://www.wikidata.org/wiki/Q4227156","display_name":"Coinduction","level":3,"score":0.8167277574539185},{"id":"https://openalex.org/C2778249326","wikidata":"https://www.wikidata.org/wiki/Q1777803","display_name":"Coalgebra","level":3,"score":0.8062341809272766},{"id":"https://openalex.org/C135315306","wikidata":"https://www.wikidata.org/wiki/Q866364","display_name":"Bisimulation","level":2,"score":0.6817520260810852},{"id":"https://openalex.org/C5274069","wikidata":"https://www.wikidata.org/wiki/Q2285707","display_name":"Categorical variable","level":2,"score":0.6210068464279175},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6115161180496216},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5765340328216553},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4932085871696472},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.4904892146587372},{"id":"https://openalex.org/C137212723","wikidata":"https://www.wikidata.org/wiki/Q1948412","display_name":"Morphism","level":2,"score":0.43650686740875244},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3911551833152771},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32899391651153564},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.28432098031044006},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.19706106185913086},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.1261424720287323},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.0595325231552124},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1016/s1571-0661(05)80265-8","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s1571-0661(05)80265-8","pdf_url":null,"source":{"id":"https://openalex.org/S50368787","display_name":"Electronic Notes in Theoretical Computer Science","issn_l":"1571-0661","issn":["1571-0661"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Notes in Theoretical Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.35.2865","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.35.2865","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.dimi.uniud.it/~lenisa/Papers/Soft-copy-ps/tcs00.ps.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.48.9395","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.48.9395","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.dimi.uniud.it/~lenisa/Papers/Compressed-ps/tec2.ps.gz","raw_type":"text"},{"id":"pmh:oai:air.uniud.it:11390/683430","is_oa":false,"landing_page_url":"http://hdl.handle.net/11390/683430","pdf_url":null,"source":{"id":"https://openalex.org/S4306401163","display_name":"Institutional Research Information System (University of Udine)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I129043915","host_organization_name":"University of Udine","host_organization_lineage":["https://openalex.org/I129043915"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":{"id":"doi:10.1016/s1571-0661(05)80265-8","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s1571-0661(05)80265-8","pdf_url":null,"source":{"id":"https://openalex.org/S50368787","display_name":"Electronic Notes in Theoretical Computer Science","issn_l":"1571-0661","issn":["1571-0661"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Notes in Theoretical Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W102335877","https://openalex.org/W1482240164","https://openalex.org/W1488482916","https://openalex.org/W1493647767","https://openalex.org/W1511902564","https://openalex.org/W1537282122","https://openalex.org/W1548548072","https://openalex.org/W1561011284","https://openalex.org/W1578809538","https://openalex.org/W1814429312","https://openalex.org/W1872588449","https://openalex.org/W1907364945","https://openalex.org/W2001748564","https://openalex.org/W2024873396","https://openalex.org/W2039697589","https://openalex.org/W2060852846","https://openalex.org/W2070034419","https://openalex.org/W2101032471","https://openalex.org/W2106530373","https://openalex.org/W2111858237","https://openalex.org/W2128932399","https://openalex.org/W2155137194","https://openalex.org/W2156829867","https://openalex.org/W2613512071","https://openalex.org/W6630359976","https://openalex.org/W6633548484","https://openalex.org/W6638778330","https://openalex.org/W7064762959"],"related_works":["https://openalex.org/W2463782052","https://openalex.org/W1541732450","https://openalex.org/W2518082944","https://openalex.org/W1488076266","https://openalex.org/W2046125821","https://openalex.org/W1562440999","https://openalex.org/W2603068949","https://openalex.org/W2126431612","https://openalex.org/W2156829867","https://openalex.org/W4246668894"],"abstract_inverted_index":{"We":[0,81],"investigate":[1,51],"the":[2,5,16,31,36,52,57,70,78],"relation":[3],"between":[4,54],"set-theoretical":[6,89],"description":[7,18],"of":[8,19,30,38,77,93,95],"coinduction":[9,20,32],"based":[10,21],"on":[11,22],"Tarski":[12],"Fixpoint":[13],"Theorem,":[14],"and":[15,42,56],"categorical":[17,45],"coalgebras.":[23],"In":[24],"particular,":[25],"we":[26,43,50],"introduce":[27],"set-theoretic":[28,96],"generalizations":[29],"proof":[33],"principle,":[34],"in":[35],"spirit":[37],"Milner's":[39],"bisimulation":[40],"\u201cup-to\u201d,":[41],"discuss":[44],"counterparts":[46],"for":[47],"these.":[48],"Moreover,":[49],"connection":[53],"these":[55],"equivalences":[58],"induced":[59],"by":[60],"T-coiterative":[61],"functions.":[62],"These":[63],"are":[64,108],"morphisms":[65],"into":[66],"final":[67],"coalgebras,":[68],"satisfying":[69],"T-coiteration":[71],"scheme,":[72],"which":[73,98],"is":[74],"a":[75],"generalization":[76],"corecursion":[79],"scheme.":[80],"show":[82],"how":[83],"to":[84,101,105],"describe":[85],"coalgebraic":[86,106],"F-bisimulations":[87],"as":[88],"ones.":[90],"A":[91],"list":[92],"examples":[94],"coinductions":[97],"appear":[99],"not":[100],"be":[102],"easily":[103],"amenable":[104],"terms":[107],"discussed.":[109]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
