{"id":"https://openalex.org/W1502441045","doi":"https://doi.org/10.1007/3-540-36576-1_15","title":"The Converse of a Stochastic Relation","display_name":"The Converse of a Stochastic Relation","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W1502441045","doi":"https://doi.org/10.1007/3-540-36576-1_15","mag":"1502441045"},"language":"en","primary_location":{"id":"doi:10.1007/3-540-36576-1_15","is_oa":true,"landing_page_url":"https://doi.org/10.1007/3-540-36576-1_15","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F3-540-36576-1_15.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007%2F3-540-36576-1_15.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060662730","display_name":"Ernst\u2013Erich Doberkat","orcid":null},"institutions":[{"id":"https://openalex.org/I200332995","display_name":"TU Dortmund University","ror":"https://ror.org/01k97gp34","country_code":"DE","type":"education","lineage":["https://openalex.org/I200332995"]},{"id":"https://openalex.org/I4210087817","display_name":"Software (Germany)","ror":"https://ror.org/004g36n56","country_code":"DE","type":"company","lineage":["https://openalex.org/I4210087817"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Ernst-Erich Doberkat","raw_affiliation_strings":["Chair for Software Technology, University of Dortmund, Dortmund, Germany","Software Technology, University of Dortmund#TAB#"],"affiliations":[{"raw_affiliation_string":"Chair for Software Technology, University of Dortmund, Dortmund, Germany","institution_ids":["https://openalex.org/I200332995"]},{"raw_affiliation_string":"Software Technology, University of Dortmund#TAB#","institution_ids":["https://openalex.org/I200332995","https://openalex.org/I4210087817"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5060662730"],"corresponding_institution_ids":["https://openalex.org/I200332995","https://openalex.org/I4210087817"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.2762,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.51915588,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"233","last_page":"249"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"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"}},"topics":[{"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"}},{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9965000152587891,"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/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.9855999946594238,"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/converse","display_name":"Converse","score":0.9845089316368103},{"id":"https://openalex.org/keywords/bisimulation","display_name":"Bisimulation","score":0.7910976409912109},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.7543594837188721},{"id":"https://openalex.org/keywords/transitive-relation","display_name":"Transitive relation","score":0.7136649489402771},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5363375544548035},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4791942536830902},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4502262473106384},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32581061124801636},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.13763120770454407},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.07855618000030518}],"concepts":[{"id":"https://openalex.org/C2776809875","wikidata":"https://www.wikidata.org/wiki/Q1375963","display_name":"Converse","level":2,"score":0.9845089316368103},{"id":"https://openalex.org/C135315306","wikidata":"https://www.wikidata.org/wiki/Q866364","display_name":"Bisimulation","level":2,"score":0.7910976409912109},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.7543594837188721},{"id":"https://openalex.org/C191399111","wikidata":"https://www.wikidata.org/wiki/Q64861","display_name":"Transitive relation","level":2,"score":0.7136649489402771},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5363375544548035},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4791942536830902},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4502262473106384},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32581061124801636},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.13763120770454407},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.07855618000030518},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/3-540-36576-1_15","is_oa":true,"landing_page_url":"https://doi.org/10.1007/3-540-36576-1_15","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F3-540-36576-1_15.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":{"id":"doi:10.1007/3-540-36576-1_15","is_oa":true,"landing_page_url":"https://doi.org/10.1007/3-540-36576-1_15","pdf_url":"https://link.springer.com/content/pdf/10.1007%2F3-540-36576-1_15.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.49000000953674316,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320320875","display_name":"Deutscher Akademischer Austauschdienst","ror":"https://ror.org/039djdh30"},{"id":"https://openalex.org/F4320323718","display_name":"Universit\u00e0 degli Studi dell'Aquila","ror":"https://ror.org/01j9p1r26"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1502441045.pdf","grobid_xml":"https://content.openalex.org/works/W1502441045.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W15499555","https://openalex.org/W108997189","https://openalex.org/W342302233","https://openalex.org/W361471363","https://openalex.org/W1543688617","https://openalex.org/W1561721581","https://openalex.org/W1571174323","https://openalex.org/W1587619098","https://openalex.org/W1964754311","https://openalex.org/W2018430837","https://openalex.org/W2018944629","https://openalex.org/W2041243111","https://openalex.org/W2044285874","https://openalex.org/W2056099894","https://openalex.org/W2088189323","https://openalex.org/W2100893927","https://openalex.org/W2120713972","https://openalex.org/W2163872159","https://openalex.org/W4302114916","https://openalex.org/W6641520439","https://openalex.org/W7052102089"],"related_works":["https://openalex.org/W2387449261","https://openalex.org/W2418518962","https://openalex.org/W2963377682","https://openalex.org/W2043159103","https://openalex.org/W2391769344","https://openalex.org/W4297790016","https://openalex.org/W2359260952","https://openalex.org/W2769269860","https://openalex.org/W2020701214","https://openalex.org/W2388752733"],"abstract_inverted_index":null,"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
