{"id":"https://openalex.org/W4297809221","doi":"https://doi.org/10.1007/978-3-031-15298-6_13","title":"The Alternation Hierarchy of the $$\\mu $$-calculus over Weakly Transitive Frames","display_name":"The Alternation Hierarchy of the $$\\mu $$-calculus over Weakly Transitive Frames","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4297809221","doi":"https://doi.org/10.1007/978-3-031-15298-6_13"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-031-15298-6_13","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-031-15298-6_13","pdf_url":null,"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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025019318","display_name":"Leonardo Pacheco","orcid":"https://orcid.org/0000-0002-7703-7990"},"institutions":[{"id":"https://openalex.org/I201537933","display_name":"Tohoku University","ror":"https://ror.org/01dq60k83","country_code":"JP","type":"education","lineage":["https://openalex.org/I201537933"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Leonardo Pacheco","raw_affiliation_strings":["Mathematical Institute, Tohoku University, Sendai, Japan"],"raw_orcid":"https://orcid.org/0000-0002-7703-7990","affiliations":[{"raw_affiliation_string":"Mathematical Institute, Tohoku University, Sendai, Japan","institution_ids":["https://openalex.org/I201537933"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110462436","display_name":"Kazuyuki Tanaka","orcid":null},"institutions":[{"id":"https://openalex.org/I201537933","display_name":"Tohoku University","ror":"https://ror.org/01dq60k83","country_code":"JP","type":"education","lineage":["https://openalex.org/I201537933"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Kazuyuki Tanaka","raw_affiliation_strings":["Mathematical Institute, Tohoku University, Sendai, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute, Tohoku University, Sendai, Japan","institution_ids":["https://openalex.org/I201537933"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":1.0233,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.79585842,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"207","last_page":"220"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9997000098228455,"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":0.9997000098228455,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9954000115394592,"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":0.9954000115394592,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/alternation","display_name":"Alternation (linguistics)","score":0.8274881839752197},{"id":"https://openalex.org/keywords/fragment","display_name":"Fragment (logic)","score":0.6259310245513916},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5954153537750244},{"id":"https://openalex.org/keywords/transitive-relation","display_name":"Transitive relation","score":0.5052352547645569},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.49327248334884644},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.4676370620727539},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.45661208033561707},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41200006008148193},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.32203209400177},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1840669810771942},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.12460082769393921}],"concepts":[{"id":"https://openalex.org/C26826806","wikidata":"https://www.wikidata.org/wiki/Q438358","display_name":"Alternation (linguistics)","level":2,"score":0.8274881839752197},{"id":"https://openalex.org/C2776235265","wikidata":"https://www.wikidata.org/wiki/Q18392052","display_name":"Fragment (logic)","level":2,"score":0.6259310245513916},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5954153537750244},{"id":"https://openalex.org/C191399111","wikidata":"https://www.wikidata.org/wiki/Q64861","display_name":"Transitive relation","level":2,"score":0.5052352547645569},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.49327248334884644},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.4676370620727539},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.45661208033561707},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41200006008148193},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32203209400177},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1840669810771942},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.12460082769393921},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-031-15298-6_13","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-031-15298-6_13","pdf_url":null,"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":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.5400000214576721,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W1511918851","https://openalex.org/W1530375570","https://openalex.org/W1881786745","https://openalex.org/W1906991491","https://openalex.org/W1929640513","https://openalex.org/W2007304763","https://openalex.org/W2020504188","https://openalex.org/W2050527500","https://openalex.org/W2078421228","https://openalex.org/W2099932469","https://openalex.org/W2126399192","https://openalex.org/W2136839729","https://openalex.org/W2142583143","https://openalex.org/W2158151856","https://openalex.org/W2168498451","https://openalex.org/W2294372906","https://openalex.org/W2478456423","https://openalex.org/W2502103274","https://openalex.org/W2609251073","https://openalex.org/W2804589645","https://openalex.org/W2954047906","https://openalex.org/W2972606755","https://openalex.org/W3156620228","https://openalex.org/W3173611724","https://openalex.org/W4211144022","https://openalex.org/W4229971457","https://openalex.org/W4245443266"],"related_works":["https://openalex.org/W2083044841","https://openalex.org/W1974770635","https://openalex.org/W3010755420","https://openalex.org/W2331003186","https://openalex.org/W1978042415","https://openalex.org/W1978539514","https://openalex.org/W2317783843","https://openalex.org/W2028945277","https://openalex.org/W2018461617","https://openalex.org/W2007304763"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
