{"id":"https://openalex.org/W4410036571","doi":"https://doi.org/10.1007/978-3-031-90897-2_7","title":"On the cut-elimination of the modal $$\\mu $$-calculus: Linear Logic to the rescue","display_name":"On the cut-elimination of the modal $$\\mu $$-calculus: Linear Logic to the rescue","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W4410036571","doi":"https://doi.org/10.1007/978-3-031-90897-2_7"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-031-90897-2_7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-90897-2_7","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-90897-2_7.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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-90897-2_7.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034658700","display_name":"Esa\u00efe Bauer","orcid":null},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210117673","display_name":"Institut de Recherche en Informatique Fondamentale","ror":"https://ror.org/02krdtz55","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I4210089394","https://openalex.org/I4210117673","https://openalex.org/I4210139971"]},{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]},{"id":"https://openalex.org/I4210091437","display_name":"Sorbonne Paris Cit\u00e9","ror":"https://ror.org/001z21q04","country_code":"FR","type":"other","lineage":["https://openalex.org/I4210091437"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Esa\u00efe Bauer","raw_affiliation_strings":["Universit\u00e9 Paris Cit\u00e9 & CNRS & INRIA, Pl. Aur\u00e9lie Nemours, 75013, Paris, France","IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale (Universit\u00e9 de Paris\r\nB\u00e2timent Sophie Germain, Case courrier 7014\r\n8 Place Aur\u00e9lie Nemours\r\n75205 Paris Cedex 13 - France)","PICUBE - Les assistants \u00e0 la d\u00e9monstration au c\u0153ur du raisonnement math\u00e9matique (IRIF\r\n8 Pl. Aur\u00e9lie Nemours, 75013 Paris - France)"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Paris Cit\u00e9 & CNRS & INRIA, Pl. Aur\u00e9lie Nemours, 75013, Paris, France","institution_ids":["https://openalex.org/I204730241","https://openalex.org/I4210091437","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale (Universit\u00e9 de Paris\r\nB\u00e2timent Sophie Germain, Case courrier 7014\r\n8 Place Aur\u00e9lie Nemours\r\n75205 Paris Cedex 13 - France)","institution_ids":["https://openalex.org/I4210117673","https://openalex.org/I204730241"]},{"raw_affiliation_string":"PICUBE - Les assistants \u00e0 la d\u00e9monstration au c\u0153ur du raisonnement math\u00e9matique (IRIF\r\n8 Pl. Aur\u00e9lie Nemours, 75013 Paris - France)","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112853151","display_name":"Alexis Saurin","orcid":null},"institutions":[{"id":"https://openalex.org/I4210091437","display_name":"Sorbonne Paris Cit\u00e9","ror":"https://ror.org/001z21q04","country_code":"FR","type":"other","lineage":["https://openalex.org/I4210091437"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210117673","display_name":"Institut de Recherche en Informatique Fondamentale","ror":"https://ror.org/02krdtz55","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I4210089394","https://openalex.org/I4210117673","https://openalex.org/I4210139971"]},{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Alexis Saurin","raw_affiliation_strings":["Universit\u00e9 Paris Cit\u00e9 & CNRS & INRIA, Pl. Aur\u00e9lie Nemours, 75013, Paris, France","IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale (Universit\u00e9 de Paris\r\nB\u00e2timent Sophie Germain, Case courrier 7014\r\n8 Place Aur\u00e9lie Nemours\r\n75205 Paris Cedex 13 - France)","PICUBE - Les assistants \u00e0 la d\u00e9monstration au c\u0153ur du raisonnement math\u00e9matique (IRIF\r\n8 Pl. Aur\u00e9lie Nemours, 75013 Paris - France)"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Paris Cit\u00e9 & CNRS & INRIA, Pl. Aur\u00e9lie Nemours, 75013, Paris, France","institution_ids":["https://openalex.org/I204730241","https://openalex.org/I4210091437","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale (Universit\u00e9 de Paris\r\nB\u00e2timent Sophie Germain, Case courrier 7014\r\n8 Place Aur\u00e9lie Nemours\r\n75205 Paris Cedex 13 - France)","institution_ids":["https://openalex.org/I4210117673","https://openalex.org/I204730241"]},{"raw_affiliation_string":"PICUBE - Les assistants \u00e0 la d\u00e9monstration au c\u0153ur du raisonnement math\u00e9matique (IRIF\r\n8 Pl. Aur\u00e9lie Nemours, 75013 Paris - France)","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5034658700"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I4210091437","https://openalex.org/I4210117673"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":{"value":5000,"currency":"EUR","value_usd":5392},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.16724678,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"133","last_page":"154"},"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9973000288009644,"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":0.9937000274658203,"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/computer-science","display_name":"Computer science","score":0.6820840239524841},{"id":"https://openalex.org/keywords/modal-logic","display_name":"Modal logic","score":0.6206918954849243},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.5939511060714722},{"id":"https://openalex.org/keywords/modal","display_name":"Modal","score":0.5826290249824524},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.43182799220085144},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.35234954953193665}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6820840239524841},{"id":"https://openalex.org/C27508121","wikidata":"https://www.wikidata.org/wiki/Q210841","display_name":"Modal logic","level":3,"score":0.6206918954849243},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.5939511060714722},{"id":"https://openalex.org/C71139939","wikidata":"https://www.wikidata.org/wiki/Q910194","display_name":"Modal","level":2,"score":0.5826290249824524},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.43182799220085144},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.35234954953193665},{"id":"https://openalex.org/C188027245","wikidata":"https://www.wikidata.org/wiki/Q750446","display_name":"Polymer chemistry","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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/978-3-031-90897-2_7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-90897-2_7","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-90897-2_7.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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:HAL:hal-05409189v1","is_oa":true,"landing_page_url":"https://hal.science/hal-05409189","pdf_url":null,"source":{"id":"https://openalex.org/S4406922461","display_name":"SPIRE - Sciences Po Institutional REpository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"FoSSaCS 2025 - 28th International Conference on Foundations of Software Science and Computation Structures, Abdulla; Kesner, May 2025, Hamilton, Canada. pp.133-154, &#x27E8;10.1007/978-3-031-90897-2_7&#x27E9;","raw_type":"Conference papers"}],"best_oa_location":{"id":"doi:10.1007/978-3-031-90897-2_7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-90897-2_7","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-90897-2_7.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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6858444455","display_name":null,"funder_award_id":"ANR-21-CE48-019-01","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4410036571.pdf","grobid_xml":"https://content.openalex.org/works/W4410036571.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W183006709","https://openalex.org/W1033924769","https://openalex.org/W1556705528","https://openalex.org/W1969548989","https://openalex.org/W2010337608","https://openalex.org/W2012615291","https://openalex.org/W2015640848","https://openalex.org/W2016326123","https://openalex.org/W2020453924","https://openalex.org/W2032188971","https://openalex.org/W2045549616","https://openalex.org/W2057183321","https://openalex.org/W2088881461","https://openalex.org/W2091739821","https://openalex.org/W2113402167","https://openalex.org/W2142803264","https://openalex.org/W2164691248","https://openalex.org/W2176705267","https://openalex.org/W2276009245","https://openalex.org/W2467982476","https://openalex.org/W2553042017","https://openalex.org/W2911865844","https://openalex.org/W2966706555","https://openalex.org/W3151088829","https://openalex.org/W4200044182","https://openalex.org/W4232563889","https://openalex.org/W4289793574","https://openalex.org/W4386723837","https://openalex.org/W6635027498"],"related_works":["https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W4409439182","https://openalex.org/W2053286651","https://openalex.org/W2181743346","https://openalex.org/W2187401768","https://openalex.org/W2028144918","https://openalex.org/W3016746667","https://openalex.org/W1587059467","https://openalex.org/W2962420748"],"abstract_inverted_index":{"Abstract":[0],"This":[1],"paper":[2],"presents":[3],"a":[4,21,49,73,147],"proof-theoretic":[5],"analysis":[6],"of":[7,76,138],"the":[8,25,77,87,90,100,139,154],"modal":[9,27,78,91,140],"$$\\mu":[10,28,52,79,92,116],"$$":[11,29,80,93],"<mml:math":[12,30,57,81,94,121],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[13,31,58,82,95,122],"<mml:mi>\u03bc</mml:mi>":[14,32,60,83,96,124],"</mml:math>":[15,33,69,84,97,133],"-calculus.":[16],"More":[17],"precisely,":[18],"we":[19,47],"prove":[20],"syntactic":[22],"cut-elimination":[23,110,114,155],"for":[24,108,115],"non-wellfounded":[26],"-calculus,":[34,85],"using":[35],"methods":[36],"from":[37,89,103],"linear":[38,74,104],"logic.":[39,105],"and":[40,134],"its":[41],"exponential":[42,101],"modalities.":[43],"To":[44],"achieve":[45],"this,":[46],"introduce":[48],"new":[50,144],"system,":[51],"\\textsf":[53,117],"{LL}_{\\Box":[54,118],"}^{\\infty":[55,119],"}$$":[56,120],"<mml:mrow>":[59,63,123,127],"<mml:msubsup>":[61,125],"<mml:mi>LL</mml:mi>":[62,126],"<mml:mo>\u25a1</mml:mo>":[64,128],"</mml:mrow>":[65,68,129,132],"<mml:mi>\u221e</mml:mi>":[66,130],"</mml:msubsup>":[67,131],",":[70],"which":[71],"is":[72],"version":[75],"intertwining":[86],"modalities":[88,102],"-calculus":[98],"with":[99],"Our":[106],"strategy":[107],"proving":[109,113],"involves":[111],"(i)":[112],"(ii)":[135],"translating":[136],"proofs":[137],"mu-calculus":[141],"into":[142],"this":[143],"system":[145],"via":[146],"\u201clinear":[148],"translation\u201d,":[149],"allowing":[150],"us":[151],"to":[152],"extract":[153],"result.":[156]},"counts_by_year":[],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
