{"id":"https://openalex.org/W2762658453","doi":"https://doi.org/10.2168/lmcs-8(4:18)2012","title":"Probabilistic modal {\\mu}-calculus with independent product","display_name":"Probabilistic modal {\\mu}-calculus with independent product","publication_year":2012,"publication_date":"2012-11-27","ids":{"openalex":"https://openalex.org/W2762658453","doi":"https://doi.org/10.2168/lmcs-8(4:18)2012","mag":"2762658453"},"language":"en","primary_location":{"id":"doi:10.2168/lmcs-8(4:18)2012","is_oa":true,"landing_page_url":"https://doi.org/10.2168/lmcs-8(4:18)2012","pdf_url":"https://lmcs.episciences.org/789/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://lmcs.episciences.org/789/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Matteo Mio","orcid":"https://orcid.org/0000-0003-4050-3617"},"institutions":[{"id":"https://openalex.org/I4210139461","display_name":"Laboratoire d'Informatique de l'\u00c9cole Polytechnique","ror":"https://ror.org/04afed728","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I142476485","https://openalex.org/I4210139461","https://openalex.org/I4210145102","https://openalex.org/I4210159245"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Matteo Mio","raw_affiliation_strings":["LIX, Ecole Polytechnique"],"raw_orcid":"https://orcid.org/0000-0003-4050-3617","affiliations":[{"raw_affiliation_string":"LIX, Ecole Polytechnique","institution_ids":["https://openalex.org/I4210139461"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210139461"],"apc_list":null,"apc_paid":null,"fwci":1.7687,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.87884783,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"Volume 8, Issue 4","issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.5817000269889832,"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":0.5817000269889832,"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":0.26249998807907104,"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/T10126","display_name":"Logic, programming, and type systems","score":0.09929999709129333,"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/probabilistic-ctl","display_name":"Probabilistic CTL","score":0.7020000219345093},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.694100022315979},{"id":"https://openalex.org/keywords/modal-logic","display_name":"Modal logic","score":0.5472000241279602},{"id":"https://openalex.org/keywords/denotational-semantics","display_name":"Denotational semantics","score":0.4471000134944916},{"id":"https://openalex.org/keywords/multimodal-logic","display_name":"Multimodal logic","score":0.41819998621940613},{"id":"https://openalex.org/keywords/operational-semantics","display_name":"Operational semantics","score":0.4180000126361847},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.40720000863075256},{"id":"https://openalex.org/keywords/normal-modal-logic","display_name":"Normal modal logic","score":0.382999986410141},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.3294999897480011}],"concepts":[{"id":"https://openalex.org/C52063229","wikidata":"https://www.wikidata.org/wiki/Q7246845","display_name":"Probabilistic CTL","level":4,"score":0.7020000219345093},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.694100022315979},{"id":"https://openalex.org/C27508121","wikidata":"https://www.wikidata.org/wiki/Q210841","display_name":"Modal logic","level":3,"score":0.5472000241279602},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5170999765396118},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45080000162124634},{"id":"https://openalex.org/C207648694","wikidata":"https://www.wikidata.org/wiki/Q1189746","display_name":"Denotational semantics","level":4,"score":0.4471000134944916},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44679999351501465},{"id":"https://openalex.org/C203659156","wikidata":"https://www.wikidata.org/wiki/Q6934805","display_name":"Multimodal logic","level":3,"score":0.41819998621940613},{"id":"https://openalex.org/C156325763","wikidata":"https://www.wikidata.org/wiki/Q1930895","display_name":"Operational semantics","level":3,"score":0.4180000126361847},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4075999855995178},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.40720000863075256},{"id":"https://openalex.org/C114092440","wikidata":"https://www.wikidata.org/wiki/Q840226","display_name":"Normal modal logic","level":4,"score":0.382999986410141},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.3294999897480011},{"id":"https://openalex.org/C30128091","wikidata":"https://www.wikidata.org/wiki/Q291929","display_name":"Predicate transformer semantics","level":4,"score":0.32519999146461487},{"id":"https://openalex.org/C184337299","wikidata":"https://www.wikidata.org/wiki/Q1437428","display_name":"Semantics (computer science)","level":2,"score":0.3138999938964844},{"id":"https://openalex.org/C2777796570","wikidata":"https://www.wikidata.org/wiki/Q2351326","display_name":"Dynamic logic (digital electronics)","level":4,"score":0.30649998784065247},{"id":"https://openalex.org/C11191006","wikidata":"https://www.wikidata.org/wiki/Q2663311","display_name":"Accessibility relation","level":4,"score":0.3061999976634979},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.299699991941452},{"id":"https://openalex.org/C89497691","wikidata":"https://www.wikidata.org/wiki/Q7981058","display_name":"Well-founded semantics","level":5,"score":0.2989000082015991},{"id":"https://openalex.org/C46274116","wikidata":"https://www.wikidata.org/wiki/Q185521","display_name":"Truth value","level":2,"score":0.28790000081062317},{"id":"https://openalex.org/C18653775","wikidata":"https://www.wikidata.org/wiki/Q1333358","display_name":"Joint probability distribution","level":2,"score":0.28209999203681946},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.28060001134872437},{"id":"https://openalex.org/C128828806","wikidata":"https://www.wikidata.org/wiki/Q7246848","display_name":"Probabilistic argumentation","level":3,"score":0.2791999876499176},{"id":"https://openalex.org/C71139939","wikidata":"https://www.wikidata.org/wiki/Q910194","display_name":"Modal","level":2,"score":0.2791000008583069},{"id":"https://openalex.org/C143017306","wikidata":"https://www.wikidata.org/wiki/Q3318133","display_name":"Probabilistic relevance model","level":4,"score":0.27810001373291016},{"id":"https://openalex.org/C65236422","wikidata":"https://www.wikidata.org/wiki/Q173740","display_name":"Cartesian product","level":2,"score":0.27489998936653137},{"id":"https://openalex.org/C25016198","wikidata":"https://www.wikidata.org/wiki/Q781833","display_name":"Temporal logic","level":2,"score":0.2743000090122223},{"id":"https://openalex.org/C9672783","wikidata":"https://www.wikidata.org/wiki/Q65122115","display_name":"Game semantics","level":5,"score":0.26820001006126404},{"id":"https://openalex.org/C198008173","wikidata":"https://www.wikidata.org/wiki/Q1040040","display_name":"Computation tree logic","level":3,"score":0.2660999894142151},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.25130000710487366}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2168/lmcs-8(4:18)2012","is_oa":true,"landing_page_url":"https://doi.org/10.2168/lmcs-8(4:18)2012","pdf_url":"https://lmcs.episciences.org/789/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1211.1511","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1211.1511","pdf_url":"https://arxiv.org/pdf/1211.1511","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:doaj.org/article:f2720e9a5c894c289bdbbf532d369642","is_oa":true,"landing_page_url":"https://doaj.org/article/f2720e9a5c894c289bdbbf532d369642","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Logical Methods in Computer Science, Vol Volume 8, Issue 4 (2012)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.2168/lmcs-8(4:18)2012","is_oa":true,"landing_page_url":"https://doi.org/10.2168/lmcs-8(4:18)2012","pdf_url":"https://lmcs.episciences.org/789/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320320885","display_name":"European Research Consortium for Informatics and Mathematics","ror":"https://ror.org/055zrhj18"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320335041","display_name":"School of Informatics, University of Edinburgh","ror":"https://ror.org/01nrxwf90"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2762658453.pdf","grobid_xml":"https://content.openalex.org/works/W2762658453.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0,117,140,203],"probabilistic":[1,13,75,121,157],"modal":[2,76,122],"{\\mu}-calculus":[3,77,123],"is":[4,54,59,78,146,196,205],"a":[5,32,60,108,165,179],"fixed-point":[6],"logic":[7,106],"designed":[8],"for":[9,24,90,154],"expressing":[10],"properties":[11,130],"of":[12,66,73,81,111,131,138,143,149,164,168,199],"labeled":[14],"transition":[15],"systems":[16],"(PLTS's).":[17],"Two":[18],"equivalent":[19],"semantics":[20,53,153],"have":[21],"been":[22],"studied":[23],"this":[25,101,144,155],"logic,":[26,119],"both":[27],"assigning":[28],"to":[29,84,181],"each":[30,187],"state":[31],"value":[33],"in":[34,64,208],"the":[35,39,42,46,50,57,74,79,105,135,147,162,197,200],"interval":[36],"[0,1]":[37],"representing":[38],"probability":[40],"that":[41],"property":[43],"expressed":[44],"by":[45,177],"formula":[47],"holds":[48],"at":[49,216],"state.":[51],"One":[52],"denotational":[55],"and":[56,115,133],"other":[58,86],"game":[61,152],"semantics,":[62],"specified":[63],"terms":[65],"two-player":[67,173],"stochastic":[68,174],"parity":[69],"games.":[70],"A":[71],"shortcoming":[72],"lack":[80],"expressiveness":[82],"required":[83],"encode":[85,128],"important":[87],"temporal":[88],"logics":[89],"PLTS's":[91],"such":[92],"as":[93],"Probabilistic":[94],"Computation":[95],"Tree":[96],"Logic":[97],"(PCTL).":[98],"To":[99],"address":[100],"limitation":[102],"we":[103],"extend":[104],"with":[107,124,213],"new":[109,166],"pair":[110],"operators:":[112],"independent":[113,125],"product":[114],"coproduct.":[116],"resulting":[118],"called":[120],"product,":[126],"can":[127],"many":[129],"interest":[132],"subsumes":[134],"qualitative":[136],"fragment":[137],"PCTL.":[139],"main":[141,193],"contribution":[142],"paper":[145],"definition":[148,163],"an":[150,217],"appropriate":[151],"extended":[156,212],"{\\mu}-calculus.":[158],"This":[159],"relies":[160],"on":[161],"class":[167],"games":[169,176],"which":[170],"generalize":[171],"standard":[172],"(parity)":[175],"allowing":[178],"play":[180],"be":[182],"split":[183],"into":[184],"concurrent":[185],"subplays,":[186],"continuing":[188],"their":[189],"evolution":[190],"independently.":[191],"Our":[192],"technical":[194],"result":[195],"equivalence":[198],"two":[201],"semantics.":[202],"proof":[204],"carried":[206],"out":[207],"ZFC":[209],"set":[210],"theory":[211],"Martin's":[214],"Axiom":[215],"uncountable":[218],"cardinal.":[219]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1}],"updated_date":"2026-03-10T14:07:55.174380","created_date":"2017-10-20T00:00:00"}
