{"id":"https://openalex.org/W2401384051","doi":"https://doi.org/10.4230/lipics.csl.2023.18","title":"A Type Theory for Probabilistic and Bayesian Reasoning","display_name":"A Type Theory for Probabilistic and Bayesian Reasoning","publication_year":2015,"publication_date":"2015-12-17","ids":{"openalex":"https://openalex.org/W2401384051","doi":"https://doi.org/10.4230/lipics.csl.2023.18","mag":"2401384051"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:1512.05813","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1512.05813","pdf_url":"https://arxiv.org/pdf/1512.05813","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":"","raw_type":null},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1512.05813","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072761054","display_name":"Kenta Cho","orcid":"https://orcid.org/0000-0001-8026-226X"},"institutions":[{"id":"https://openalex.org/I4210114274","display_name":"Laboratoire d\u2019Informatique et Syst\u00e8mes","ror":"https://ror.org/0257sgk90","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I143002897","https://openalex.org/I21491767","https://openalex.org/I4210114274"]},{"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/I21491767","display_name":"Aix-Marseille Universit\u00e9","ror":"https://ror.org/035xkbk20","country_code":"FR","type":"education","lineage":["https://openalex.org/I21491767"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"de Lacroix, C\u00e9dric","raw_affiliation_strings":["LIS, CNRS UMR 7020, Aix-Marseille Universit\u00e9, Marseille, France"],"affiliations":[{"raw_affiliation_string":"LIS, CNRS UMR 7020, Aix-Marseille Universit\u00e9, Marseille, France","institution_ids":["https://openalex.org/I21491767","https://openalex.org/I4210114274","https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042359645","display_name":"Bart Jacobs","orcid":"https://orcid.org/0000-0002-3605-249X"},"institutions":[{"id":"https://openalex.org/I4210114274","display_name":"Laboratoire d\u2019Informatique et Syst\u00e8mes","ror":"https://ror.org/0257sgk90","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I143002897","https://openalex.org/I21491767","https://openalex.org/I4210114274"]},{"id":"https://openalex.org/I21491767","display_name":"Aix-Marseille Universit\u00e9","ror":"https://ror.org/035xkbk20","country_code":"FR","type":"education","lineage":["https://openalex.org/I21491767"]},{"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"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Santocanale, Luigi","raw_affiliation_strings":["LIS, CNRS UMR 7020, Aix-Marseille Universit\u00e9, Marseille, France"],"affiliations":[{"raw_affiliation_string":"LIS, CNRS UMR 7020, Aix-Marseille Universit\u00e9, Marseille, France","institution_ids":["https://openalex.org/I21491767","https://openalex.org/I4210114274","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5072761054"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I21491767","https://openalex.org/I4210114274"],"apc_list":null,"apc_paid":null,"fwci":5.53161568,"has_fulltext":false,"cited_by_count":45,"citation_normalized_percentile":{"value":0.97117296,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.953000009059906,"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"}},"topics":[{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.953000009059906,"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/mathematics","display_name":"Mathematics","score":0.5500954985618591},{"id":"https://openalex.org/keywords/quantum-logic","display_name":"Quantum logic","score":0.5242952704429626},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.496528685092926},{"id":"https://openalex.org/keywords/algebraic-logic","display_name":"Algebraic logic","score":0.4854496121406555},{"id":"https://openalex.org/keywords/categorical-quantum-mechanics","display_name":"Categorical quantum mechanics","score":0.45601820945739746},{"id":"https://openalex.org/keywords/predicate-logic","display_name":"Predicate logic","score":0.44531163573265076},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.42113327980041504},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.37835636734962463},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35130587220191956},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.25492048263549805},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.21619746088981628},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.14268672466278076},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.13788530230522156}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5500954985618591},{"id":"https://openalex.org/C169460222","wikidata":"https://www.wikidata.org/wiki/Q1206311","display_name":"Quantum logic","level":4,"score":0.5242952704429626},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.496528685092926},{"id":"https://openalex.org/C86523455","wikidata":"https://www.wikidata.org/wiki/Q1005222","display_name":"Algebraic logic","level":3,"score":0.4854496121406555},{"id":"https://openalex.org/C105295557","wikidata":"https://www.wikidata.org/wiki/Q5051814","display_name":"Categorical quantum mechanics","level":5,"score":0.45601820945739746},{"id":"https://openalex.org/C19689857","wikidata":"https://www.wikidata.org/wiki/Q4055684","display_name":"Predicate logic","level":3,"score":0.44531163573265076},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.42113327980041504},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37835636734962463},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35130587220191956},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25492048263549805},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.21619746088981628},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.14268672466278076},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.13788530230522156},{"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/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.0},{"id":"https://openalex.org/C5320026","wikidata":"https://www.wikidata.org/wiki/Q2122216","display_name":"Quantum information science","level":4,"score":0.0},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"pmh:oai:arXiv.org:1512.05813","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1512.05813","pdf_url":"https://arxiv.org/pdf/1512.05813","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":"","raw_type":null},{"id":"pmh:oai:drops-oai.dagstuhl.de:17479","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2023.18","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol252-csl2023/LIPIcs.CSL.2023.18/LIPIcs.CSL.2023.18.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"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":"","raw_type":"InProceedings"},{"id":"pmh:oai:HAL:hal-03739197v1","is_oa":true,"landing_page_url":"https://hal.science/hal-03739197","pdf_url":null,"source":null,"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://hal.science/hal-03739197","raw_type":"info:eu-repo/semantics/preprint"},{"id":"doi:10.48550/arxiv.1512.05813","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1512.05813","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"},{"id":"doi:10.4230/lipics.csl.2023.18","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.csl.2023.18","pdf_url":null,"source":{"id":"https://openalex.org/S7407052059","display_name":"Dagstuhl Research Online Publication Server","issn_l":null,"issn":[],"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":""},{"id":"doi:10.4230/lipics.types.2015.1","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.types.2015.1","pdf_url":null,"source":{"id":"https://openalex.org/S7407052059","display_name":"Dagstuhl Research Online Publication Server","issn_l":null,"issn":[],"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":""}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1512.05813","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1512.05813","pdf_url":"https://arxiv.org/pdf/1512.05813","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":"","raw_type":null},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":1,"referenced_works":["https://openalex.org/W2031248193"],"related_works":["https://openalex.org/W1559092270","https://openalex.org/W4230722377","https://openalex.org/W2062251184","https://openalex.org/W79229857","https://openalex.org/W2960477163","https://openalex.org/W1965820848","https://openalex.org/W4205826349","https://openalex.org/W2112103497","https://openalex.org/W1978916097","https://openalex.org/W1984461684"],"abstract_inverted_index":{"Effectus":[0],"theory":[1,29,65,71,156],"is":[2,79,141,157,184,209],"a":[3,34,109,199],"new":[4],"branch":[5],"of":[6,15,54,74,82,85,104,154,163],"categorical":[7],"logic":[8,22],"that":[9,116],"aims":[10],"to":[11,159,174,180,193],"capture":[12],"the":[13,83,90,98,155,160,206],"essentials":[14],"quantum":[16,64],"logic,":[17,56],"with":[18,97,198],"probabilistic":[19,136],"and":[20,66,95,125,130,137,165,176,188],"Boolean":[21,145],"as":[23,171,177],"special":[24],"cases.":[25],"Predicates":[26],"in":[27,39,57,63,69,108,122],"effectus":[28,86,203],"are":[30,51,133,147,168,190],"not":[31,210],"subobjects":[32],"having":[33],"Heyting":[35],"algebra":[36],"structure,":[37],"like":[38],"topos":[40],"theory,":[41,204],"but":[42],"`characteristic'":[43],"functions,":[44],"forming":[45],"effect":[46,49,75,106],"algebras.":[47,76],"Such":[48],"algebras":[50],"algebraic":[52],"models":[53],"quantitative":[55],"which":[58,167],"double":[59],"negation":[60],"holds.":[61],"Effects":[62],"fuzzy":[67],"predicates":[68],"probability":[70],"form":[72],"examples":[73],"This":[77],"text":[78],"an":[80,105],"account":[81],"basics":[84],"theory.":[87],"It":[88,140,183],"includes":[89],"fundamental":[91],"duality":[92],"between":[93],"states":[94],"effects,":[96],"associated":[99],"Born":[100],"rule":[101],"for":[102,135],"validity":[103],"(predicate)":[107],"particular":[110],"state.":[111],"A":[112,151],"basic":[113],"result":[114],"says":[115],"effectuses":[117,132,146],"can":[118],"be":[119],"described":[120,169],"equivalently":[121],"both":[123],"`total'":[124],"`partial'":[126],"form.":[127],"So-called":[128],"`commutative'":[129],"`Boolean'":[131],"distinguished,":[134],"classical":[138],"models.":[139],"shown":[142],"how":[143,186],"these":[144],"essentially":[148],"extensive":[149],"categories.":[150],"large":[152],"part":[153],"devoted":[158],"logical":[161],"notions":[162],"comprehension":[164,187],"quotient,":[166],"abstractly":[170],"right":[172],"adjoint":[173,179],"truth,":[175],"left":[178],"falisity,":[181],"respectively.":[182],"illustrated":[185],"quotients":[189],"closely":[191],"related":[192],"measurement.":[194],"The":[195],"paper":[196],"closes":[197],"section":[200],"on":[201],"`non-commutative'":[202],"where":[205],"appropriate":[207],"formalisation":[208],"entirely":[211],"clear":[212],"yet.":[213]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":6}],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2016-06-24T00:00:00"}
