{"id":"https://openalex.org/W2796622197","doi":"https://doi.org/10.1017/s0960129519000197","title":"Modal dependent type theory and dependent right adjoints","display_name":"Modal dependent type theory and dependent right adjoints","publication_year":2019,"publication_date":"2019-12-12","ids":{"openalex":"https://openalex.org/W2796622197","doi":"https://doi.org/10.1017/s0960129519000197","mag":"2796622197"},"language":"en","primary_location":{"id":"doi:10.1017/s0960129519000197","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0960129519000197","pdf_url":null,"source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://pure.itu.dk/portal/da/publications/daf56809-22d1-4eb0-9b22-618c114e5e07","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Lars Birkedal","orcid":null},"institutions":[{"id":"https://openalex.org/I204337017","display_name":"Aarhus University","ror":"https://ror.org/01aj84f44","country_code":"DK","type":"education","lineage":["https://openalex.org/I204337017"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Lars Birkedal","raw_affiliation_strings":["Department of Computer Science, Aarhus University, Denmark"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Aarhus University, Denmark","institution_ids":["https://openalex.org/I204337017"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Ranald Clouston","orcid":null},"institutions":[{"id":"https://openalex.org/I118347636","display_name":"Australian National University","ror":"https://ror.org/019wvm592","country_code":"AU","type":"education","lineage":["https://openalex.org/I118347636"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Ranald Clouston","raw_affiliation_strings":["Research School of Computer Science, Australian National University, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Research School of Computer Science, Australian National University, Australia","institution_ids":["https://openalex.org/I118347636"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Bassel Mannaa","orcid":"https://orcid.org/0000-0003-0097-6188"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Bassel Mannaa","raw_affiliation_strings":["eToroX Labs, Denmark"],"raw_orcid":"https://orcid.org/0000-0003-0097-6188","affiliations":[{"raw_affiliation_string":"eToroX Labs, Denmark","institution_ids":[]}]},{"author_position":"middle","author":{"id":null,"display_name":"Rasmus Ejlers M\u00f8gelberg","orcid":null},"institutions":[{"id":"https://openalex.org/I83467386","display_name":"IT University of Copenhagen","ror":"https://ror.org/02309jg23","country_code":"DK","type":"education","lineage":["https://openalex.org/I83467386"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Rasmus Ejlers M\u00f8gelberg","raw_affiliation_strings":["IT University of Copenhagen, Denmark"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IT University of Copenhagen, Denmark","institution_ids":["https://openalex.org/I83467386"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Andrew M. Pitts","orcid":"https://orcid.org/0000-0001-7775-3471"},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Andrew M. Pitts","raw_affiliation_strings":["Department of Computer Science and Technology, University of Cambridge, UK"],"raw_orcid":"https://orcid.org/0000-0001-7775-3471","affiliations":[{"raw_affiliation_string":"Department of Computer Science and Technology, University of Cambridge, UK","institution_ids":["https://openalex.org/I241749"]}]},{"author_position":"last","author":{"id":null,"display_name":"Bas Spitters","orcid":null},"institutions":[{"id":"https://openalex.org/I204337017","display_name":"Aarhus University","ror":"https://ror.org/01aj84f44","country_code":"DK","type":"education","lineage":["https://openalex.org/I204337017"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Bas Spitters","raw_affiliation_strings":["Department of Computer Science, Aarhus University, Denmark"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Aarhus University, Denmark","institution_ids":["https://openalex.org/I204337017"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.1607,"has_fulltext":true,"cited_by_count":19,"citation_normalized_percentile":{"value":0.83695235,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"30","issue":"2","first_page":"118","last_page":"138"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.8984000086784363,"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":0.8984000086784363,"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":0.04580000042915344,"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.011800000444054604,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/adjunction","display_name":"Adjunction","score":0.6880999803543091},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.6539000272750854},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.6503000259399414},{"id":"https://openalex.org/keywords/type-theory","display_name":"Type theory","score":0.6211000084877014},{"id":"https://openalex.org/keywords/modal","display_name":"Modal","score":0.6184999942779541},{"id":"https://openalex.org/keywords/semantics","display_name":"Semantics (computer science)","score":0.5455999970436096},{"id":"https://openalex.org/keywords/dependent-type","display_name":"Dependent type","score":0.49549999833106995},{"id":"https://openalex.org/keywords/normal-modal-logic","display_name":"Normal modal logic","score":0.4830000102519989},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.460999995470047}],"concepts":[{"id":"https://openalex.org/C2780580338","wikidata":"https://www.wikidata.org/wiki/Q577835","display_name":"Adjunction","level":2,"score":0.6880999803543091},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.6539000272750854},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.6503000259399414},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6313999891281128},{"id":"https://openalex.org/C93682546","wikidata":"https://www.wikidata.org/wiki/Q1056428","display_name":"Type theory","level":3,"score":0.6211000084877014},{"id":"https://openalex.org/C71139939","wikidata":"https://www.wikidata.org/wiki/Q910194","display_name":"Modal","level":2,"score":0.6184999942779541},{"id":"https://openalex.org/C184337299","wikidata":"https://www.wikidata.org/wiki/Q1437428","display_name":"Semantics (computer science)","level":2,"score":0.5455999970436096},{"id":"https://openalex.org/C20528804","wikidata":"https://www.wikidata.org/wiki/Q997433","display_name":"Dependent type","level":3,"score":0.49549999833106995},{"id":"https://openalex.org/C114092440","wikidata":"https://www.wikidata.org/wiki/Q840226","display_name":"Normal modal logic","level":4,"score":0.4830000102519989},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.460999995470047},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.4575999975204468},{"id":"https://openalex.org/C11191006","wikidata":"https://www.wikidata.org/wiki/Q2663311","display_name":"Accessibility relation","level":4,"score":0.4514999985694885},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.44429999589920044},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.40880000591278076},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3970000147819519},{"id":"https://openalex.org/C84999194","wikidata":"https://www.wikidata.org/wiki/Q1","display_name":"Universe","level":2,"score":0.3610000014305115},{"id":"https://openalex.org/C60048249","wikidata":"https://www.wikidata.org/wiki/Q37437","display_name":"Syntax","level":2,"score":0.3580999970436096},{"id":"https://openalex.org/C151797676","wikidata":"https://www.wikidata.org/wiki/Q179692","display_name":"Axiom of choice","level":4,"score":0.3458999991416931},{"id":"https://openalex.org/C114408938","wikidata":"https://www.wikidata.org/wiki/Q333373","display_name":"Abstract syntax","level":3,"score":0.3353999853134155},{"id":"https://openalex.org/C78344899","wikidata":"https://www.wikidata.org/wiki/Q638442","display_name":"Modal operator","level":4,"score":0.3264999985694885},{"id":"https://openalex.org/C160131679","wikidata":"https://www.wikidata.org/wiki/Q2462350","display_name":"Kripke semantics","level":4,"score":0.31700000166893005},{"id":"https://openalex.org/C161913894","wikidata":"https://www.wikidata.org/wiki/Q1077740","display_name":"Kripke structure","level":3,"score":0.3156999945640564},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30379998683929443},{"id":"https://openalex.org/C2776235265","wikidata":"https://www.wikidata.org/wiki/Q18392052","display_name":"Fragment (logic)","level":2,"score":0.29019999504089355},{"id":"https://openalex.org/C54884031","wikidata":"https://www.wikidata.org/wiki/Q217413","display_name":"Category theory","level":2,"score":0.28459998965263367},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2791999876499176},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.27399998903274536},{"id":"https://openalex.org/C192609573","wikidata":"https://www.wikidata.org/wiki/Q7388341","display_name":"S5","level":5,"score":0.25360000133514404}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1017/s0960129519000197","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0960129519000197","pdf_url":null,"source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:pure.atira.dk:openaire/daf56809-22d1-4eb0-9b22-618c114e5e07","is_oa":true,"landing_page_url":"https://pure.itu.dk/portal/da/publications/daf56809-22d1-4eb0-9b22-618c114e5e07","pdf_url":null,"source":{"id":"https://openalex.org/S4377196680","display_name":"IT University Of Copenhagen (IT University of Copenhagen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I83467386","host_organization_name":"IT University of Copenhagen","host_organization_lineage":["https://openalex.org/I83467386"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Birkedal, L, Clouston, R, Mannaa, B, M\u00f8gelberg, R E, M. Pitts, A & Spitters, B 2019, 'Modal dependent type theory and dependent right adjoints', Mathematical Structures in Computer Science. https://doi.org/10.1017/S0960129519000197","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:arXiv.org:1804.05236","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1804.05236","pdf_url":"https://arxiv.org/pdf/1804.05236","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:pure.atira.dk:publications/6d47a574-9aaa-4c69-8485-c8a490847236","is_oa":false,"landing_page_url":"https://arxiv.org/pdf/1804.05236.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Birkedal, L, Clouston, R, Mannaa, B, Ejlers M\u00f8gelberg, R, Pitts, A M & Spitters, B 2020, 'Modal dependent type theory and dependent right adjoints', Mathematical Structures in Computer Science, vol. 30, no. 2, pp. 118-138. https://doi.org/10.1017/S0960129519000197","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:openresearch-repository.anu.edu.au:1885/309788","is_oa":false,"landing_page_url":"http://hdl.handle.net/1885/309788","pdf_url":null,"source":{"id":"https://openalex.org/S4306402539","display_name":"ANU Open Research (Australian National University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I118347636","host_organization_name":"Australian National University","host_organization_lineage":["https://openalex.org/I118347636"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"Journal article"}],"best_oa_location":{"id":"pmh:oai:pure.atira.dk:openaire/daf56809-22d1-4eb0-9b22-618c114e5e07","is_oa":true,"landing_page_url":"https://pure.itu.dk/portal/da/publications/daf56809-22d1-4eb0-9b22-618c114e5e07","pdf_url":null,"source":{"id":"https://openalex.org/S4377196680","display_name":"IT University Of Copenhagen (IT University of Copenhagen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I83467386","host_organization_name":"IT University of Copenhagen","host_organization_lineage":["https://openalex.org/I83467386"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Birkedal, L, Clouston, R, Mannaa, B, M\u00f8gelberg, R E, M. Pitts, A & Spitters, B 2019, 'Modal dependent type theory and dependent right adjoints', Mathematical Structures in Computer Science. https://doi.org/10.1017/S0960129519000197","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W1484639702","https://openalex.org/W1566288082","https://openalex.org/W1678412398","https://openalex.org/W1828583149","https://openalex.org/W1892525621","https://openalex.org/W1969167499","https://openalex.org/W1984902166","https://openalex.org/W2029408547","https://openalex.org/W2053194822","https://openalex.org/W2114058479","https://openalex.org/W2121730419","https://openalex.org/W2124729849","https://openalex.org/W2132181573","https://openalex.org/W2165952355","https://openalex.org/W2472614804","https://openalex.org/W2550513301","https://openalex.org/W2578225362","https://openalex.org/W2743482027","https://openalex.org/W2757812197","https://openalex.org/W2765937481","https://openalex.org/W2796955244","https://openalex.org/W2951673578","https://openalex.org/W2963638222","https://openalex.org/W2964301529","https://openalex.org/W2964305797","https://openalex.org/W6617430481","https://openalex.org/W6629426662","https://openalex.org/W6632170738","https://openalex.org/W6655408893","https://openalex.org/W6730287135","https://openalex.org/W6739834935","https://openalex.org/W6740246205","https://openalex.org/W6763078161"],"related_works":["https://openalex.org/W2149896447","https://openalex.org/W2130852886","https://openalex.org/W2353397064","https://openalex.org/W2899686601","https://openalex.org/W1554721881","https://openalex.org/W1993195187","https://openalex.org/W26274647","https://openalex.org/W2069376434","https://openalex.org/W2980859210","https://openalex.org/W3105116513"],"abstract_inverted_index":{"Abstract":[0],"In":[1,37],"recent":[2],"years,":[3],"we":[4,40,73,96,122],"have":[5],"seen":[6],"several":[7],"new":[8],"models":[9],"of":[10,18,61,107,128],"dependent":[11,43,47,55,80],"type":[12,24,29,35,44,48],"theory":[13,30,45,49],"extended":[14],"with":[15,50,76,78,101,153],"some":[16],"form":[17],"modal":[19,42,62,130],"necessity":[20],"operator,":[21],"including":[22],"nominal":[23],"theory,":[25],"guarded":[26],"and":[27,31,33,68,84,104,142,151],"clocked":[28],"spatial":[32],"cohesive":[34],"theory.":[36],"this":[38],"paper,":[39],"study":[41],":":[46],"an":[51,105],"operator":[52],"satisfying":[53],"(a":[54],"version":[56],"of)":[57],"the":[58,71,87,115,120,149],"K":[59],"axiom":[60],"logic.":[63],"We":[64,147],"investigate":[65],"both":[66],"semantics":[67,152],"syntax.":[69],"For":[70,119],"semantics,":[72],"introduce":[74,123],"categories":[75],"families":[77],"a":[79,112,124,144],"right":[81],"adjoint":[82],"(CwDRA)":[83],"show":[85,97,133],"that":[86,98,134],"examples":[88],"above":[89],"can":[90,136],"be":[91,137],"presented":[92],"as":[93],"such.":[94],"Indeed,":[95],"any":[99,140],"category":[100],"finite":[102],"limits":[103],"adjunction":[106],"endofunctors":[108],"give":[109],"rise":[110],"to":[111],"CwDRA":[113],"via":[114],"local":[116],"universe":[117],"construction.":[118],"syntax,":[121],"dependently":[125],"typed":[126],"extension":[127],"Fitch-style":[129],"\u03bb":[131],"-calculus,":[132],"it":[135],"interpreted":[138],"in":[139],"CwDRA,":[141],"build":[143],"term":[145],"model.":[146],"extend":[148],"syntax":[150],"universes.":[154]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2018-04-24T00:00:00"}