{"id":"https://openalex.org/W3109831021","doi":"https://doi.org/10.46298/lmcs-17(3:11)2021","title":"Multimodal Dependent Type Theory","display_name":"Multimodal Dependent Type Theory","publication_year":2021,"publication_date":"2021-07-28","ids":{"openalex":"https://openalex.org/W3109831021","doi":"https://doi.org/10.46298/lmcs-17(3:11)2021","mag":"3109831021"},"language":"en","primary_location":{"id":"doi:10.46298/lmcs-17(3:11)2021","is_oa":true,"landing_page_url":"https://doi.org/10.46298/lmcs-17(3:11)2021","pdf_url":"https://lmcs.episciences.org/7713/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":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://lmcs.episciences.org/7713/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056800630","display_name":"Daniel Gratzer","orcid":"https://orcid.org/0000-0003-1944-0789"},"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":"Daniel Gratzer","raw_affiliation_strings":["Aarhus university;"],"raw_orcid":"https://orcid.org/0000-0003-1944-0789","affiliations":[{"raw_affiliation_string":"Aarhus university;","institution_ids":["https://openalex.org/I204337017"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037972894","display_name":"G. A. Kavvos","orcid":"https://orcid.org/0000-0001-7953-7975"},"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":"G. A. Kavvos","raw_affiliation_strings":["Aarhus university;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Aarhus university;","institution_ids":["https://openalex.org/I204337017"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036983503","display_name":"Andreas Nuyts","orcid":"https://orcid.org/0000-0002-1571-5063"},"institutions":[{"id":"https://openalex.org/I36234482","display_name":"University of Bristol","ror":"https://ror.org/0524sp257","country_code":"GB","type":"education","lineage":["https://openalex.org/I36234482"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Andreas Nuyts","raw_affiliation_strings":["University of Bristol"],"raw_orcid":"https://orcid.org/0000-0002-1571-5063","affiliations":[{"raw_affiliation_string":"University of Bristol","institution_ids":["https://openalex.org/I36234482"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055959064","display_name":"Lars Birkedal","orcid":"https://orcid.org/0000-0003-1320-0098"},"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":["Aarhus university;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Aarhus university;","institution_ids":["https://openalex.org/I204337017"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01065271,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"Volume 17, Issue 3","issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9988999962806702,"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":0.9988999962806702,"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/T10181","display_name":"Natural Language Processing Techniques","score":0.9919999837875366,"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":0.9703999757766724,"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/computer-science","display_name":"Computer science","score":0.6606206893920898},{"id":"https://openalex.org/keywords/type-theory","display_name":"Type theory","score":0.6006367802619934},{"id":"https://openalex.org/keywords/modal","display_name":"Modal","score":0.5885009765625},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.5847799777984619},{"id":"https://openalex.org/keywords/recursion","display_name":"Recursion (computer science)","score":0.5184042453765869},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.514491081237793},{"id":"https://openalex.org/keywords/modalities","display_name":"Modalities","score":0.5119670629501343},{"id":"https://openalex.org/keywords/usable","display_name":"USable","score":0.42636731266975403},{"id":"https://openalex.org/keywords/soundness","display_name":"Soundness","score":0.4178098142147064},{"id":"https://openalex.org/keywords/metatheory","display_name":"Metatheory","score":0.41686156392097473},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.407470166683197},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3852255940437317},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3449123799800873},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2970033884048462},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.19920727610588074},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.19334948062896729}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6606206893920898},{"id":"https://openalex.org/C93682546","wikidata":"https://www.wikidata.org/wiki/Q1056428","display_name":"Type theory","level":3,"score":0.6006367802619934},{"id":"https://openalex.org/C71139939","wikidata":"https://www.wikidata.org/wiki/Q910194","display_name":"Modal","level":2,"score":0.5885009765625},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.5847799777984619},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.5184042453765869},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.514491081237793},{"id":"https://openalex.org/C2779903281","wikidata":"https://www.wikidata.org/wiki/Q6888026","display_name":"Modalities","level":2,"score":0.5119670629501343},{"id":"https://openalex.org/C2780615836","wikidata":"https://www.wikidata.org/wiki/Q2471869","display_name":"USable","level":2,"score":0.42636731266975403},{"id":"https://openalex.org/C39920170","wikidata":"https://www.wikidata.org/wiki/Q693083","display_name":"Soundness","level":2,"score":0.4178098142147064},{"id":"https://openalex.org/C39387531","wikidata":"https://www.wikidata.org/wiki/Q1096708","display_name":"Metatheory","level":2,"score":0.41686156392097473},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.407470166683197},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3852255940437317},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3449123799800873},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2970033884048462},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.19920727610588074},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.19334948062896729},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C36289849","wikidata":"https://www.wikidata.org/wiki/Q34749","display_name":"Social science","level":1,"score":0.0},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":10,"locations":[{"id":"doi:10.46298/lmcs-17(3:11)2021","is_oa":true,"landing_page_url":"https://doi.org/10.46298/lmcs-17(3:11)2021","pdf_url":"https://lmcs.episciences.org/7713/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:pure.atira.dk:openaire/87531c56-30b6-485a-a836-41b375ffcba1","is_oa":true,"landing_page_url":"https://pure.au.dk/portal/en/publications/87531c56-30b6-485a-a836-41b375ffcba1","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Gratzer, D, Kavvos, G A, Nuyts, A & Birkedal, L 2021, 'Multimodal Dependent Type Theory', Logical Methods in Computer Science, vol. 17, no. 3, 11. https://doi.org/10.46298/lmcs-17(3:11)2021","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/682220","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/123456789/682220","pdf_url":null,"source":{"id":"https://openalex.org/S7407055369","display_name":"Lirias","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Logical Methods In Computer Science, vol. 17 (3), Art.No. ARTN 11","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:arXiv.org:2011.15021","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2011.15021","pdf_url":"https://arxiv.org/pdf/2011.15021","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":"mag:3109831021","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2011.15021","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:doaj.org/article:07e0c9691a85467f9ebe85fa9649460a","is_oa":true,"landing_page_url":"https://doaj.org/article/07e0c9691a85467f9ebe85fa9649460a","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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-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 17, Issue 3 (2021)","raw_type":"article"},{"id":"pmh:oai:pure.atira.dk:publications/87531c56-30b6-485a-a836-41b375ffcba1","is_oa":true,"landing_page_url":"https://lmcs.episciences.org/7713","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Gratzer, D, Kavvos, G A, Nuyts, A & Birkedal, L 2021, 'Multimodal Dependent Type Theory', Logical Methods in Computer Science, vol. 17, no. 3, 11. https://doi.org/10.46298/lmcs-17(3:11)2021","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"doi:10.48550/arxiv.2011.15021","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2011.15021","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"},{"id":"doi:10.5446/48035","is_oa":true,"landing_page_url":"https://doi.org/10.5446/48035","pdf_url":null,"source":{"id":"https://openalex.org/S7407052952","display_name":"TIB KMO / FLOWWORKS GmbH","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"},{"id":"doi:10.5446/49282","is_oa":true,"landing_page_url":"https://doi.org/10.5446/49282","pdf_url":null,"source":{"id":"https://openalex.org/S7407052952","display_name":"TIB KMO / FLOWWORKS GmbH","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.46298/lmcs-17(3:11)2021","is_oa":true,"landing_page_url":"https://doi.org/10.46298/lmcs-17(3:11)2021","pdf_url":"https://lmcs.episciences.org/7713/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":[{"id":"https://openalex.org/G6851704783","display_name":null,"funder_award_id":"25804","funder_id":"https://openalex.org/F4320310490","funder_display_name":"Villum Fonden"},{"id":"https://openalex.org/G8591999491","display_name":null,"funder_award_id":"12386","funder_id":"https://openalex.org/F4320310490","funder_display_name":"Villum Fonden"}],"funders":[{"id":"https://openalex.org/F4320310490","display_name":"Villum Fonden","ror":"https://ror.org/007ww2d15"},{"id":"https://openalex.org/F4320321730","display_name":"Fonds Wetenschappelijk Onderzoek","ror":"https://ror.org/03qtxy027"},{"id":"https://openalex.org/F4320322308","display_name":"KU Leuven","ror":"https://ror.org/05f950310"},{"id":"https://openalex.org/F4320327336","display_name":"Vlaamse regering","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3109831021.pdf","grobid_xml":"https://content.openalex.org/works/W3109831021.grobid-xml"},"referenced_works_count":68,"referenced_works":["https://openalex.org/W104819362","https://openalex.org/W159354440","https://openalex.org/W1488538795","https://openalex.org/W1520936552","https://openalex.org/W1533094521","https://openalex.org/W1534018603","https://openalex.org/W1678412398","https://openalex.org/W1882235344","https://openalex.org/W1969167499","https://openalex.org/W1988824860","https://openalex.org/W1990204174","https://openalex.org/W1995581828","https://openalex.org/W1997143185","https://openalex.org/W2006941708","https://openalex.org/W2020900140","https://openalex.org/W2033146968","https://openalex.org/W2036676170","https://openalex.org/W2070324762","https://openalex.org/W2090046646","https://openalex.org/W2099665514","https://openalex.org/W2104412665","https://openalex.org/W2116813111","https://openalex.org/W2120777523","https://openalex.org/W2132181573","https://openalex.org/W2144747140","https://openalex.org/W2162592943","https://openalex.org/W2165952355","https://openalex.org/W2175195909","https://openalex.org/W2221454492","https://openalex.org/W2293895310","https://openalex.org/W2295838772","https://openalex.org/W2406839271","https://openalex.org/W2472614804","https://openalex.org/W2510726753","https://openalex.org/W2515656721","https://openalex.org/W2731470241","https://openalex.org/W2733079097","https://openalex.org/W2743482027","https://openalex.org/W2757812197","https://openalex.org/W2765937481","https://openalex.org/W2798299123","https://openalex.org/W2798556801","https://openalex.org/W2803581054","https://openalex.org/W2902687082","https://openalex.org/W2905232526","https://openalex.org/W2911827163","https://openalex.org/W2916755420","https://openalex.org/W2934040968","https://openalex.org/W2962920088","https://openalex.org/W2963638222","https://openalex.org/W2963765784","https://openalex.org/W2964181739","https://openalex.org/W2964301529","https://openalex.org/W2964305797","https://openalex.org/W2964659165","https://openalex.org/W2964755768","https://openalex.org/W2965097461","https://openalex.org/W2997807514","https://openalex.org/W2999721086","https://openalex.org/W3030119148","https://openalex.org/W3090793260","https://openalex.org/W3102362637","https://openalex.org/W3104964042","https://openalex.org/W3105116513","https://openalex.org/W3105262158","https://openalex.org/W3105908601","https://openalex.org/W3106009785","https://openalex.org/W3149816478"],"related_works":["https://openalex.org/W3188877929","https://openalex.org/W2897341314","https://openalex.org/W2399399745","https://openalex.org/W3099982020","https://openalex.org/W2944379287","https://openalex.org/W2964325613","https://openalex.org/W2660255895","https://openalex.org/W2590672467","https://openalex.org/W2910182226","https://openalex.org/W2159159702","https://openalex.org/W1492249171","https://openalex.org/W2524305909","https://openalex.org/W1996152169","https://openalex.org/W2032094818","https://openalex.org/W2940475269","https://openalex.org/W142319970","https://openalex.org/W2288327229","https://openalex.org/W2058199794","https://openalex.org/W40564209","https://openalex.org/W92930600"],"abstract_inverted_index":{"We":[0,29,61,120],"introduce":[1],"MTT,":[2],"a":[3,15,20,78,99,103,151],"dependent":[4],"type":[5,43,91,106],"theory":[6,17,36,44,107],"which":[7,18],"supports":[8],"multiple":[9],"modalities.":[10],"MTT":[11,76,97,125],"is":[12],"parametrized":[13],"by":[14],"mode":[16,35,145],"specifies":[19],"collection":[21],"of":[22,34,118,124,132,141,144,154],"modes,":[23],"modalities,":[24],"and":[25,47,58,70,80,126,147],"transformations":[26],"between":[27],"them.":[28],"show":[30],"that":[31,75,108],"different":[32],"choices":[33],"allow":[37],"us":[38],"to":[39,45,87,98,150],"use":[40],"the":[41,116,122,142],"same":[42],"compute":[46],"reason":[48],"in":[49,67],"many":[50],"modal":[51,90,155],"situations,":[52],"including":[53],"guarded":[54,68],"recursion,":[55],"axiomatic":[56,71],"cohesion,":[57,72],"parametric":[59],"quantification.":[60],"reproduce":[62],"examples":[63],"from":[64],"prior":[65,111],"work":[66],"recursion":[69],"thereby":[73],"demonstrating":[74],"constitutes":[77],"simple":[79],"usable":[81],"syntax":[82],"whose":[83],"instantiations":[84],"intuitively":[85],"correspond":[86],"previous":[88],"handcrafted":[89],"theories.":[92],"In":[93],"some":[94],"cases,":[95],"instantiating":[96],"particular":[100],"situation":[101],"unearths":[102],"previously":[104],"unknown":[105],"improves":[109],"upon":[110],"systems.":[112],"Finally,":[113],"we":[114],"investigate":[115],"metatheory":[117],"MTT.":[119],"prove":[121],"consistency":[123],"establish":[127],"canonicity":[128],"through":[129],"an":[130],"extension":[131],"recent":[133],"type-theoretic":[134],"gluing":[135],"techniques.":[136],"These":[137],"results":[138],"hold":[139],"irrespective":[140],"choice":[143],"theory,":[146],"thus":[148],"apply":[149],"wide":[152],"variety":[153],"situations.":[156]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
