{"id":"https://openalex.org/W4366548651","doi":"https://doi.org/10.1007/978-3-031-30829-1_6","title":"A Formal Logic for Formal Category Theory","display_name":"A Formal Logic for Formal Category Theory","publication_year":2023,"publication_date":"2023-01-01","ids":{"openalex":"https://openalex.org/W4366548651","doi":"https://doi.org/10.1007/978-3-031-30829-1_6"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-031-30829-1_6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-30829-1_6","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-30829-1_6.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/10.1007/978-3-031-30829-1_6.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050680882","display_name":"Max S. New","orcid":"https://orcid.org/0000-0001-8141-195X"},"institutions":[{"id":"https://openalex.org/I100538780","display_name":"Wesleyan University","ror":"https://ror.org/05h7xva58","country_code":"US","type":"education","lineage":["https://openalex.org/I100538780"]},{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Max S. New","raw_affiliation_strings":["University of Michigan, Ann Arbor, USA","Wesleyan University, Middletown, USA"],"affiliations":[{"raw_affiliation_string":"University of Michigan, Ann Arbor, USA","institution_ids":["https://openalex.org/I27837315"]},{"raw_affiliation_string":"Wesleyan University, Middletown, USA","institution_ids":["https://openalex.org/I100538780"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009198759","display_name":"Daniel R. Licata","orcid":"https://orcid.org/0000-0003-0697-7405"},"institutions":[{"id":"https://openalex.org/I100538780","display_name":"Wesleyan University","ror":"https://ror.org/05h7xva58","country_code":"US","type":"education","lineage":["https://openalex.org/I100538780"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Daniel R. Licata","raw_affiliation_strings":["Wesleyan University, Middletown, USA"],"affiliations":[{"raw_affiliation_string":"Wesleyan University, Middletown, USA","institution_ids":["https://openalex.org/I100538780"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5050680882"],"corresponding_institution_ids":["https://openalex.org/I100538780","https://openalex.org/I27837315"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":{"value":5000,"currency":"EUR","value_usd":5392},"fwci":1.5627,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.82843882,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"113","last_page":"134"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9822999835014343,"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/T10215","display_name":"Semantic Web and Ontologies","score":0.9724000096321106,"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/type-theory","display_name":"Type theory","score":0.7562527656555176},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.7159842252731323},{"id":"https://openalex.org/keywords/category-theory","display_name":"Category theory","score":0.7116755247116089},{"id":"https://openalex.org/keywords/proof-theory","display_name":"Proof theory","score":0.6092174649238586},{"id":"https://openalex.org/keywords/partial-function","display_name":"Partial function","score":0.575965166091919},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.5383532643318176},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5100348591804504},{"id":"https://openalex.org/keywords/predicate","display_name":"Predicate (mathematical logic)","score":0.46923476457595825},{"id":"https://openalex.org/keywords/predicate-logic","display_name":"Predicate logic","score":0.46258091926574707},{"id":"https://openalex.org/keywords/functor","display_name":"Functor","score":0.4590508043766022},{"id":"https://openalex.org/keywords/natural-deduction","display_name":"Natural deduction","score":0.454842209815979},{"id":"https://openalex.org/keywords/domain-theory","display_name":"Domain theory","score":0.4543239176273346},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.451049268245697},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4218778908252716},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3730798363685608},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.344930499792099},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.32124602794647217},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.20564883947372437},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.16077476739883423}],"concepts":[{"id":"https://openalex.org/C93682546","wikidata":"https://www.wikidata.org/wiki/Q1056428","display_name":"Type theory","level":3,"score":0.7562527656555176},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.7159842252731323},{"id":"https://openalex.org/C54884031","wikidata":"https://www.wikidata.org/wiki/Q217413","display_name":"Category theory","level":2,"score":0.7116755247116089},{"id":"https://openalex.org/C2318724","wikidata":"https://www.wikidata.org/wiki/Q852732","display_name":"Proof theory","level":3,"score":0.6092174649238586},{"id":"https://openalex.org/C182359184","wikidata":"https://www.wikidata.org/wiki/Q1756942","display_name":"Partial function","level":2,"score":0.575965166091919},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.5383532643318176},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5100348591804504},{"id":"https://openalex.org/C140146324","wikidata":"https://www.wikidata.org/wiki/Q1144319","display_name":"Predicate (mathematical logic)","level":2,"score":0.46923476457595825},{"id":"https://openalex.org/C19689857","wikidata":"https://www.wikidata.org/wiki/Q4055684","display_name":"Predicate logic","level":3,"score":0.46258091926574707},{"id":"https://openalex.org/C156772000","wikidata":"https://www.wikidata.org/wiki/Q864475","display_name":"Functor","level":2,"score":0.4590508043766022},{"id":"https://openalex.org/C62073222","wikidata":"https://www.wikidata.org/wiki/Q1572108","display_name":"Natural deduction","level":2,"score":0.454842209815979},{"id":"https://openalex.org/C29585364","wikidata":"https://www.wikidata.org/wiki/Q1079166","display_name":"Domain theory","level":2,"score":0.4543239176273346},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.451049268245697},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4218778908252716},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3730798363685608},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.344930499792099},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32124602794647217},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.20564883947372437},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.16077476739883423},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-031-30829-1_6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-30829-1_6","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-30829-1_6.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"}],"best_oa_location":{"id":"doi:10.1007/978-3-031-30829-1_6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-30829-1_6","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-30829-1_6.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/G3339474184","display_name":null,"funder_award_id":"CCF-1909517","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7090116110","display_name":null,"funder_award_id":"FA9550","funder_id":"https://openalex.org/F4320332467","funder_display_name":"U.S. Air Force"},{"id":"https://openalex.org/G7491292904","display_name":"SHF: Small: Collaborative Research: Foundations for Gradual Typing","funder_award_id":"1909517","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320332467","display_name":"U.S. Air Force","ror":"https://ror.org/006gmme17"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4366548651.pdf"},"referenced_works_count":43,"referenced_works":["https://openalex.org/W111511002","https://openalex.org/W158035142","https://openalex.org/W1480685649","https://openalex.org/W1494555245","https://openalex.org/W1599663594","https://openalex.org/W1761411969","https://openalex.org/W1923962694","https://openalex.org/W1997143185","https://openalex.org/W2006941708","https://openalex.org/W2020900140","https://openalex.org/W2022837260","https://openalex.org/W2031120504","https://openalex.org/W2080801189","https://openalex.org/W2099684400","https://openalex.org/W2103988001","https://openalex.org/W2114058479","https://openalex.org/W2123329569","https://openalex.org/W2147323041","https://openalex.org/W2148713425","https://openalex.org/W2150941507","https://openalex.org/W2155221538","https://openalex.org/W2550513301","https://openalex.org/W2734361589","https://openalex.org/W2793945803","https://openalex.org/W2809523162","https://openalex.org/W2883252932","https://openalex.org/W2911865844","https://openalex.org/W2912512531","https://openalex.org/W2955445504","https://openalex.org/W2963037676","https://openalex.org/W2963912390","https://openalex.org/W3031494424","https://openalex.org/W3101768401","https://openalex.org/W3102482356","https://openalex.org/W3104449041","https://openalex.org/W3114375010","https://openalex.org/W3181070739","https://openalex.org/W4206010916","https://openalex.org/W4206073431","https://openalex.org/W4226301578","https://openalex.org/W4248290615","https://openalex.org/W4288641035","https://openalex.org/W4306801340"],"related_works":["https://openalex.org/W4236197624","https://openalex.org/W4244218901","https://openalex.org/W2022028240","https://openalex.org/W1520530519","https://openalex.org/W2295569337","https://openalex.org/W2158086586","https://openalex.org/W1502495923","https://openalex.org/W1872634431","https://openalex.org/W1559554426","https://openalex.org/W2024873396"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"present":[2],"a":[3,24,113],"domain-specific":[4],"type":[5,15,31,106,133],"theory":[6,16,32,107,134],"for":[7,112],"constructions":[8,148],"and":[9,23,55,75,88,92,110,124,147,153],"proofs":[10,65,69,81,130,146],"in":[11,102,116,131],"category":[12,126],"theory.":[13,127],"The":[14,30,105],"axiomatizes":[17],"notions":[18],"of":[19,27,100],"category,":[20],"functor,":[21],"profunctor":[22],"generalized":[25],"form":[26],"natural":[28,59],"transformations.":[29],"imposes":[33],"an":[34],"ordered":[35,98],"linear":[36],"restriction":[37],"on":[38],"standard":[39,137],"predicate":[40,103],"logic,":[41],"which":[42,120],"guarantees":[43],"that":[44,144],"all":[45,51,56,145],"functions":[46],"between":[47,85],"categories":[48],"are":[49,53,58],"functorial,":[50],"relations":[52],"profunctorial,":[54],"transformations":[57],"by":[60],"construction,":[61],"with":[62],"no":[63],"separate":[64],"necessary.":[66],"Important":[67],"category-theoretic":[68],"such":[70],"as":[71,156],"the":[72,83,129,140],"Yoneda":[73],"lemma":[74,77],"Co-yoneda":[76],"become":[78],"simple":[79],"type-theoretic":[80],"about":[82],"relationship":[84],"unit,":[86],"tensor":[87],"(ordered)":[89],"function":[90],"types,":[91],"can":[93],"be":[94,97],"seen":[95],"to":[96,151],"refinements":[99],"theorems":[101],"logic.":[104],"is":[108],"sound":[109],"complete":[111],"categorical":[114],"model":[115,121],"virtual":[117],"equipments":[118],",":[119],"both":[122],"internal":[123,154],"enriched":[125,152],"While":[128],"our":[132],"look":[135],"like":[136],"set-based":[138],"arguments,":[139],"syntactic":[141],"discipline":[142],"ensure":[143],"carry":[149],"over":[150],"settings":[155],"well.":[157]},"counts_by_year":[{"year":2024,"cited_by_count":3}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}