{"id":"https://openalex.org/W2092185282","doi":"https://doi.org/10.1017/s0960129502003717","title":"The logic of linear functors","display_name":"The logic of linear functors","publication_year":2002,"publication_date":"2002-08-01","ids":{"openalex":"https://openalex.org/W2092185282","doi":"https://doi.org/10.1017/s0960129502003717","mag":"2092185282"},"language":"en","primary_location":{"id":"doi:10.1017/s0960129502003717","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0960129502003717","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":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087503903","display_name":"Richard Blute","orcid":null},"institutions":[{"id":"https://openalex.org/I153718931","display_name":"University of Ottawa","ror":"https://ror.org/03c4mmv16","country_code":"CA","type":"education","lineage":["https://openalex.org/I153718931"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"R. BLUTE","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Ottawa, 585 King Edward St, Ottawa, ON, K1N6N5, Canada. Email:","Department of Mathematics and Statistics, University of Ottawa, 585 King Edward St, Ottawa, ON, K1N6N5, Canada. Email: rblute@mathstat.uottawa.ca#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Ottawa, 585 King Edward St, Ottawa, ON, K1N6N5, Canada. Email:","institution_ids":["https://openalex.org/I153718931"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Ottawa, 585 King Edward St, Ottawa, ON, K1N6N5, Canada. Email: rblute@mathstat.uottawa.ca#TAB#","institution_ids":["https://openalex.org/I153718931"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053636420","display_name":"J.R.B. Cockett","orcid":null},"institutions":[{"id":"https://openalex.org/I153718931","display_name":"University of Ottawa","ror":"https://ror.org/03c4mmv16","country_code":"CA","type":"education","lineage":["https://openalex.org/I153718931"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"J. R. B. COCKETT","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Ottawa, 585 King Edward St, Ottawa, ON, K1N6N5, Canada. Email:","Department of Mathematics and Statistics, University of Ottawa, 585 King Edward St, Ottawa, ON, K1N6N5, Canada. Email: rblute@mathstat.uottawa.ca#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Ottawa, 585 King Edward St, Ottawa, ON, K1N6N5, Canada. Email:","institution_ids":["https://openalex.org/I153718931"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Ottawa, 585 King Edward St, Ottawa, ON, K1N6N5, Canada. Email: rblute@mathstat.uottawa.ca#TAB#","institution_ids":["https://openalex.org/I153718931"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084038892","display_name":"R. A. G. Seely","orcid":null},"institutions":[{"id":"https://openalex.org/I153718931","display_name":"University of Ottawa","ror":"https://ror.org/03c4mmv16","country_code":"CA","type":"education","lineage":["https://openalex.org/I153718931"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"R. A. G. SEELY","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Ottawa, 585 King Edward St, Ottawa, ON, K1N6N5, Canada. Email:","Department of Mathematics and Statistics, University of Ottawa, 585 King Edward St, Ottawa, ON, K1N6N5, Canada. Email: rblute@mathstat.uottawa.ca#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Ottawa, 585 King Edward St, Ottawa, ON, K1N6N5, Canada. Email:","institution_ids":["https://openalex.org/I153718931"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Ottawa, 585 King Edward St, Ottawa, ON, K1N6N5, Canada. Email: rblute@mathstat.uottawa.ca#TAB#","institution_ids":["https://openalex.org/I153718931"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5087503903"],"corresponding_institution_ids":["https://openalex.org/I153718931"],"apc_list":null,"apc_paid":null,"fwci":1.7046,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.86189837,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"12","issue":"4","first_page":"513","last_page":"539"},"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9922999739646912,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9914000034332275,"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/functor","display_name":"Functor","score":0.7075687050819397},{"id":"https://openalex.org/keywords/linear-logic","display_name":"Linear logic","score":0.6191142201423645},{"id":"https://openalex.org/keywords/substructural-logic","display_name":"Substructural logic","score":0.5865064263343811},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5632486939430237},{"id":"https://openalex.org/keywords/noncommutative-geometry","display_name":"Noncommutative geometry","score":0.5444530248641968},{"id":"https://openalex.org/keywords/intermediate-logic","display_name":"Intermediate logic","score":0.5198045969009399},{"id":"https://openalex.org/keywords/multimodal-logic","display_name":"Multimodal logic","score":0.5136899352073669},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.47764813899993896},{"id":"https://openalex.org/keywords/predicate-logic","display_name":"Predicate logic","score":0.47098490595817566},{"id":"https://openalex.org/keywords/higher-order-logic","display_name":"Higher-order logic","score":0.46873006224632263},{"id":"https://openalex.org/keywords/normal-modal-logic","display_name":"Normal modal logic","score":0.460018128156662},{"id":"https://openalex.org/keywords/linear-temporal-logic","display_name":"Linear temporal logic","score":0.43494710326194763},{"id":"https://openalex.org/keywords/modal-logic","display_name":"Modal logic","score":0.43328070640563965},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.41317373514175415},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3285647928714752},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3072226345539093},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.28632378578186035},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.28452181816101074},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.23859769105911255},{"id":"https://openalex.org/keywords/modal","display_name":"Modal","score":0.20074811577796936}],"concepts":[{"id":"https://openalex.org/C156772000","wikidata":"https://www.wikidata.org/wiki/Q864475","display_name":"Functor","level":2,"score":0.7075687050819397},{"id":"https://openalex.org/C28077239","wikidata":"https://www.wikidata.org/wiki/Q841728","display_name":"Linear logic","level":2,"score":0.6191142201423645},{"id":"https://openalex.org/C144760519","wikidata":"https://www.wikidata.org/wiki/Q839490","display_name":"Substructural logic","level":4,"score":0.5865064263343811},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5632486939430237},{"id":"https://openalex.org/C68797384","wikidata":"https://www.wikidata.org/wiki/Q2746792","display_name":"Noncommutative geometry","level":2,"score":0.5444530248641968},{"id":"https://openalex.org/C33203268","wikidata":"https://www.wikidata.org/wiki/Q5361594","display_name":"Intermediate logic","level":3,"score":0.5198045969009399},{"id":"https://openalex.org/C203659156","wikidata":"https://www.wikidata.org/wiki/Q6934805","display_name":"Multimodal logic","level":3,"score":0.5136899352073669},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.47764813899993896},{"id":"https://openalex.org/C19689857","wikidata":"https://www.wikidata.org/wiki/Q4055684","display_name":"Predicate logic","level":3,"score":0.47098490595817566},{"id":"https://openalex.org/C169896238","wikidata":"https://www.wikidata.org/wiki/Q1644136","display_name":"Higher-order logic","level":3,"score":0.46873006224632263},{"id":"https://openalex.org/C114092440","wikidata":"https://www.wikidata.org/wiki/Q840226","display_name":"Normal modal logic","level":4,"score":0.460018128156662},{"id":"https://openalex.org/C4777664","wikidata":"https://www.wikidata.org/wiki/Q1536492","display_name":"Linear temporal logic","level":2,"score":0.43494710326194763},{"id":"https://openalex.org/C27508121","wikidata":"https://www.wikidata.org/wiki/Q210841","display_name":"Modal logic","level":3,"score":0.43328070640563965},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.41317373514175415},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3285647928714752},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3072226345539093},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28632378578186035},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.28452181816101074},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.23859769105911255},{"id":"https://openalex.org/C71139939","wikidata":"https://www.wikidata.org/wiki/Q910194","display_name":"Modal","level":2,"score":0.20074811577796936},{"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1017/s0960129502003717","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0960129502003717","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:CiteSeerX.psu:10.1.1.27.1241","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.27.1241","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.mcgill.ca/rags/linear/lfl.ps.gz","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W33924498","https://openalex.org/W157609137","https://openalex.org/W367533796","https://openalex.org/W1519339236","https://openalex.org/W1596067335","https://openalex.org/W1598954248","https://openalex.org/W1661352576","https://openalex.org/W1968357837","https://openalex.org/W1975997375","https://openalex.org/W1978469611","https://openalex.org/W2008132476","https://openalex.org/W2010407999","https://openalex.org/W2018773995","https://openalex.org/W2041917765","https://openalex.org/W2064911842","https://openalex.org/W2075367647","https://openalex.org/W2078432227","https://openalex.org/W2140500391","https://openalex.org/W2155393363","https://openalex.org/W2163751633","https://openalex.org/W2497183712","https://openalex.org/W2739060726","https://openalex.org/W2911865844"],"related_works":["https://openalex.org/W2170042182","https://openalex.org/W362162902","https://openalex.org/W2396926180","https://openalex.org/W1518114393","https://openalex.org/W2351986896","https://openalex.org/W2086167281","https://openalex.org/W3201792443","https://openalex.org/W1577476108","https://openalex.org/W2110141919","https://openalex.org/W1540220550"],"abstract_inverted_index":{"This":[0,22],"paper":[1,84],"describes":[2],"a":[3,70,124,131],"family":[4],"of":[5,26,66,72,93,134],"logics":[6,27,53,120],"whose":[7,34],"categorical":[8,91],"semantics":[9],"is":[10],"based":[11,122],"on":[12,18,114,123],"functors":[13],"with":[14,20],"structure":[15],"rather":[16],"than":[17],"categories":[19],"structure.":[21],"allows":[23],"the":[24,63,90,102,109,115,119],"consideration":[25],"that":[28,75,105,142],"contain":[29],"possibly":[30],"distinct":[31],"logical":[32],"subsystems":[33],"interactions":[35],"are":[36,121],"mediated":[37],"by":[38],"functorial":[39],"mappings.":[40],"For":[41],"example,":[42],"within":[43],"one":[44],"unified":[45],"framework,":[46],"we":[47,111],"shall":[48,112],"be":[49,140],"able":[50],"to":[51,96,100,129,145],"handle":[52],"as":[54,56],"diverse":[55],"modal":[57],"logic,":[58,61,97,110],"ordinary":[59],"linear":[60,73,125],"and":[62,68,79],"\u2018noncommutative":[64],"logic\u2019":[65],"Abrusci":[67],"Ruet,":[69],"variant":[71],"logic":[74,146],"has":[76,147],"both":[77],"commutative":[78],"noncommutative":[80],"connectives.":[81],"Although":[82],"this":[83,94,143],"will":[85,139],"not":[86],"consider":[87],"in":[88,108,127],"depth":[89],"basis":[92],"approach":[95,144],"preferring":[98],"instead":[99],"emphasise":[101],"syntactic":[103],"novelties":[104],"it":[106,138],"generates":[107],"focus":[113],"particular":[116],"case":[117],"when":[118],"functor,":[126],"order":[128],"give":[130],"definite":[132],"presentation":[133],"these":[135],"ideas.":[136],"However,":[137],"clear":[141],"considerable":[148],"generality.":[149]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}