{"id":"https://openalex.org/W4289793388","doi":"https://doi.org/10.1145/3531130.3533373","title":"Linear-Algebraic Models of Linear Logic as Categories of Modules over \u03a3-Semirings\u2731","display_name":"Linear-Algebraic Models of Linear Logic as Categories of Modules over \u03a3-Semirings\u2731","publication_year":2022,"publication_date":"2022-08-02","ids":{"openalex":"https://openalex.org/W4289793388","doi":"https://doi.org/10.1145/3531130.3533373"},"language":"en","primary_location":{"id":"doi:10.1145/3531130.3533373","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3531130.3533373","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science","raw_type":"proceedings-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/A5090766554","display_name":"Takeshi Tsukada","orcid":"https://orcid.org/0000-0002-2824-8708"},"institutions":[{"id":"https://openalex.org/I159385669","display_name":"Chiba University","ror":"https://ror.org/01hjzeq58","country_code":"JP","type":"education","lineage":["https://openalex.org/I159385669"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Takeshi Tsukada","raw_affiliation_strings":["Chiba University, Japan"],"affiliations":[{"raw_affiliation_string":"Chiba University, Japan","institution_ids":["https://openalex.org/I159385669"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026592834","display_name":"Kazuyuki Asada","orcid":"https://orcid.org/0000-0001-8782-2119"},"institutions":[{"id":"https://openalex.org/I201537933","display_name":"Tohoku University","ror":"https://ror.org/01dq60k83","country_code":"JP","type":"education","lineage":["https://openalex.org/I201537933"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Kazuyuki Asada","raw_affiliation_strings":["Tohoku University, Japan"],"affiliations":[{"raw_affiliation_string":"Tohoku University, Japan","institution_ids":["https://openalex.org/I201537933"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5090766554"],"corresponding_institution_ids":["https://openalex.org/I159385669"],"apc_list":null,"apc_paid":null,"fwci":0.5303,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.70599989,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"13"},"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":0.9988999962806702,"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/T10142","display_name":"Formal Methods in Verification","score":0.9983000159263611,"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":0.6995682120323181},{"id":"https://openalex.org/keywords/morphism","display_name":"Morphism","score":0.6938892006874084},{"id":"https://openalex.org/keywords/linear-logic","display_name":"Linear logic","score":0.628198504447937},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5795958042144775},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.5098578333854675},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4974081814289093},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3862813413143158},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.358306348323822}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6995682120323181},{"id":"https://openalex.org/C137212723","wikidata":"https://www.wikidata.org/wiki/Q1948412","display_name":"Morphism","level":2,"score":0.6938892006874084},{"id":"https://openalex.org/C28077239","wikidata":"https://www.wikidata.org/wiki/Q841728","display_name":"Linear logic","level":2,"score":0.628198504447937},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5795958042144775},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.5098578333854675},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4974081814289093},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3862813413143158},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.358306348323822},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3531130.3533373","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3531130.3533373","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6595427402","display_name":null,"funder_award_id":"20H05703,18K11156","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W147093031","https://openalex.org/W1502758407","https://openalex.org/W1532754343","https://openalex.org/W1560529447","https://openalex.org/W1563218161","https://openalex.org/W1595870841","https://openalex.org/W1976800160","https://openalex.org/W1999626800","https://openalex.org/W2007411063","https://openalex.org/W2033104047","https://openalex.org/W2035353176","https://openalex.org/W2048626648","https://openalex.org/W2053791527","https://openalex.org/W2059456146","https://openalex.org/W2065261632","https://openalex.org/W2072411754","https://openalex.org/W2077767673","https://openalex.org/W2079873887","https://openalex.org/W2090319048","https://openalex.org/W2099951171","https://openalex.org/W2102548545","https://openalex.org/W2102723093","https://openalex.org/W2113447082","https://openalex.org/W2129290355","https://openalex.org/W2144311135","https://openalex.org/W2486680525","https://openalex.org/W2513421427","https://openalex.org/W2606916197","https://openalex.org/W2614105559","https://openalex.org/W2798871919","https://openalex.org/W2911865844","https://openalex.org/W2911874855","https://openalex.org/W4224863583","https://openalex.org/W4238692953","https://openalex.org/W4244792815","https://openalex.org/W4289793388"],"related_works":["https://openalex.org/W4375947497","https://openalex.org/W3126773016","https://openalex.org/W2158253985","https://openalex.org/W2963288673","https://openalex.org/W1996580892","https://openalex.org/W2561284090","https://openalex.org/W2150706552","https://openalex.org/W2787271079","https://openalex.org/W1701381474","https://openalex.org/W4300537419"],"abstract_inverted_index":{"A":[0],"number":[1],"of":[2,4,64,107,115,131,143,154],"models":[3,29,67,92,145,151],"linear":[5,14,61,133],"logic":[6,134],"are":[7,21,78,93,152],"based":[8,30,55],"on":[9,31,56],"or":[10],"closely":[11],"related":[12],"to":[13],"algebra,":[15],"in":[16,89,97],"the":[17,43,60,65,90,98,113,136,149],"sense":[18,101],"that":[19,87,112,125,148],"morphisms":[20,88],"\u201cmatrices\u201d":[22],"over":[23,74],"appropriate":[24,103],"coefficient":[25],"sets.":[26],"Examples":[27],"include":[28],"coherence":[32,38],"spaces,":[33,39],"finiteness":[34],"spaces":[35],"and":[36,45,85,146],"probabilistic":[37],"as":[40,42],"well":[41],"relational":[44,47],"weighted":[46],"models.":[48],"This":[49],"paper":[50],"introduces":[51],"a":[52,129],"unified":[53],"framework":[54],"module":[57],"theory,":[58],"making":[59],"algebraic":[62,100,109],"aspect":[63],"above":[66,91],"more":[68],"explicit.":[69],"Specifically":[70],"we":[71],"consider":[72],"modules":[73],"\u03a3-semirings":[75],"R,":[76],"which":[77,121],"ring-like":[79],"structures":[80],"with":[81,135],"partially-defined":[82],"countable":[83],"sums,":[84],"show":[86,147],"actually":[94],"R-linear":[95],"maps":[96],"standard":[99],"for":[102],"R.":[104],"An":[105],"advantage":[106],"our":[108,155],"treatment":[110],"is":[111,117],"category":[114,127],"R-modules":[116],"locally":[118],"presentable,":[119],"from":[120],"it":[122],"easily":[123],"follows":[124],"this":[126],"becomes":[128],"model":[130],"intuitionistic":[132],"cofree":[137],"exponential.":[138],"We":[139],"then":[140],"discuss":[141],"constructions":[142],"classical":[144],"above-mentioned":[150],"examples":[153],"constructions.":[156]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}