{"id":"https://openalex.org/W4385064979","doi":"https://doi.org/10.1002/malq.202200062","title":"A categorical equivalence between logical quantale modules and quantum B\u2010modules","display_name":"A categorical equivalence between logical quantale modules and quantum B\u2010modules","publication_year":2023,"publication_date":"2023-07-20","ids":{"openalex":"https://openalex.org/W4385064979","doi":"https://doi.org/10.1002/malq.202200062"},"language":"en","primary_location":{"id":"doi:10.1002/malq.202200062","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.202200062","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0044-3050","issn":["0044-3050","0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","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/A5007613856","display_name":"Xianglong Ruan","orcid":null},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xianglong Ruan","raw_affiliation_strings":["School of Mathematics and Statistics Xi'an Jiaotong University Xi'an China","School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, China"],"raw_orcid":"https://orcid.org/0000-0002-5409-583X","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics Xi'an Jiaotong University Xi'an China","institution_ids":["https://openalex.org/I87445476"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100698267","display_name":"Xiaochuan Liu","orcid":"https://orcid.org/0000-0001-7575-8279"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaochuan Liu","raw_affiliation_strings":["School of Mathematics and Statistics Xi'an Jiaotong University Xi'an China","School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics Xi'an Jiaotong University Xi'an China","institution_ids":["https://openalex.org/I87445476"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, China","institution_ids":["https://openalex.org/I87445476"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5007613856"],"corresponding_institution_ids":["https://openalex.org/I87445476"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":0.1727,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.5163378,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"69","issue":"4","first_page":"446","last_page":"459"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9993000030517578,"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"}},"topics":[{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9993000030517578,"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"}},{"id":"https://openalex.org/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9764999747276306,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9702000021934509,"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/mathematics","display_name":"Mathematics","score":0.8863383531570435},{"id":"https://openalex.org/keywords/categorical-variable","display_name":"Categorical variable","score":0.672732412815094},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.6378165483474731},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.5903159379959106},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5673198699951172},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5636127591133118},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.46427103877067566},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4226994216442108},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3242048919200897},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08099165558815002},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06646728515625},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.044084906578063965}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8863383531570435},{"id":"https://openalex.org/C5274069","wikidata":"https://www.wikidata.org/wiki/Q2285707","display_name":"Categorical variable","level":2,"score":0.672732412815094},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.6378165483474731},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.5903159379959106},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5673198699951172},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5636127591133118},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.46427103877067566},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4226994216442108},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3242048919200897},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08099165558815002},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06646728515625},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.044084906578063965},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/malq.202200062","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.202200062","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0044-3050","issn":["0044-3050","0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.4300000071525574}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W118412823","https://openalex.org/W1965338471","https://openalex.org/W1970065243","https://openalex.org/W1990882135","https://openalex.org/W2019966378","https://openalex.org/W2033804681","https://openalex.org/W2066667341","https://openalex.org/W2120713972","https://openalex.org/W2122876637","https://openalex.org/W2162303771","https://openalex.org/W2572078071","https://openalex.org/W2602178304","https://openalex.org/W2803827492","https://openalex.org/W2943396731","https://openalex.org/W4212826843","https://openalex.org/W4239527120","https://openalex.org/W4290603386","https://openalex.org/W4297472956","https://openalex.org/W4300609043","https://openalex.org/W4413966096","https://openalex.org/W6680259707"],"related_works":["https://openalex.org/W4386799044","https://openalex.org/W2773208253","https://openalex.org/W2560646951","https://openalex.org/W4297454206","https://openalex.org/W65104662","https://openalex.org/W1871748041","https://openalex.org/W2362286668","https://openalex.org/W2133382151","https://openalex.org/W2153339597","https://openalex.org/W1528412344"],"abstract_inverted_index":{"Abstract":[0],"This":[1],"paper":[2],"introduces":[3],"the":[4,19,26,32,47],"notion":[5],"of":[6,21,28],"logical":[7,22,44],"quantale":[8,23,45,49],"module.":[9,50],"It":[10],"proves":[11],"that":[12,34],"there":[13],"is":[14],"a":[15,39,43],"dual":[16],"equivalence":[17],"between":[18],"category":[20,27],"modules":[24],"and":[25],"quantum":[29,36],"B\u2010modules,":[30],"in":[31],"way":[33],"every":[35],"B\u2010module":[37],"admits":[38],"natural":[40],"embedding":[41],"into":[42],"module,":[46],"enveloping":[48]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}