{"id":"https://openalex.org/W2135641508","doi":"https://doi.org/10.2178/jsl/1164060460","title":"Glivenko theorems for substructural logics over FL","display_name":"Glivenko theorems for substructural logics over FL","publication_year":2006,"publication_date":"2006-12-01","ids":{"openalex":"https://openalex.org/W2135641508","doi":"https://doi.org/10.2178/jsl/1164060460","mag":"2135641508"},"language":"en","primary_location":{"id":"doi:10.2178/jsl/1164060460","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1164060460","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"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":"Journal of Symbolic Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://dspace.jaist.ac.jp/dspace/bitstream/10119/8554/1/9278.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5006796466","display_name":"Nikolaos Galatos","orcid":"https://orcid.org/0000-0001-8707-8844"},"institutions":[{"id":"https://openalex.org/I177738480","display_name":"Japan Advanced Institute of Science and Technology","ror":"https://ror.org/03frj4r98","country_code":"JP","type":"education","lineage":["https://openalex.org/I177738480"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Nikolaos Galatos","raw_affiliation_strings":["Japan Advanced Institute of Science and Technology School, of Information Science, 1-1 Asahidai, Nomi, Ishikawa, 923-1292, Japan, E-mail:","Japan Advanced Institute of Science and Technology School"],"affiliations":[{"raw_affiliation_string":"Japan Advanced Institute of Science and Technology School, of Information Science, 1-1 Asahidai, Nomi, Ishikawa, 923-1292, Japan, E-mail:","institution_ids":["https://openalex.org/I177738480"]},{"raw_affiliation_string":"Japan Advanced Institute of Science and Technology School","institution_ids":["https://openalex.org/I177738480"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112179462","display_name":"Hiroakira Ono","orcid":null},"institutions":[{"id":"https://openalex.org/I177738480","display_name":"Japan Advanced Institute of Science and Technology","ror":"https://ror.org/03frj4r98","country_code":"JP","type":"education","lineage":["https://openalex.org/I177738480"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Hiroakira Ono","raw_affiliation_strings":["Japan Advanced Institute of Science and Technology School, of Information Science, 1-1 Asahidai, Nomi, Ishikawa, 923-1292, Japan, E-mail:","Japan Advanced Institute of Science and Technology School"],"affiliations":[{"raw_affiliation_string":"Japan Advanced Institute of Science and Technology School, of Information Science, 1-1 Asahidai, Nomi, Ishikawa, 923-1292, Japan, E-mail:","institution_ids":["https://openalex.org/I177738480"]},{"raw_affiliation_string":"Japan Advanced Institute of Science and Technology School","institution_ids":["https://openalex.org/I177738480"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5006796466"],"corresponding_institution_ids":["https://openalex.org/I177738480"],"apc_list":null,"apc_paid":null,"fwci":2.0223,"has_fulltext":true,"cited_by_count":28,"citation_normalized_percentile":{"value":0.86963441,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"71","issue":"4","first_page":"1353","last_page":"1384"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9998999834060669,"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":0.9998999834060669,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9997000098228455,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9957000017166138,"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":0.8062102198600769},{"id":"https://openalex.org/keywords/monoidal-t-norm-logic","display_name":"Monoidal t-norm logic","score":0.749389111995697},{"id":"https://openalex.org/keywords/negation","display_name":"Negation","score":0.654340386390686},{"id":"https://openalex.org/keywords/intuitionistic-logic","display_name":"Intuitionistic logic","score":0.6126439571380615},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.48594391345977783},{"id":"https://openalex.org/keywords/intermediate-logic","display_name":"Intermediate logic","score":0.48070889711380005},{"id":"https://openalex.org/keywords/classical-logic","display_name":"Classical logic","score":0.47744208574295044},{"id":"https://openalex.org/keywords/t-norm-fuzzy-logics","display_name":"T-norm fuzzy logics","score":0.4717239737510681},{"id":"https://openalex.org/keywords/substructural-logic","display_name":"Substructural logic","score":0.4517570734024048},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4424525201320648},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4330865740776062},{"id":"https://openalex.org/keywords/translation","display_name":"Translation (biology)","score":0.4286355674266815},{"id":"https://openalex.org/keywords/many-valued-logic","display_name":"Many-valued logic","score":0.41134247183799744},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4103240370750427},{"id":"https://openalex.org/keywords/propositional-calculus","display_name":"Propositional calculus","score":0.3420088291168213},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.11064782738685608},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10842987895011902},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08362686634063721},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07914701104164124},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.05998349189758301}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8062102198600769},{"id":"https://openalex.org/C98224912","wikidata":"https://www.wikidata.org/wiki/Q6901647","display_name":"Monoidal t-norm logic","level":5,"score":0.749389111995697},{"id":"https://openalex.org/C2185349","wikidata":"https://www.wikidata.org/wiki/Q190558","display_name":"Negation","level":2,"score":0.654340386390686},{"id":"https://openalex.org/C178421362","wikidata":"https://www.wikidata.org/wiki/Q176786","display_name":"Intuitionistic logic","level":3,"score":0.6126439571380615},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.48594391345977783},{"id":"https://openalex.org/C33203268","wikidata":"https://www.wikidata.org/wiki/Q5361594","display_name":"Intermediate logic","level":3,"score":0.48070889711380005},{"id":"https://openalex.org/C32241873","wikidata":"https://www.wikidata.org/wiki/Q236975","display_name":"Classical logic","level":2,"score":0.47744208574295044},{"id":"https://openalex.org/C86602344","wikidata":"https://www.wikidata.org/wiki/Q7667918","display_name":"T-norm fuzzy logics","level":5,"score":0.4717239737510681},{"id":"https://openalex.org/C144760519","wikidata":"https://www.wikidata.org/wiki/Q839490","display_name":"Substructural logic","level":4,"score":0.4517570734024048},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4424525201320648},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4330865740776062},{"id":"https://openalex.org/C149364088","wikidata":"https://www.wikidata.org/wiki/Q185917","display_name":"Translation (biology)","level":4,"score":0.4286355674266815},{"id":"https://openalex.org/C150889026","wikidata":"https://www.wikidata.org/wiki/Q185502","display_name":"Many-valued logic","level":3,"score":0.41134247183799744},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4103240370750427},{"id":"https://openalex.org/C69562738","wikidata":"https://www.wikidata.org/wiki/Q200694","display_name":"Propositional calculus","level":2,"score":0.3420088291168213},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.11064782738685608},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10842987895011902},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08362686634063721},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07914701104164124},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.05998349189758301},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C105580179","wikidata":"https://www.wikidata.org/wiki/Q188928","display_name":"Messenger RNA","level":3,"score":0.0},{"id":"https://openalex.org/C5263885","wikidata":"https://www.wikidata.org/wiki/Q1967302","display_name":"Membership function","level":4,"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.2178/jsl/1164060460","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1164060460","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"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":"Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:irdb.nii.ac.jp:01333:0002022181","is_oa":true,"landing_page_url":"http://hdl.handle.net/10119/8554","pdf_url":"https://dspace.jaist.ac.jp/dspace/bitstream/10119/8554/1/9278.pdf","source":{"id":"https://openalex.org/S7407056385","display_name":"Institutional Repositories DataBase (IRDB)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I184597095","host_organization_name":"National Institute of Informatics","host_organization_lineage":["https://openalex.org/I184597095"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"The Journal of Symbolic Logic","raw_type":"journal article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1164060460","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1164060460","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"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":"","raw_type":"Text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.98.4368","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.98.4368","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.jaist.ac.jp/~galatos/research/slgt.pdf","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:irdb.nii.ac.jp:01333:0002022181","is_oa":true,"landing_page_url":"http://hdl.handle.net/10119/8554","pdf_url":"https://dspace.jaist.ac.jp/dspace/bitstream/10119/8554/1/9278.pdf","source":{"id":"https://openalex.org/S7407056385","display_name":"Institutional Repositories DataBase (IRDB)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I184597095","host_organization_name":"National Institute of Informatics","host_organization_lineage":["https://openalex.org/I184597095"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"The Journal of Symbolic Logic","raw_type":"journal article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2135641508.pdf","grobid_xml":"https://content.openalex.org/works/W2135641508.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W1554619471","https://openalex.org/W1566552629","https://openalex.org/W2047865342","https://openalex.org/W2051838285","https://openalex.org/W2057500258","https://openalex.org/W2057843935","https://openalex.org/W2062581225","https://openalex.org/W2110182592","https://openalex.org/W2146205527","https://openalex.org/W2149406562","https://openalex.org/W2156760583","https://openalex.org/W2293835309","https://openalex.org/W4252113473","https://openalex.org/W4285719527","https://openalex.org/W4388313858"],"related_works":["https://openalex.org/W16267316","https://openalex.org/W4294175725","https://openalex.org/W2310799747","https://openalex.org/W637989598","https://openalex.org/W2153288022","https://openalex.org/W193449051","https://openalex.org/W1591042624","https://openalex.org/W3010532782","https://openalex.org/W1989043907","https://openalex.org/W2030948396"],"abstract_inverted_index":{"Abstract":[0],"It":[1],"is":[2,24,33,67,70],"well":[3],"known":[4],"that":[5,21,44,56],"classical":[6],"propositional":[7],"logic":[8,49,55],"can":[9],"be":[10],"interpreted":[11],"in":[12,26,35,72],"intuitionistic":[13],"prepositional":[14],"logic.":[15],"In":[16,78],"particular":[17],"Glivenko's":[18,40],"theorem":[19,41],"states":[20],"a":[22,52,61],"formula":[23],"provable":[25,34],"the":[27,36,58,73,79,83,92,100],"former":[28],"iff":[29],"its":[30],"double":[31,62],"negation":[32,63],"latter.":[37],"We":[38],"extend":[39],"and":[42,69,95],"show":[43],"for":[45],"every":[46],"involutive":[47],"substructural":[48,54],"there":[50],"exists":[51],"minimum":[53],"contains":[57],"first":[59],"via":[60],"interpretation.":[64],"Our":[65],"presentation":[66],"algebraic":[68],"formulated":[71],"context":[74],"of":[75,82,91],"residuated":[76],"lattices.":[77],"last":[80],"part":[81],"paper,":[84],"we":[85,96],"also":[86],"discuss":[87],"some":[88],"extended":[89],"forms":[90],"Koltnogorov":[93],"translation":[94],"compare":[97],"it":[98],"to":[99],"Glivenko":[101],"translation.":[102]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}