{"id":"https://openalex.org/W3127142129","doi":"https://doi.org/10.1093/jigpal/jzac043","title":"Finite axiomatizability of logics of distributive lattices with negation","display_name":"Finite axiomatizability of logics of distributive lattices with negation","publication_year":2022,"publication_date":"2022-03-10","ids":{"openalex":"https://openalex.org/W3127142129","doi":"https://doi.org/10.1093/jigpal/jzac043","mag":"3127142129"},"language":"en","primary_location":{"id":"doi:10.1093/jigpal/jzac043","is_oa":false,"landing_page_url":"https://doi.org/10.1093/jigpal/jzac043","pdf_url":null,"source":{"id":"https://openalex.org/S2734381524","display_name":"Logic Journal of IGPL","issn_l":"1367-0751","issn":["1367-0751","1368-9894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logic Journal of the IGPL","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2102.05421","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5083165777","display_name":"S\u00e9rgio Marcelino","orcid":"https://orcid.org/0000-0002-6941-7555"},"institutions":[{"id":"https://openalex.org/I141596103","display_name":"University of Lisbon","ror":"https://ror.org/01c27hj86","country_code":"PT","type":"education","lineage":["https://openalex.org/I141596103"]},{"id":"https://openalex.org/I4210120471","display_name":"Instituto de Telecomunica\u00e7\u00f5es","ror":"https://ror.org/02ht4fk33","country_code":"PT","type":"nonprofit","lineage":["https://openalex.org/I4210120471"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"S\u00e9rgio Marcelino","raw_affiliation_strings":["SQIG\u2013Instituto de Telecomunica\u00e7\u00f5es, Departamento de Matem\u00e1tica , Instituto Superior T\u00e9cnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"SQIG\u2013Instituto de Telecomunica\u00e7\u00f5es, Departamento de Matem\u00e1tica , Instituto Superior T\u00e9cnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal","institution_ids":["https://openalex.org/I4210120471","https://openalex.org/I141596103"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008197317","display_name":"Umberto Rivieccio","orcid":"https://orcid.org/0000-0003-1364-5003"},"institutions":[{"id":"https://openalex.org/I35046152","display_name":"Universidade Federal do Rio Grande do Norte","ror":"https://ror.org/04wn09761","country_code":"BR","type":"education","lineage":["https://openalex.org/I35046152"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Umberto Rivieccio","raw_affiliation_strings":["Departamento de Inform\u00e1tica e Matem\u00e1tica Aplicada, Universidade Federal do Rio Grande do Norte , 59072-970 Natal (RN), Brasil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Inform\u00e1tica e Matem\u00e1tica Aplicada, Universidade Federal do Rio Grande do Norte , 59072-970 Natal (RN), Brasil","institution_ids":["https://openalex.org/I35046152"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5008197317"],"corresponding_institution_ids":["https://openalex.org/I35046152"],"apc_list":{"value":4151,"currency":"USD","value_usd":4151},"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01215238,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"31","issue":"3","first_page":"510","last_page":"533"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9912999868392944,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9607999920845032,"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/distributive-property","display_name":"Distributive property","score":0.7865049839019775},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.7358274459838867},{"id":"https://openalex.org/keywords/negation","display_name":"Negation","score":0.7047361135482788},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.661560595035553},{"id":"https://openalex.org/keywords/subvariety","display_name":"Subvariety","score":0.6277281045913696},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5091409087181091},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4994845390319824},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.4729204773902893},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4233132302761078},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.41102269291877747},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20626163482666016}],"concepts":[{"id":"https://openalex.org/C11821877","wikidata":"https://www.wikidata.org/wiki/Q187959","display_name":"Distributive property","level":2,"score":0.7865049839019775},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.7358274459838867},{"id":"https://openalex.org/C2185349","wikidata":"https://www.wikidata.org/wiki/Q190558","display_name":"Negation","level":2,"score":0.7047361135482788},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.661560595035553},{"id":"https://openalex.org/C2777183706","wikidata":"https://www.wikidata.org/wiki/Q630771","display_name":"Subvariety","level":3,"score":0.6277281045913696},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5091409087181091},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4994845390319824},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.4729204773902893},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4233132302761078},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.41102269291877747},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20626163482666016},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1093/jigpal/jzac043","is_oa":false,"landing_page_url":"https://doi.org/10.1093/jigpal/jzac043","pdf_url":null,"source":{"id":"https://openalex.org/S2734381524","display_name":"Logic Journal of IGPL","issn_l":"1367-0751","issn":["1367-0751","1368-9894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logic Journal of the IGPL","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2102.05421","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2102.05421","pdf_url":"https://arxiv.org/pdf/2102.05421","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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:philarchive.org/rec/MARFAO-9","is_oa":true,"landing_page_url":"https://philarchive.org/rec/MARFAO-9","pdf_url":"https://philpapers.org/archive/MARFAO-9.pdf","source":{"id":"https://openalex.org/S4306402130","display_name":"PhilPapers (PhilPapers Foundation)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"mag:3127142129","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2102.05421","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:philpapers.org/rec/MARFAO-9","is_oa":false,"landing_page_url":"https://philpapers.org/rec/MARFAO-9","pdf_url":null,"source":{"id":"https://openalex.org/S4306402131","display_name":"PhilPapers (PhilPapers Foundation)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.2102.05421","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2102.05421","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2102.05421","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2102.05421","pdf_url":"https://arxiv.org/pdf/2102.05421","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"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"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2144570049","display_name":null,"funder_award_id":"UIDB/50008","funder_id":"https://openalex.org/F4320334779","funder_display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia"},{"id":"https://openalex.org/G3375535518","display_name":"Instituto de Telecomunica\u00e7\u00f5es","funder_award_id":"UIDB/50008/2020","funder_id":"https://openalex.org/F4320334779","funder_display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia"},{"id":"https://openalex.org/G3850789590","display_name":null,"funder_award_id":"50008","funder_id":"https://openalex.org/F4320334779","funder_display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia"},{"id":"https://openalex.org/G8734216529","display_name":null,"funder_award_id":"UIDB/50008/2020","funder_id":"https://openalex.org/F4320323642","funder_display_name":"Minist\u00e9rio da Ci\u00eancia, Tecnologia e Ensino Superior"}],"funders":[{"id":"https://openalex.org/F4320323642","display_name":"Minist\u00e9rio da Ci\u00eancia, Tecnologia e Ensino Superior","ror":"https://ror.org/045b9pr88"},{"id":"https://openalex.org/F4320334779","display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","ror":"https://ror.org/00snfqn58"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W98985150","https://openalex.org/W1487409515","https://openalex.org/W1816742207","https://openalex.org/W1989947827","https://openalex.org/W1991062829","https://openalex.org/W1991442995","https://openalex.org/W1999679315","https://openalex.org/W2000323020","https://openalex.org/W2023648368","https://openalex.org/W2031575844","https://openalex.org/W2038185098","https://openalex.org/W2039928244","https://openalex.org/W2041551352","https://openalex.org/W2048528677","https://openalex.org/W2073897909","https://openalex.org/W2076945216","https://openalex.org/W2116712528","https://openalex.org/W2292330827","https://openalex.org/W2724163406","https://openalex.org/W2741242605","https://openalex.org/W2765635985","https://openalex.org/W2792567301","https://openalex.org/W2904412515","https://openalex.org/W2952657320","https://openalex.org/W2964208418","https://openalex.org/W2964333818","https://openalex.org/W2998490647","https://openalex.org/W3127632810","https://openalex.org/W4211036707","https://openalex.org/W4238300779","https://openalex.org/W4298032519","https://openalex.org/W6603990812","https://openalex.org/W6673906170","https://openalex.org/W6697031970","https://openalex.org/W6759849416","https://openalex.org/W6772427866","https://openalex.org/W6790290216"],"related_works":["https://openalex.org/W3174039900","https://openalex.org/W2154470989","https://openalex.org/W161795538","https://openalex.org/W3081881033","https://openalex.org/W2902041117","https://openalex.org/W2014676306","https://openalex.org/W2974085155","https://openalex.org/W2310915119","https://openalex.org/W2246175728","https://openalex.org/W1596140841","https://openalex.org/W3036305938","https://openalex.org/W1758688309","https://openalex.org/W3082020351","https://openalex.org/W2549454486","https://openalex.org/W2106838905","https://openalex.org/W425284565","https://openalex.org/W2162319107","https://openalex.org/W2043389664","https://openalex.org/W3099647140","https://openalex.org/W3140688773"],"abstract_inverted_index":{"Abstract":[0],"This":[1,145],"paper":[2],"focuses":[3],"on":[4,18,53],"order-preserving":[5,94,136,212],"logics":[6,222,234],"defined":[7],"from":[8],"varieties":[9],"of":[10,21,40,57,63,72,79,96,99,118,128,152,156,171,200,203,235,239],"distributive":[11,81],"lattices":[12,82],"with":[13,83],"negation,":[14],"and":[15,131,214],"in":[16,189,229],"particular":[17,230],"the":[19,45,54,67,77,93,97,109,134,168,210,220,225,232],"problem":[20],"whether":[22],"these":[23],"can":[24],"be":[25],"axiomatized":[26,123,139],"by":[27,124,140],"means":[28],"Hilbert-style":[29,143,183,207],"calculi":[30],"that":[31,35,60,76,92,114,167,190,231],"are":[32,187,243],"finite":[33,38,64,126,142],"(i.e.":[34],"contain":[36],"a":[37,50,58,125,141,153,162,164,180,201,206],"number":[39,127],"finitary":[41],"rule":[42],"schemata).":[43],"On":[44,108],"negative":[46],"side,":[47,111],"we":[48,89,112],"provide":[49],"syntactic":[51],"condition":[52],"equational":[55,198],"presentation":[56,199],"variety":[59,98,155,202],"entails":[61],"failure":[62],"axiomatizability":[65],"for":[66,149,209],"corresponding":[68,135,182,211],"logic.":[69],"An":[70],"application":[71],"this":[73],"result":[74],"is":[75,85,103,122,138,174],"logic":[78,95,137,173],"all":[80,100],"negation":[84],"not":[86,105],"finitely":[87,106,175,236,244],"axiomatizable;":[88],"likewise":[90],"establish":[91],"Ockham":[101,157],"algebras":[102,121,204,242],"also":[104,147,218],"axiomatizable.":[107],"positive":[110],"show":[113],"an":[115,197],"arbitrary":[116],"subvariety":[117,151],"semi-De":[119,240],"Morgan":[120,241],"equations":[129],"if":[130,133],"only":[132],"calculus.":[144,184],"equivalence":[146],"holds":[148],"every":[150],"Berman":[154],"algebras.":[158],"We":[159,217],"obtain,":[160],"as":[161,177,179,246],"corollary,":[163],"new":[165,181],"proof":[166],"implication-free":[169],"fragment":[170],"intuitionistic":[172],"axiomatizable,":[176],"well":[178],"Our":[185],"proofs":[186],"constructive":[188],"they":[191],"allow":[192],"us":[193],"to":[194,224],"effectively":[195],"convert":[196],"into":[205],"calculus":[208],"logic,":[213],"vice":[215],"versa.":[216],"consider":[219],"assertional":[221,233],"associated":[223],"above-mentioned":[226],"varieties,":[227],"showing":[228],"axiomatizable":[237,245],"subvarieties":[238],"well.":[247]},"counts_by_year":[],"updated_date":"2026-07-01T08:55:40.977307","created_date":"2025-10-10T00:00:00"}