{"id":"https://openalex.org/W3153150069","doi":"https://doi.org/10.1007/s11225-021-09946-1","title":"Residuated Structures and Orthomodular Lattices","display_name":"Residuated Structures and Orthomodular Lattices","publication_year":2021,"publication_date":"2021-04-17","ids":{"openalex":"https://openalex.org/W3153150069","doi":"https://doi.org/10.1007/s11225-021-09946-1","mag":"3153150069"},"language":"en","primary_location":{"id":"doi:10.1007/s11225-021-09946-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11225-021-09946-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11225-021-09946-1.pdf","source":{"id":"https://openalex.org/S30880287","display_name":"Studia Logica","issn_l":"0039-3215","issn":["0039-3215","1572-8730"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Studia Logica","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11225-021-09946-1.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019950782","display_name":"Davide Fazio","orcid":"https://orcid.org/0000-0001-8136-732X"},"institutions":[{"id":"https://openalex.org/I172446870","display_name":"University of Cagliari","ror":"https://ror.org/003109y17","country_code":"IT","type":"education","lineage":["https://openalex.org/I172446870"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"D. Fazio","raw_affiliation_strings":["Department of Pedagogy, Psychology, Philosophy, University of Cagliari, Cagliari, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Pedagogy, Psychology, Philosophy, University of Cagliari, Cagliari, Italy","institution_ids":["https://openalex.org/I172446870"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010857507","display_name":"Antonio Ledda","orcid":"https://orcid.org/0000-0003-2569-7214"},"institutions":[{"id":"https://openalex.org/I172446870","display_name":"University of Cagliari","ror":"https://ror.org/003109y17","country_code":"IT","type":"education","lineage":["https://openalex.org/I172446870"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"A. Ledda","raw_affiliation_strings":["Department of Pedagogy, Psychology, Philosophy, University of Cagliari, Cagliari, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Pedagogy, Psychology, Philosophy, University of Cagliari, Cagliari, Italy","institution_ids":["https://openalex.org/I172446870"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101735626","display_name":"Francesco Paoli","orcid":"https://orcid.org/0000-0001-7915-3832"},"institutions":[{"id":"https://openalex.org/I172446870","display_name":"University of Cagliari","ror":"https://ror.org/003109y17","country_code":"IT","type":"education","lineage":["https://openalex.org/I172446870"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"F. Paoli","raw_affiliation_strings":["Department of Pedagogy, Psychology, Philosophy, University of Cagliari, Cagliari, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Pedagogy, Psychology, Philosophy, University of Cagliari, Cagliari, Italy","institution_ids":["https://openalex.org/I172446870"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5019950782"],"corresponding_institution_ids":["https://openalex.org/I172446870"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":1.0602,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.8001949,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"109","issue":"6","first_page":"1201","last_page":"1239"},"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/T11567","display_name":"semigroups and automata theory","score":0.9941999912261963,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9908000230789185,"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/residuated-lattice","display_name":"Residuated lattice","score":0.8776205778121948},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5229381322860718},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.48325592279434204},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4401531517505646},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.41722628474235535},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.41277194023132324},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.40849751234054565},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3546401858329773},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3294066786766052},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.31915992498397827},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.24962368607521057},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.216361403465271},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1545110046863556},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09041514992713928},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07648855447769165}],"concepts":[{"id":"https://openalex.org/C2781278839","wikidata":"https://www.wikidata.org/wiki/Q9462417","display_name":"Residuated lattice","level":3,"score":0.8776205778121948},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5229381322860718},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.48325592279434204},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4401531517505646},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.41722628474235535},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.41277194023132324},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.40849751234054565},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3546401858329773},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3294066786766052},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31915992498397827},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.24962368607521057},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.216361403465271},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1545110046863556},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09041514992713928},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07648855447769165},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s11225-021-09946-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11225-021-09946-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11225-021-09946-1.pdf","source":{"id":"https://openalex.org/S30880287","display_name":"Studia Logica","issn_l":"0039-3215","issn":["0039-3215","1572-8730"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Studia Logica","raw_type":"journal-article"},{"id":"pmh:oai:iris.unica.it:11584/317252","is_oa":true,"landing_page_url":"https://hdl.handle.net/11584/317252","pdf_url":null,"source":{"id":"https://openalex.org/S4377196293","display_name":"UNICA IRIS Institutional Research Information System (University of Cagliari)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I172446870","host_organization_name":"University of Cagliari","host_organization_lineage":["https://openalex.org/I172446870"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:research.unite.it:11575/141522","is_oa":false,"landing_page_url":"https://hdl.handle.net/11575/141522","pdf_url":null,"source":{"id":"https://openalex.org/S4306401171","display_name":"UniTERAMO Research Catalog (University of Teramo)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I124326101","host_organization_name":"University of Teramo","host_organization_lineage":["https://openalex.org/I124326101"],"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":"pmh:oai:zenodo.org:81029","is_oa":true,"landing_page_url":"https://www.openaccessrepository.it/record/81029","pdf_url":null,"source":{"id":"https://openalex.org/S4306402478","display_name":"INFM-OAR (INFN Catania)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210116497","host_organization_name":"Istituto Nazionale di Fisica Nucleare, Sezione di Catania","host_organization_lineage":["https://openalex.org/I4210116497"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s11225-021-09946-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11225-021-09946-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11225-021-09946-1.pdf","source":{"id":"https://openalex.org/S30880287","display_name":"Studia Logica","issn_l":"0039-3215","issn":["0039-3215","1572-8730"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Studia Logica","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1616377592","display_name":null,"funder_award_id":"20173WKCM5","funder_id":"https://openalex.org/F4320321873","funder_display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca"},{"id":"https://openalex.org/G3149841404","display_name":null,"funder_award_id":"F72F20000410007","funder_id":"https://openalex.org/F4320315324","funder_display_name":"Fondazione di Sardegna"},{"id":"https://openalex.org/G3422143364","display_name":null,"funder_award_id":"PRIN 2017","funder_id":"https://openalex.org/F4320321873","funder_display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca"},{"id":"https://openalex.org/G6609750531","display_name":null,"funder_award_id":"RAS: SR40341","funder_id":"https://openalex.org/F4320326069","funder_display_name":"Regione Autonoma della Sardegna"},{"id":"https://openalex.org/G7084739564","display_name":null,"funder_award_id":"CUP: 2013YP4N3","funder_id":"https://openalex.org/F4320321873","funder_display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca"},{"id":"https://openalex.org/G7918463332","display_name":null,"funder_award_id":"PRIN 2017","funder_id":"https://openalex.org/F4320313987","funder_display_name":"Universit\u00e0 degli Studi di Cagliari"},{"id":"https://openalex.org/G8646970273","display_name":null,"funder_award_id":"2013YP4N3","funder_id":"https://openalex.org/F4320321873","funder_display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca"}],"funders":[{"id":"https://openalex.org/F4320313987","display_name":"Universit\u00e0 degli Studi di Cagliari","ror":"https://ror.org/003109y17"},{"id":"https://openalex.org/F4320315324","display_name":"Fondazione di Sardegna","ror":"https://ror.org/02sryfh37"},{"id":"https://openalex.org/F4320321873","display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca","ror":"https://ror.org/0166hxq48"},{"id":"https://openalex.org/F4320326069","display_name":"Regione Autonoma della Sardegna","ror":null}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3153150069.pdf"},"referenced_works_count":54,"referenced_works":["https://openalex.org/W823309","https://openalex.org/W31810340","https://openalex.org/W54723808","https://openalex.org/W300334468","https://openalex.org/W656700481","https://openalex.org/W806636517","https://openalex.org/W1503075583","https://openalex.org/W1514758454","https://openalex.org/W1529494625","https://openalex.org/W1599237352","https://openalex.org/W1599755535","https://openalex.org/W1730763053","https://openalex.org/W1969313366","https://openalex.org/W1970852047","https://openalex.org/W1986583380","https://openalex.org/W1988000631","https://openalex.org/W2002685092","https://openalex.org/W2003452157","https://openalex.org/W2004451289","https://openalex.org/W2026466059","https://openalex.org/W2033948719","https://openalex.org/W2040917575","https://openalex.org/W2047865342","https://openalex.org/W2057821078","https://openalex.org/W2066155850","https://openalex.org/W2073214104","https://openalex.org/W2078256130","https://openalex.org/W2079430192","https://openalex.org/W2080236494","https://openalex.org/W2080412456","https://openalex.org/W2094251352","https://openalex.org/W2097678272","https://openalex.org/W2108395784","https://openalex.org/W2108408993","https://openalex.org/W2130243322","https://openalex.org/W2154114798","https://openalex.org/W2169981414","https://openalex.org/W2324821402","https://openalex.org/W2534514413","https://openalex.org/W2622125585","https://openalex.org/W2624681464","https://openalex.org/W2735159178","https://openalex.org/W2745927295","https://openalex.org/W2792241587","https://openalex.org/W2912415988","https://openalex.org/W3021045375","https://openalex.org/W3026122526","https://openalex.org/W3098795864","https://openalex.org/W3101676970","https://openalex.org/W3102819501","https://openalex.org/W4211185072","https://openalex.org/W4230874796","https://openalex.org/W4239173363","https://openalex.org/W4249911606"],"related_works":["https://openalex.org/W2186053625","https://openalex.org/W2777780798","https://openalex.org/W2032233321","https://openalex.org/W2063151284","https://openalex.org/W2052933125","https://openalex.org/W3121970507","https://openalex.org/W1968222062","https://openalex.org/W5819577","https://openalex.org/W2359831739","https://openalex.org/W2074091008"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"variety":[2],"of":[3,11,14,47,76,78,94,102,105,107,124],"(pointed)":[4],"residuated":[5,63,108],"lattices":[6,43],"includes":[7],"a":[8,52,92,121],"vast":[9],"proportion":[10],"the":[12,38,74,103,117],"classes":[13],"algebras":[15],"that":[16],"are":[17],"relevant":[18],"for":[19,127],"algebraic":[20],"logic,":[21],"e.g.,":[22],"$$\\ell":[23,56,81,109],"$$":[24,57,82,110],"<mml:math":[25,58,83,111],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[26,59,84,112],"<mml:mi>\u2113</mml:mi>":[27,60,85,113],"</mml:math>":[28,61,86,114],"-groups,":[29],"Heyting":[30],"algebras,":[31],"MV-algebras,":[32],"or":[33],"De":[34],"Morgan":[35],"monoids.":[36],"Among":[37],"outliers,":[39],"one":[40],"counts":[41],"orthomodular":[42,128],"and":[44,65,90],"other":[45],"varieties":[46],"quantum":[48,66],"algebras.":[49],"We":[50,72],"suggest":[51],"common":[53],"framework\u2014pointed":[54],"left-residuated":[55,80,118],"-groupoids\u2014where":[62],"structures":[64,67],"can":[68],"all":[69],"be":[70],"accommodated.":[71],"investigate":[73],"lattice":[75],"subvarieties":[77],"pointed":[79],"-groupoids,":[87],"their":[88],"ideals,":[89],"develop":[91],"theory":[93,104],"left":[95],"nuclei.":[96],"Finally,":[97],"we":[98],"extend":[99],"some":[100],"parts":[101],"join-completions":[106],"-groupoids":[115],"to":[116],"case,":[119],"giving":[120],"new":[122],"proof":[123],"MacLaren\u2019s":[125],"theorem":[126],"lattices.":[129]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2}],"updated_date":"2026-04-20T07:46:08.049788","created_date":"2025-10-10T00:00:00"}
