{"id":"https://openalex.org/W4408439209","doi":"https://doi.org/10.1007/s00153-025-00969-2","title":"An algebraic investigation of Linear Logic","display_name":"An algebraic investigation of Linear Logic","publication_year":2025,"publication_date":"2025-03-14","ids":{"openalex":"https://openalex.org/W4408439209","doi":"https://doi.org/10.1007/s00153-025-00969-2"},"language":"en","primary_location":{"id":"doi:10.1007/s00153-025-00969-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00153-025-00969-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00153-025-00969-2.pdf","source":{"id":"https://openalex.org/S188076996","display_name":"Archive for Mathematical Logic","issn_l":"0933-5846","issn":["0933-5846","1432-0665"],"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":"Archive for Mathematical Logic","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/s00153-025-00969-2.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084297676","display_name":"Paolo Aglian\u00f2","orcid":"https://orcid.org/0000-0002-2860-6157"},"institutions":[{"id":"https://openalex.org/I102064193","display_name":"University of Siena","ror":"https://ror.org/01tevnk56","country_code":"IT","type":"education","lineage":["https://openalex.org/I102064193"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Paolo Aglian\u00f2","raw_affiliation_strings":["DIISM, Universit\u00e0 di Siena, Siena, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DIISM, Universit\u00e0 di Siena, Siena, Italy","institution_ids":["https://openalex.org/I102064193"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5084297676"],"corresponding_institution_ids":["https://openalex.org/I102064193"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.05428411,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"64","issue":"5-6","first_page":"893","last_page":"915"},"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":0.9965000152587891,"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/T11567","display_name":"semigroups and automata theory","score":0.9958999752998352,"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/variety","display_name":"Variety (cybernetics)","score":0.776879072189331},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7438946962356567},{"id":"https://openalex.org/keywords/congruence-relation","display_name":"Congruence relation","score":0.6239436268806458},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.6066511869430542},{"id":"https://openalex.org/keywords/linear-logic","display_name":"Linear logic","score":0.543806254863739},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.45773035287857056},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.45048001408576965},{"id":"https://openalex.org/keywords/congruence","display_name":"Congruence (geometry)","score":0.4434128403663635},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.43142277002334595},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.42298126220703125},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3475674092769623}],"concepts":[{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.776879072189331},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7438946962356567},{"id":"https://openalex.org/C9973445","wikidata":"https://www.wikidata.org/wiki/Q8349849","display_name":"Congruence relation","level":2,"score":0.6239436268806458},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.6066511869430542},{"id":"https://openalex.org/C28077239","wikidata":"https://www.wikidata.org/wiki/Q841728","display_name":"Linear logic","level":2,"score":0.543806254863739},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.45773035287857056},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.45048001408576965},{"id":"https://openalex.org/C132074034","wikidata":"https://www.wikidata.org/wiki/Q154210","display_name":"Congruence (geometry)","level":2,"score":0.4434128403663635},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.43142277002334595},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.42298126220703125},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3475674092769623},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00153-025-00969-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00153-025-00969-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00153-025-00969-2.pdf","source":{"id":"https://openalex.org/S188076996","display_name":"Archive for Mathematical Logic","issn_l":"0933-5846","issn":["0933-5846","1432-0665"],"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":"Archive for Mathematical Logic","raw_type":"journal-article"},{"id":"pmh:oai:usiena-air.unisi.it:11365/1289274","is_oa":true,"landing_page_url":"https://link.springer.com/article/10.1007/s00153-025-00969-2","pdf_url":null,"source":{"id":"https://openalex.org/S4377196319","display_name":"Use Siena air (University of Siena)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I102064193","host_organization_name":"University of Siena","host_organization_lineage":["https://openalex.org/I102064193"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s00153-025-00969-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00153-025-00969-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00153-025-00969-2.pdf","source":{"id":"https://openalex.org/S188076996","display_name":"Archive for Mathematical Logic","issn_l":"0933-5846","issn":["0933-5846","1432-0665"],"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":"Archive for Mathematical Logic","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320313975","display_name":"Universit\u00e0 degli Studi di Siena","ror":"https://ror.org/01tevnk56"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4408439209.pdf"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W91153459","https://openalex.org/W1554516311","https://openalex.org/W1974484530","https://openalex.org/W1983453585","https://openalex.org/W2012915371","https://openalex.org/W2035678888","https://openalex.org/W2054033244","https://openalex.org/W2074070481","https://openalex.org/W2080357819","https://openalex.org/W2099602798","https://openalex.org/W2102134079","https://openalex.org/W2112576833","https://openalex.org/W2911865844","https://openalex.org/W3128976560","https://openalex.org/W4246761341","https://openalex.org/W4252113473","https://openalex.org/W4388313844","https://openalex.org/W4389805639","https://openalex.org/W4400977938"],"related_works":["https://openalex.org/W2385511935","https://openalex.org/W77573719","https://openalex.org/W3134823879","https://openalex.org/W2382432157","https://openalex.org/W4391061523","https://openalex.org/W2801977597","https://openalex.org/W2382598115","https://openalex.org/W2949692723","https://openalex.org/W2254343561","https://openalex.org/W2963246490"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"paper":[3],"we":[4,87,130],"investigate":[5,88],"two":[6,18],"logics":[7,19,39],"(and":[8],"their":[9,54],"fragments)":[10],"from":[11],"an":[12],"algebraic":[13,56],"point":[14],"of":[15,49,62,68,75,91,112,118,134,140],"view.":[16],"The":[17],"are:":[20],"$$\\textsf{MALL}$$":[21],"<mml:math":[22,31],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[23,32],"<mml:mi>MALL</mml:mi>":[24],"</mml:math>":[25,34],"(multiplicative-additive":[26],"Linear":[27,36],"Logic)":[28],"and":[29,51,53,65,80,104,125],"$$\\textsf{LL}$$":[30],"<mml:mi>LL</mml:mi>":[33],"(classical":[35],"Logic).":[37],"Both":[38],"turn":[40],"out":[41],"to":[42],"be":[43],"strongly":[44],"algebraizable":[45],"in":[46,94],"the":[47,60,66,89,92,123,138],"sense":[48],"Blok":[50],"Pigozzi":[52],"equivalent":[55],"semantics":[57],"are,":[58],"respectively,":[59],"variety":[61,67,74,139],"Girard":[63,102],"algebras":[64,93,103],"girales.":[69,105,128],"We":[70,106],"show":[71],"that":[72,109,137],"any":[73],"girales":[76,113,141],"has":[77],"a":[78,98,132],"TD-term":[79],"hence":[81],"equationally":[82],"definable":[83],"principal":[84],"congruences.":[85],"Also":[86],"structure":[90],"question,":[95],"thus":[96,121],"obtaining":[97],"representation":[99],"theorem":[100],"for":[101],"also":[107],"prove":[108],"congruence":[110,116],"lattices":[111,117],"are":[114],"really":[115],"Heyting":[119],"algebras,":[120],"determining":[122],"simple":[124,147],"subdirectly":[126],"irreducible":[127],"Finally":[129],"introduce":[131],"class":[133],"examples":[135],"showing":[136],"contains":[142],"infinitely":[143],"many":[144],"nonisomorphic":[145],"finite":[146],"algebras.":[148]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}