{"id":"https://openalex.org/W4406930833","doi":"https://doi.org/10.46298/lmcs-21(1:7)2025","title":"Quantitative Equality in Substructural Logic via Lipschitz Doctrines","display_name":"Quantitative Equality in Substructural Logic via Lipschitz Doctrines","publication_year":2025,"publication_date":"2025-01-28","ids":{"openalex":"https://openalex.org/W4406930833","doi":"https://doi.org/10.46298/lmcs-21(1:7)2025"},"language":"en","primary_location":{"id":"doi:10.46298/lmcs-21(1:7)2025","is_oa":true,"landing_page_url":"https://doi.org/10.46298/lmcs-21(1:7)2025","pdf_url":"https://lmcs.episciences.org/15159/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://lmcs.episciences.org/15159/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046176286","display_name":"Francesco Dagnino","orcid":"https://orcid.org/0000-0003-3599-3535"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Francesco Dagnino","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5038306122","display_name":"Fabio Pasquali","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fabio Pasquali","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5046176286"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.669,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.8125757,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"Volume 21, Issue 1","issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.961899995803833,"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":0.961899995803833,"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/computer-science","display_name":"Computer science","score":0.5255205631256104},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.49613890051841736},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.4180673360824585},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41329771280288696},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3204754590988159},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.22543546557426453}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5255205631256104},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.49613890051841736},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.4180673360824585},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41329771280288696},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3204754590988159},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.22543546557426453}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.46298/lmcs-21(1:7)2025","is_oa":true,"landing_page_url":"https://doi.org/10.46298/lmcs-21(1:7)2025","pdf_url":"https://lmcs.episciences.org/15159/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:air.unimi.it:2434/1156653","is_oa":true,"landing_page_url":"https://hdl.handle.net/2434/1156653","pdf_url":null,"source":{"id":"https://openalex.org/S4306400516","display_name":"Archivio Istituzionale della Ricerca (Universita Degli Studi Di Milano)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I189158943","host_organization_name":"University of Milan","host_organization_lineage":["https://openalex.org/I189158943"],"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:doaj.org/article:0408401dc2a0499ca2dccf09eaf49115","is_oa":true,"landing_page_url":"https://doaj.org/article/0408401dc2a0499ca2dccf09eaf49115","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Logical Methods in Computer Science, Vol Volume 21, Issue 1 (2025)","raw_type":"article"},{"id":"pmh:oai:unige.iris.cineca.it:11567/1272522","is_oa":false,"landing_page_url":"https://hdl.handle.net/11567/1272522","pdf_url":null,"source":{"id":"https://openalex.org/S4377196291","display_name":"CINECA IRIS Institutial Research Information System (University of Genoa)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I83816512","host_organization_name":"University of Genoa","host_organization_lineage":["https://openalex.org/I83816512"],"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"}],"best_oa_location":{"id":"doi:10.46298/lmcs-21(1:7)2025","is_oa":true,"landing_page_url":"https://doi.org/10.46298/lmcs-21(1:7)2025","pdf_url":"https://lmcs.episciences.org/15159/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4406930833.pdf","grobid_xml":"https://content.openalex.org/works/W4406930833.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W3185235544","https://openalex.org/W4297791327","https://openalex.org/W1979597421","https://openalex.org/W2897842840","https://openalex.org/W2007980826","https://openalex.org/W2911623553","https://openalex.org/W2051487156"],"abstract_inverted_index":{"Substructural":[0],"logics":[1],"naturally":[2],"support":[3],"a":[4,52,72,87,99,104,116,133],"quantitative":[5,19,96,146],"interpretation":[6,97],"of":[7,21,66,75,110,124,127],"formulas,":[8],"as":[9,13,98],"they":[10,24,37,43],"are":[11,17,30,38,83],"seen":[12],"consumable":[14],"resources.":[15],"Distances":[16],"the":[18,45,63,108],"counterpart":[20],"equivalence":[22],"relations:":[23],"measure":[25],"how":[26,151],"much":[27],"two":[28],"objects":[29],"similar,":[31],"rather":[32],"than":[33],"just":[34],"saying":[35],"whether":[36],"equivalent":[39],"or":[40],"not.":[41],"Hence,":[42],"provide":[44],"natural":[46],"choice":[47],"for":[48,92,140],"modelling":[49],"equality":[50],"in":[51,71],"substructural":[53,159],"setting.":[54],"In":[55],"this":[56,60],"paper,":[57],"we":[58,149],"develop":[59],"idea,":[61],"using":[62],"categorical":[64,120],"language":[65],"Lawvere's":[67],"doctrines.":[68],"We":[69,101],"work":[70],"minimal":[73],"fragment":[74],"Linear":[76,164],"Logic":[77,165],"enriched":[78],"by":[79],"graded":[80],"modalities,":[81],"which":[82,136],"needed":[84],"to":[85,113,152,157,162],"write":[86],"resource":[88],"sensitive":[89],"substitution":[90],"rule":[91],"equality,":[93],"enabling":[94],"its":[95],"distance.":[100],"introduce":[102],"both":[103],"deductive":[105],"calculus":[106],"and":[107,118,145],"notion":[109],"Lipschitz":[111,128],"doctrine":[112],"give":[114],"it":[115],"sound":[117],"complete":[119],"semantics.":[121],"The":[122],"study":[123],"2-categorical":[125],"properties":[126],"doctrines":[129],"provides":[130],"us":[131],"with":[132,166],"universal":[134],"construction,":[135],"generates":[137],"examples":[138],"based":[139],"instance":[141],"on":[142],"metric":[143],"spaces":[144],"realisability.":[147],"Finally,":[148],"show":[150],"smoothly":[153],"extend":[154],"our":[155],"results":[156],"richer":[158],"logics,":[160],"up":[161],"full":[163],"quantifiers.":[167]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}