{"id":"https://openalex.org/W6947838969","doi":"https://doi.org/10.4230/lipics.fscd.2025.29","title":"Linear Logic Using Negative Connectives","display_name":"Linear Logic Using Negative Connectives","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W6947838969","doi":"https://doi.org/10.4230/lipics.fscd.2025.29"},"language":"en","primary_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:23644","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2025.29","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol337-fscd2025/LIPIcs.FSCD.2025.29/LIPIcs.FSCD.2025.29.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"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":"publishedVersion"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol337-fscd2025/LIPIcs.FSCD.2025.29/LIPIcs.FSCD.2025.29.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Miller, Dale","orcid":"https://orcid.org/0000-0003-0274-4954"},"institutions":[{"id":"https://openalex.org/I4210126360","display_name":"Centre Inria de Saclay","ror":"https://ror.org/0315e5x55","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4210126360"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Miller, Dale","raw_affiliation_strings":["Inria Saclay & LIX Institut Polytechnique de Paris, France"],"raw_orcid":"https://orcid.org/0000-0003-0274-4954","affiliations":[{"raw_affiliation_string":"Inria Saclay & LIX Institut Polytechnique de Paris, France","institution_ids":["https://openalex.org/I4210126360"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210126360"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.24067524,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":true,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.5449000000953674,"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"}},"topics":[{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.5449000000953674,"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":0.34279999136924744,"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/T10142","display_name":"Formal Methods in Verification","score":0.033399999141693115,"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/linear-logic","display_name":"Linear logic","score":0.7278000116348267},{"id":"https://openalex.org/keywords/sequent-calculus","display_name":"Sequent calculus","score":0.6834999918937683},{"id":"https://openalex.org/keywords/natural-deduction","display_name":"Natural deduction","score":0.636900007724762},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.5878999829292297},{"id":"https://openalex.org/keywords/sequent","display_name":"Sequent","score":0.5318999886512756},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5227000117301941},{"id":"https://openalex.org/keywords/intuitionistic-logic","display_name":"Intuitionistic logic","score":0.49000000953674316},{"id":"https://openalex.org/keywords/curry\u2013howard-correspondence","display_name":"Curry\u2013Howard correspondence","score":0.48899999260902405},{"id":"https://openalex.org/keywords/proof-theory","display_name":"Proof theory","score":0.4632999897003174},{"id":"https://openalex.org/keywords/rule-of-inference","display_name":"Rule of inference","score":0.414000004529953}],"concepts":[{"id":"https://openalex.org/C28077239","wikidata":"https://www.wikidata.org/wiki/Q841728","display_name":"Linear logic","level":2,"score":0.7278000116348267},{"id":"https://openalex.org/C65880906","wikidata":"https://www.wikidata.org/wiki/Q1771121","display_name":"Sequent calculus","level":3,"score":0.6834999918937683},{"id":"https://openalex.org/C62073222","wikidata":"https://www.wikidata.org/wiki/Q1572108","display_name":"Natural deduction","level":2,"score":0.636900007724762},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5985000133514404},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.5878999829292297},{"id":"https://openalex.org/C89421646","wikidata":"https://www.wikidata.org/wiki/Q843632","display_name":"Sequent","level":2,"score":0.5318999886512756},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5227000117301941},{"id":"https://openalex.org/C178421362","wikidata":"https://www.wikidata.org/wiki/Q176786","display_name":"Intuitionistic logic","level":3,"score":0.49000000953674316},{"id":"https://openalex.org/C85343465","wikidata":"https://www.wikidata.org/wiki/Q975734","display_name":"Curry\u2013Howard correspondence","level":3,"score":0.48899999260902405},{"id":"https://openalex.org/C2318724","wikidata":"https://www.wikidata.org/wiki/Q852732","display_name":"Proof theory","level":3,"score":0.4632999897003174},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43720000982284546},{"id":"https://openalex.org/C3746660","wikidata":"https://www.wikidata.org/wiki/Q1068763","display_name":"Rule of inference","level":2,"score":0.414000004529953},{"id":"https://openalex.org/C195653647","wikidata":"https://www.wikidata.org/wiki/Q7625047","display_name":"Structural proof theory","level":4,"score":0.4002000093460083},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.39809998869895935},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.36410000920295715},{"id":"https://openalex.org/C111404639","wikidata":"https://www.wikidata.org/wiki/Q376166","display_name":"Cut-elimination theorem","level":4,"score":0.36059999465942383},{"id":"https://openalex.org/C194989596","wikidata":"https://www.wikidata.org/wiki/Q211790","display_name":"Logical connective","level":2,"score":0.3587999939918518},{"id":"https://openalex.org/C69562738","wikidata":"https://www.wikidata.org/wiki/Q200694","display_name":"Propositional calculus","level":2,"score":0.3531999886035919},{"id":"https://openalex.org/C144760519","wikidata":"https://www.wikidata.org/wiki/Q839490","display_name":"Substructural logic","level":4,"score":0.3465999960899353},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.34599998593330383},{"id":"https://openalex.org/C2780432614","wikidata":"https://www.wikidata.org/wiki/Q864213","display_name":"Conservative extension","level":2,"score":0.3425000011920929},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3377000093460083},{"id":"https://openalex.org/C171482190","wikidata":"https://www.wikidata.org/wiki/Q3257974","display_name":"Minimal logic","level":5,"score":0.329800009727478},{"id":"https://openalex.org/C6489637","wikidata":"https://www.wikidata.org/wiki/Q7250002","display_name":"Proof calculus","level":3,"score":0.3255000114440918},{"id":"https://openalex.org/C33203268","wikidata":"https://www.wikidata.org/wiki/Q5361594","display_name":"Intermediate logic","level":3,"score":0.3188999891281128},{"id":"https://openalex.org/C150889026","wikidata":"https://www.wikidata.org/wiki/Q185502","display_name":"Many-valued logic","level":3,"score":0.31779998540878296},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.28769999742507935},{"id":"https://openalex.org/C11821877","wikidata":"https://www.wikidata.org/wiki/Q187959","display_name":"Distributive property","level":2,"score":0.2782000005245209},{"id":"https://openalex.org/C46274116","wikidata":"https://www.wikidata.org/wiki/Q185521","display_name":"Truth value","level":2,"score":0.27630001306533813},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2761000096797943},{"id":"https://openalex.org/C56949724","wikidata":"https://www.wikidata.org/wiki/Q219079","display_name":"Truth table","level":2,"score":0.27219998836517334},{"id":"https://openalex.org/C161505775","wikidata":"https://www.wikidata.org/wiki/Q3240280","display_name":"Direct proof","level":2,"score":0.26899999380111694},{"id":"https://openalex.org/C193885149","wikidata":"https://www.wikidata.org/wiki/Q655742","display_name":"Modus ponens","level":3,"score":0.25859999656677246},{"id":"https://openalex.org/C206321295","wikidata":"https://www.wikidata.org/wiki/Q8080919","display_name":"\u0141ukasiewicz logic","level":5,"score":0.2581000030040741},{"id":"https://openalex.org/C166374712","wikidata":"https://www.wikidata.org/wiki/Q209555","display_name":"Tautology (logic)","level":5,"score":0.25429999828338623},{"id":"https://openalex.org/C49766605","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear map","level":2,"score":0.2526000142097473},{"id":"https://openalex.org/C195344581","wikidata":"https://www.wikidata.org/wiki/Q2555318","display_name":"Automated reasoning","level":2,"score":0.2517000138759613}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:drops-oai.dagstuhl.de:23644","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2025.29","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol337-fscd2025/LIPIcs.FSCD.2025.29/LIPIcs.FSCD.2025.29.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"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":"publishedVersion"},{"id":"doi:10.4230/lipics.fscd.2025.29","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.fscd.2025.29","pdf_url":null,"source":{"id":"https://openalex.org/S7407052059","display_name":"Dagstuhl Research Online Publication Server","issn_l":null,"issn":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":""}],"best_oa_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:23644","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2025.29","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol337-fscd2025/LIPIcs.FSCD.2025.29/LIPIcs.FSCD.2025.29.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"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":"publishedVersion"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.4366135001182556}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W6947838969.pdf","grobid_xml":"https://content.openalex.org/works/W6947838969.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"In":[0],"linear":[1,46,96,120,137],"logic,":[2],"the":[3,13,22,76,89,144,172,222],"invertibility":[4],"of":[5,15,24,67,78,91,117,176,183,190,194,207],"a":[6,26,53,61,149,156,212],"connective\u2019s":[7],"right-introduction":[8,33],"rule":[9,34,203],"is":[10,28,35,140,154],"equivalent":[11],"to":[12,174,215],"non-invertibility":[14],"its":[16,32,124],"left-introduction":[17,191],"rule.":[18],"This":[19,205],"duality":[20],"motivates":[21],"concept":[23],"polarity:":[25],"connective":[27],"termed":[29],"negative":[30,50],"if":[31],"invertible,":[36],"and":[37,71,80,111,127,134,178,196,218],"positive":[38],"otherwise.":[39],"A":[40],"two-sided":[41],"sequent":[42],"calculus":[43],"for":[44,158,226],"first-order":[45],"logic":[47,97,107,161],"featuring":[48],"only":[49],"connectives":[51],"exhibits":[52],"compelling":[54],"proof":[55],"theory.":[56],"Proof":[57],"search":[58],"in":[59,221],"such":[60,201],"system":[62,225],"unfolds":[63],"through":[64],"alternating":[65],"phases":[66,84],"invertible":[68],"(right-introduction)":[69],"rules":[70],"non-invertible":[72],"(left-introduction)":[73],"rules,":[74,192],"mirroring":[75],"processes":[77],"goal-reduction":[79],"backchaining,":[81],"respectively.":[82],"These":[83],"are":[85],"formalized":[86],"here":[87],"using":[88],"framework":[90],"multifocused":[92,181],"proofs.":[93],"We":[94],"analyze":[95],"by":[98,152,170],"dissecting":[99],"it":[100,167],"into":[101],"three":[102],"sublogics:":[103],"L\u2080":[104,118,177,195],"(first-order":[105],"intuitionistic":[106,125,160,227],"with":[108],"conjunction,":[109],"implication,":[110],"universal":[112],"quantification);":[113],"L\u2081":[114,197],"(an":[115],"extension":[116],"incorporating":[119],"implication":[121],"which":[122],"preserves":[123],"nature);":[126],"L\u2082":[128,184],"(which":[129],"includes":[130],"multiplicative":[131],"falsity":[132],"\u22a5":[133],"encompasses":[135],"classical":[136],"logic).":[138],"It":[139],"worth":[141],"noting":[142],"that":[143],"single-conclusion":[145],"restriction":[146],"on":[147],"sequents,":[148],"constraint":[150],"imposed":[151],"Gentzen,":[153],"not":[155],"prerequisite":[157],"defining":[159],"proofs":[162,182,193,210],"within":[163,209],"this":[164],"framework,":[165],"as":[166],"emerges":[168],"naturally":[169],"restricting":[171],"formulas":[173],"those":[175],"L\u2081.":[179],"While":[180],"sequents":[185,198],"can":[186],"accommodate":[187],"parallel":[188,202],"applications":[189],"cannot":[199],"leverage":[200],"applications.":[204],"notion":[206],"parallelism":[208],"enables":[211],"novel":[213],"approach":[214],"handling":[216],"disjunctions":[217],"existential":[219],"quantifiers":[220],"natural":[223],"deduction":[224],"logic.":[228]},"counts_by_year":[],"updated_date":"2025-11-06T06:51:31.235846","created_date":"2025-10-10T00:00:00"}
