{"id":"https://openalex.org/W4285088085","doi":"https://doi.org/10.1017/s1755020322000272","title":"COLLECTION FRAMES FOR DISTRIBUTIVE SUBSTRUCTURAL LOGICS","display_name":"COLLECTION FRAMES FOR DISTRIBUTIVE SUBSTRUCTURAL LOGICS","publication_year":2022,"publication_date":"2022-07-13","ids":{"openalex":"https://openalex.org/W4285088085","doi":"https://doi.org/10.1017/s1755020322000272"},"language":"en","primary_location":{"id":"doi:10.1017/s1755020322000272","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s1755020322000272","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/FED69B94A9E3C17A9D1E008380DA2497/S1755020322000272a.pdf/div-class-title-collection-frames-for-distributive-substructural-logics-div.pdf","source":{"id":"https://openalex.org/S24077076","display_name":"The Review of Symbolic Logic","issn_l":"1755-0203","issn":["1755-0203","1755-0211"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Review of Symbolic Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/FED69B94A9E3C17A9D1E008380DA2497/S1755020322000272a.pdf/div-class-title-collection-frames-for-distributive-substructural-logics-div.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5009371587","display_name":"Greg Restall","orcid":"https://orcid.org/0000-0001-8257-6764"},"institutions":[{"id":"https://openalex.org/I16835326","display_name":"University of St Andrews","ror":"https://ror.org/02wn5qz54","country_code":"GB","type":"education","lineage":["https://openalex.org/I16835326"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"GREG RESTALL","raw_affiliation_strings":["PHILOSOPHY DEPARTMENT UNIVERSITY OF ST ANDREWS ST ANDREWS, UKE-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"PHILOSOPHY DEPARTMENT UNIVERSITY OF ST ANDREWS ST ANDREWS, UKE-mail:","institution_ids":["https://openalex.org/I16835326"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000723552","display_name":"Shawn Standefer","orcid":"https://orcid.org/0000-0002-3032-5290"},"institutions":[{"id":"https://openalex.org/I16733864","display_name":"National Taiwan University","ror":"https://ror.org/05bqach95","country_code":"TW","type":"education","lineage":["https://openalex.org/I16733864"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"SHAWN STANDEFER","raw_affiliation_strings":["DEPARTMENT OF PHILOSOPHY NATIONAL TAIWAN UNIVERSITYTAIPEI, TAIWANE-mail:"],"raw_orcid":"https://orcid.org/0000-0002-3032-5290","affiliations":[{"raw_affiliation_string":"DEPARTMENT OF PHILOSOPHY NATIONAL TAIWAN UNIVERSITYTAIPEI, TAIWANE-mail:","institution_ids":["https://openalex.org/I16733864"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5009371587"],"corresponding_institution_ids":["https://openalex.org/I16835326"],"apc_list":null,"apc_paid":null,"fwci":0.7542,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.73937389,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"16","issue":"4","first_page":"1120","last_page":"1157"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9980999827384949,"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":0.9980999827384949,"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":0.9966999888420105,"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":0.9959999918937683,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6479777097702026},{"id":"https://openalex.org/keywords/distributive-property","display_name":"Distributive property","score":0.5930549502372742},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5197895765304565},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.4615800976753235},{"id":"https://openalex.org/keywords/frame","display_name":"Frame (networking)","score":0.4357983469963074},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.28016263246536255},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.19633114337921143}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6479777097702026},{"id":"https://openalex.org/C11821877","wikidata":"https://www.wikidata.org/wiki/Q187959","display_name":"Distributive property","level":2,"score":0.5930549502372742},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5197895765304565},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.4615800976753235},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.4357983469963074},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28016263246536255},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.19633114337921143},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1017/s1755020322000272","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s1755020322000272","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/FED69B94A9E3C17A9D1E008380DA2497/S1755020322000272a.pdf/div-class-title-collection-frames-for-distributive-substructural-logics-div.pdf","source":{"id":"https://openalex.org/S24077076","display_name":"The Review of Symbolic Logic","issn_l":"1755-0203","issn":["1755-0203","1755-0211"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Review of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:philarchive.org/rec/RESCFF-2","is_oa":true,"landing_page_url":"https://philarchive.org/rec/RESCFF-2","pdf_url":"https://philpapers.org/archive/RESCFF-2.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":"pmh:oai:research-repository.st-andrews.ac.uk:10023/26749","is_oa":true,"landing_page_url":"https://hdl.handle.net/10023/26749","pdf_url":"https://research-repository.st-andrews.ac.uk/bitstream/10023/26749/1/Restall_2023_RSL_Collection_frames_CC.pdf","source":{"id":"https://openalex.org/S4306400230","display_name":"St Andrews Research Repository (St Andrews Research Repository)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I16835326","host_organization_name":"University of St Andrews","host_organization_lineage":["https://openalex.org/I16835326"],"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":"Journal article"},{"id":"pmh:oai:philpapers.org/rec/RESCFF-2","is_oa":false,"landing_page_url":"https://philpapers.org/rec/RESCFF-2","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"}],"best_oa_location":{"id":"doi:10.1017/s1755020322000272","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s1755020322000272","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/FED69B94A9E3C17A9D1E008380DA2497/S1755020322000272a.pdf/div-class-title-collection-frames-for-distributive-substructural-logics-div.pdf","source":{"id":"https://openalex.org/S24077076","display_name":"The Review of Symbolic Logic","issn_l":"1755-0203","issn":["1755-0203","1755-0211"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Review of Symbolic Logic","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Industry, innovation and infrastructure","id":"https://metadata.un.org/sdg/9","score":0.6399999856948853}],"awards":[],"funders":[{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4285088085.pdf","grobid_xml":"https://content.openalex.org/works/W4285088085.grobid-xml"},"referenced_works_count":46,"referenced_works":["https://openalex.org/W52144438","https://openalex.org/W60391671","https://openalex.org/W81761572","https://openalex.org/W1032524570","https://openalex.org/W1505359507","https://openalex.org/W1527995180","https://openalex.org/W1551030425","https://openalex.org/W1593617641","https://openalex.org/W1967371638","https://openalex.org/W1975812803","https://openalex.org/W1978629563","https://openalex.org/W1991316067","https://openalex.org/W2002791110","https://openalex.org/W2014646251","https://openalex.org/W2051198079","https://openalex.org/W2058110538","https://openalex.org/W2058694821","https://openalex.org/W2070878538","https://openalex.org/W2072341634","https://openalex.org/W2073764215","https://openalex.org/W2082707306","https://openalex.org/W2085716418","https://openalex.org/W2120747446","https://openalex.org/W2162300758","https://openalex.org/W2315064349","https://openalex.org/W2328580899","https://openalex.org/W2347158114","https://openalex.org/W2781122117","https://openalex.org/W2794051391","https://openalex.org/W2806389218","https://openalex.org/W2835790746","https://openalex.org/W2874049253","https://openalex.org/W3000046285","https://openalex.org/W4200068094","https://openalex.org/W4200429540","https://openalex.org/W4210848565","https://openalex.org/W4233571494","https://openalex.org/W4247269955","https://openalex.org/W4248743978","https://openalex.org/W4252068692","https://openalex.org/W4252137238","https://openalex.org/W4388313844","https://openalex.org/W4399955992","https://openalex.org/W6701828768","https://openalex.org/W6704964719","https://openalex.org/W6751899563"],"related_works":["https://openalex.org/W2382957647","https://openalex.org/W2094667621","https://openalex.org/W1509295490","https://openalex.org/W1979597421","https://openalex.org/W1749534632","https://openalex.org/W3013987451","https://openalex.org/W2007980826","https://openalex.org/W1977269832","https://openalex.org/W2369038733","https://openalex.org/W2351462424"],"abstract_inverted_index":{"Abstract":[0],"We":[1,70],"present":[2],"a":[3,19,26,40],"new":[4],"frame":[5,15],"semantics":[6,16,35],"for":[7,81,100,121,133,146],"positive":[8,84,113,135],"relevant":[9,104,136],"and":[10,25,79,98,115,125],"substructural":[11,86],"propositional":[12],"logics.":[13],"This":[14],"is":[17,36],"both":[18],"generalisation":[20],"of":[21,28,33,39,47,59,143],"Routley\u2013Meyer":[22],"ternary":[23],"frames":[24,74,93,128,145],"simplification":[27],"them.":[29],"The":[30,141],"key":[31],"innovation":[32],"this":[34],"the":[37,57,82,122,134],"use":[38],"single":[41],"accessibility":[42],"relation":[43],"to":[44,49],"relate":[45],"collections":[46,60],"points":[48],"points.":[50],"Different":[51],"logics":[52],"are":[53,77,96,131],"modeled":[54],"by":[55],"varying":[56],"kinds":[58],"used:":[61],"they":[62],"can":[63],"be":[64],"sets,":[65],"multisets,":[66],"lists":[67],"or":[68,111],"trees.":[69],"show":[71],"that":[72,91,126],"collection":[73,92,127],"on":[75,94,129],"trees":[76],"sound":[78,97,132],"complete":[80,99],"basic":[83],"distributive":[85],"logic":[87,105,118,137],"$\\mathsf":[88,101,106,138,147],"{B}^+$":[89],",":[90,108],"multisets":[95],"{RW}^+$":[102],"(the":[103],"{R}^+$":[107,139,148],"without":[109],"contraction,":[110],"equivalently,":[112],"multiplicative":[114],"additive":[116,123],"linear":[117],"with":[119],"distribution":[120],"connectives),":[124],"sets":[130],".":[140],"completeness":[142],"set":[144],"is,":[149],"currently,":[150],"an":[151],"open":[152],"question.":[153]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}