{"id":"https://openalex.org/W2161495932","doi":"https://doi.org/10.2307/2275666","title":"Gentzenizations of relevant logics without distribution. I","display_name":"Gentzenizations of relevant logics without distribution. I","publication_year":1996,"publication_date":"1996-06-01","ids":{"openalex":"https://openalex.org/W2161495932","doi":"https://doi.org/10.2307/2275666","mag":"2161495932"},"language":"en","primary_location":{"id":"doi:10.2307/2275666","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2275666","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112409645","display_name":"Ross T. Brady","orcid":null},"institutions":[{"id":"https://openalex.org/I196829312","display_name":"La Trobe University","ror":"https://ror.org/01rxfrp27","country_code":"AU","type":"education","lineage":["https://openalex.org/I196829312"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Ross T. Brady","raw_affiliation_strings":["La Trobe University, Bundoora, Victoria 3083, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"La Trobe University, Bundoora, Victoria 3083, Australia","institution_ids":["https://openalex.org/I196829312"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5112409645"],"corresponding_institution_ids":["https://openalex.org/I196829312"],"apc_list":null,"apc_paid":null,"fwci":1.139,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.84808853,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"61","issue":"2","first_page":"353","last_page":"378"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9998000264167786,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9998000264167786,"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":0.9968000054359436,"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/decidability","display_name":"Decidability","score":0.8025417923927307},{"id":"https://openalex.org/keywords/negation","display_name":"Negation","score":0.5962063074111938},{"id":"https://openalex.org/keywords/kripke-semantics","display_name":"Kripke semantics","score":0.5886005163192749},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5151294469833374},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.43571510910987854},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.36755889654159546},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.29676252603530884},{"id":"https://openalex.org/keywords/intermediate-logic","display_name":"Intermediate logic","score":0.20227265357971191},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.08128777146339417},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.07543021440505981}],"concepts":[{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.8025417923927307},{"id":"https://openalex.org/C2185349","wikidata":"https://www.wikidata.org/wiki/Q190558","display_name":"Negation","level":2,"score":0.5962063074111938},{"id":"https://openalex.org/C160131679","wikidata":"https://www.wikidata.org/wiki/Q2462350","display_name":"Kripke semantics","level":4,"score":0.5886005163192749},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5151294469833374},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43571510910987854},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.36755889654159546},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29676252603530884},{"id":"https://openalex.org/C33203268","wikidata":"https://www.wikidata.org/wiki/Q5361594","display_name":"Intermediate logic","level":3,"score":0.20227265357971191},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.08128777146339417},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.07543021440505981},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2275666","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2275666","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1183745005","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183745005","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1505359507","https://openalex.org/W1574367593","https://openalex.org/W1593617641","https://openalex.org/W1974484530","https://openalex.org/W1984344621","https://openalex.org/W1989799540","https://openalex.org/W2002732107","https://openalex.org/W2002791110","https://openalex.org/W2003464476","https://openalex.org/W2012449337","https://openalex.org/W2025063685","https://openalex.org/W2026838265","https://openalex.org/W2040400857","https://openalex.org/W2041574133","https://openalex.org/W2043493426","https://openalex.org/W2051198079","https://openalex.org/W2058110538","https://openalex.org/W2074025367","https://openalex.org/W2080462204","https://openalex.org/W2088847726","https://openalex.org/W2154114798","https://openalex.org/W2162300758","https://openalex.org/W2911865844","https://openalex.org/W4240400578","https://openalex.org/W4248156396","https://openalex.org/W4254619632","https://openalex.org/W4302314483","https://openalex.org/W6672888892"],"related_works":["https://openalex.org/W2059922809","https://openalex.org/W2053762111","https://openalex.org/W2440791454","https://openalex.org/W4297670065","https://openalex.org/W1618267488","https://openalex.org/W1543051890","https://openalex.org/W4205250428","https://openalex.org/W1563786920","https://openalex.org/W1567962086","https://openalex.org/W2056142535"],"abstract_inverted_index":{"The":[0],"history":[1],"of":[2,5,35,53,91,153,199,201,218,228,245],"the":[3,32,36,38,51,54,92,97,151,154,162,165,170,243],"Gentzenization":[4,85,227],"relevant":[6,202],"logics":[7],"goes":[8],"back":[9],"to":[10,22,50,122,150,161,241],"Kripke":[11,44],"[17],":[12],"who":[13],"in":[14,76,95,110,116,132,139,184,215,222],"1959":[15],"Gentzenized":[16,78,109,135],"R":[17,99,136],"\u2192":[18],"and":[19,74,79,148,156,169,193,238],"went":[20,120],"on":[21,31,88,121,208],"prove":[23,242],"its":[24,81],"decidability.":[25],"Formulae":[26],"were":[27],"separated":[28],"by":[29,114,127,213],"commas":[30,39,87,166],"left":[33,152],"side":[34],"turnstile,":[37,155],"just":[40,46],"representing":[41],"nested":[42],"implications.":[43],"employed":[45,86],"a":[47,111,158,197,216,226],"singleton":[48],"formula":[49,160],"right":[52],"turnstile.":[55,93],"He":[56,118],"also":[57,119,189],"considered":[58],"adding":[59],"negation,":[60],"as":[61,63],"well":[62],"other":[64],"connectives,":[65],"but":[66],"it":[67,240],"was":[68,108,211],"not":[69],"until":[70],"1961":[71],"that":[72],"Belnap":[73],"Wallace,":[75],"[5],":[77],"proved":[80],"decidability,":[82],"though":[83],"their":[84],"both":[89],"sides":[90],"Subsequently,":[94],"1966,":[96],"logic":[98,210],"without":[100,231],"distribution,":[101],"now":[102],"called":[103,176],"LR":[104,126],"(for":[105],"lattice":[106],"R),":[107],"similar":[112],"style":[113],"Meyer":[115],"[20].":[117],"show":[123],"decidability":[124,244],"for":[125,196],"extending":[128],"Kripke's":[129],"argument.":[130],"Later,":[131],"1969,":[133],"Dunn":[134],"+":[137],"(published":[138],"[1],":[140],"pp.":[141],"381\u2013391)":[142],"using":[143],"two":[144],"structural":[145],"connectives":[146],"(commas":[147],"semicolons)":[149],"with":[157],"single":[159],"right.":[163],"Here,":[164],"represent":[167,172],"conjunction":[168],"semicolons":[171],"an":[173],"intensional":[174],"conjunction,":[175],"\u201cfusion\u201d.":[177],"This":[178],"is":[179],"all":[180],"nicely":[181],"set":[182],"out":[183],"McRobbie":[185],"[19],":[186],"where":[187],"he":[188,224],"introduces":[190],"left-handed":[191],"Gentzenizations":[192],"analytic":[194],"tableaux":[195],"number":[198],"fragments":[200],"logics.":[203],"In":[204],"1979,":[205],"further":[206],"work":[207],"distributionless":[209],"done":[212],"Grishin,":[214],"series":[217],"papers,":[219],"including":[220],"[16],":[221],"which":[223],"produced":[225],"quantified":[229,247],"RW":[230],"distribution":[232],"(which":[233],"we":[234],"will":[235],"call":[236],"LRWQ),":[237],"used":[239],"this":[246],"logic.":[248]},"counts_by_year":[{"year":2020,"cited_by_count":4},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
