{"id":"https://openalex.org/W4229830739","doi":"https://doi.org/10.2307/2275667","title":"Gentzenizations of relevant logics without distribution. II","display_name":"Gentzenizations of relevant logics without distribution. II","publication_year":1996,"publication_date":"1996-06-01","ids":{"openalex":"https://openalex.org/W4229830739","doi":"https://doi.org/10.2307/2275667"},"language":"en","primary_location":{"id":"doi:10.2307/2275667","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2275667","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":0.0,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.39857811,"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":"379","last_page":"401"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9896000027656555,"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":0.9896000027656555,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9868000149726868,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9757999777793884,"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/decidability","display_name":"Decidability","score":0.8874214291572571},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5662122368812561},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5629507303237915},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4197462201118469},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3993506133556366},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.39383524656295776},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.36761409044265747},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3244801461696625},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1295594573020935},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.1106242835521698},{"id":"https://openalex.org/keywords/motion","display_name":"Motion (physics)","score":0.06297069787979126}],"concepts":[{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.8874214291572571},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5662122368812561},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5629507303237915},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4197462201118469},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3993506133556366},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.39383524656295776},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.36761409044265747},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3244801461696625},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1295594573020935},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.1106242835521698},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.06297069787979126}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2275667","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2275667","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/1183745006","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183745006","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":4,"referenced_works":["https://openalex.org/W1984344621","https://openalex.org/W2041574133","https://openalex.org/W2043493426","https://openalex.org/W4240400578"],"related_works":["https://openalex.org/W2331020993","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":{"In":[0,50],"Part":[1,46,51,93],"I,":[2],"we":[3,56],"produced":[4],"a":[5,115,136,186,196],"Gentzenization":[6,154],"L":[7],"6":[8],"LBQ":[9,91],"of":[10,42,45,53,118,138],"the":[11,19,32,67,84,103,109,153,182],"distributionless":[12,69],"relevant":[13],"logic":[14],"LBQ,":[15],"which":[16],"contained":[17],"just":[18],"one":[20],"structural":[21,26],"connective":[22,188],"\u2018:\u2019":[23],"and":[24,36,40,63,80,108,125,142,155,170,179,191],"no":[25],"rules.":[27],"We":[28,162],"compared":[29],"it":[30,148],"with":[31,60],"corresponding":[33],"\u201cright-handed\u201d":[34],"system":[35],"then":[37],"proved":[38,113,145],"interpolability":[39],"decidability":[41,64,110],"LBQ.":[43],"Knowledge":[44],"I":[47],"is":[48,106,112],"presupposed.":[49],"II":[52],"this":[54],"paper,":[55],"will":[57],"establish":[58],"Gentzenizations,":[59],"appropriate":[61],"interpolation":[62,104,146,156],"results,":[65],"for":[66,90,147],"further":[68],"logics":[70,165],"LDWQ,":[71],"LTWQ":[72,178],"o":[73],",":[74,77],"LEWQ":[75,180,192],"ot":[76],"LRWQ,":[78],"LRWKQ":[79],"LRQ,":[81],"using":[82],"essentially":[83],"same":[85],"methods":[86],"as":[87,166,174],"were":[88],"used":[89],"in":[92,132,140,149],"I.":[94],"LRWQ":[95],"has":[96,122,144],"been":[97,123],"Gentzenized":[98,124],"by":[99,114,130,134],"Grishin":[100],"[2],":[101],"but":[102,151],"result":[105,111],"new":[107],"substantial":[116],"simplification":[117],"his":[119],"method.":[120],"LR":[121],"shown":[126],"to":[127,160],"be":[128],"decidable":[129],"Meyer":[131],"[5],":[133],"extending":[135],"method":[137],"Kripke":[139],"[3],":[141],"McRobbie":[143],"[4],":[150],"here":[152],"results":[157],"are":[158,173],"extended":[159],"quantifiers.":[161],"axiomatize":[163],"these":[164],"follows.":[167],"The":[168],"primitives":[169],"formation":[171],"rules":[172],"before,":[175],"except":[176],"that":[177],"require":[181],"extra":[183],"primitive":[184],"\u2018o\u2019,":[185],"2-place":[187],"(called":[189],"\u2018fusion\u2019),":[190],"also":[193],"requires":[194],"\u2018t\u2019,":[195],"sentential":[197],"constant.":[198]},"counts_by_year":[{"year":2018,"cited_by_count":3},{"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"}