{"id":"https://openalex.org/W2082042052","doi":"https://doi.org/10.1215/00294527-1722719","title":"New Consecution Calculi for R\u2192t","display_name":"New Consecution Calculi for R\u2192t","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2082042052","doi":"https://doi.org/10.1215/00294527-1722719","mag":"2082042052"},"language":"en","primary_location":{"id":"doi:10.1215/00294527-1722719","is_oa":true,"landing_page_url":"https://doi.org/10.1215/00294527-1722719","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-53/issue-4/New-Consecution-Calculi-for-Rt/10.1215/00294527-1722719.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-53/issue-4/New-Consecution-Calculi-for-Rt/10.1215/00294527-1722719.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064142183","display_name":"Katalin Bimb\u00f3","orcid":"https://orcid.org/0000-0002-6769-9704"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Katalin Bimb\u00f3","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5104193079","display_name":"J. Michael Dunn","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. Michael Dunn","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5064142183"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.2109,"has_fulltext":true,"cited_by_count":15,"citation_normalized_percentile":{"value":0.89014388,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"53","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9998000264167786,"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/T10317","display_name":"Advanced Database Systems and Queries","score":0.9947999715805054,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/fragment","display_name":"Fragment (logic)","score":0.6827991008758545},{"id":"https://openalex.org/keywords/sequent-calculus","display_name":"Sequent calculus","score":0.6763980388641357},{"id":"https://openalex.org/keywords/decidability","display_name":"Decidability","score":0.6759411096572876},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.6153438687324524},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5812489986419678},{"id":"https://openalex.org/keywords/natural-deduction","display_name":"Natural deduction","score":0.5560292601585388},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5140122175216675},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4219772219657898},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1844203770160675},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.09655675292015076}],"concepts":[{"id":"https://openalex.org/C2776235265","wikidata":"https://www.wikidata.org/wiki/Q18392052","display_name":"Fragment (logic)","level":2,"score":0.6827991008758545},{"id":"https://openalex.org/C65880906","wikidata":"https://www.wikidata.org/wiki/Q1771121","display_name":"Sequent calculus","level":3,"score":0.6763980388641357},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.6759411096572876},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.6153438687324524},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5812489986419678},{"id":"https://openalex.org/C62073222","wikidata":"https://www.wikidata.org/wiki/Q1572108","display_name":"Natural deduction","level":2,"score":0.5560292601585388},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5140122175216675},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4219772219657898},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1844203770160675},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.09655675292015076},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1215/00294527-1722719","is_oa":true,"landing_page_url":"https://doi.org/10.1215/00294527-1722719","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-53/issue-4/New-Consecution-Calculi-for-Rt/10.1215/00294527-1722719.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.ndjfl/1352383228","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.ndjfl/1352383228","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":{"id":"doi:10.1215/00294527-1722719","is_oa":true,"landing_page_url":"https://doi.org/10.1215/00294527-1722719","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-53/issue-4/New-Consecution-Calculi-for-Rt/10.1215/00294527-1722719.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.47999998927116394,"id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G6527745763","display_name":"Socialism in postcolonial Mali, 1960-1968","funder_award_id":"47408","funder_id":"https://openalex.org/F4320334617","funder_display_name":"Social Sciences and Humanities Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320319946","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27"},{"id":"https://openalex.org/F4320332953","display_name":"Indiana University Bloomington","ror":"https://ror.org/02k40bc56"},{"id":"https://openalex.org/F4320334617","display_name":"Social Sciences and Humanities Research Council of Canada","ror":"https://ror.org/04j5jqy92"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2082042052.pdf","grobid_xml":"https://content.openalex.org/works/W2082042052.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W40425547","https://openalex.org/W60391671","https://openalex.org/W135778027","https://openalex.org/W975991832","https://openalex.org/W1506910973","https://openalex.org/W1554516311","https://openalex.org/W1574367593","https://openalex.org/W1969075264","https://openalex.org/W1969972084","https://openalex.org/W2009732936","https://openalex.org/W2039977878","https://openalex.org/W2051668492","https://openalex.org/W2057185140","https://openalex.org/W2066761871","https://openalex.org/W2072341634","https://openalex.org/W2153111627","https://openalex.org/W2155581733","https://openalex.org/W2166144087","https://openalex.org/W2512995482","https://openalex.org/W3128843429","https://openalex.org/W3135320517","https://openalex.org/W4211095208","https://openalex.org/W4249835483","https://openalex.org/W4252068692","https://openalex.org/W4400722360"],"related_works":["https://openalex.org/W2137780954","https://openalex.org/W2023557900","https://openalex.org/W1488351281","https://openalex.org/W2891688494","https://openalex.org/W2584381231","https://openalex.org/W4236940717","https://openalex.org/W2096191306","https://openalex.org/W2752930545","https://openalex.org/W4289719533","https://openalex.org/W4251049234"],"abstract_inverted_index":{"The":[0,27],"implicational":[1,89],"fragment":[2,90],"of":[3,6,12,91,103,124,141,144],"the":[4,13,41,55,83,88,111,117,120,137,142],"logic":[5],"relevant":[7],"implication,":[8],"R\u2192":[9],"is":[10,29,70],"one":[11],"oldest":[14],"relevance":[15],"logics":[16],"and":[17],"in":[18,67,149],"1959":[19],"was":[20],"shown":[21],"by":[22,72],"Kripke":[23],"to":[24,45,53,119,136],"be":[25],"decidable.":[26],"proof":[28],"based":[30],"on":[31],"LR\u2192,":[32,46],"a":[33,59,63,130],"Gentzen-style":[34],"calculus.":[35],"In":[36],"this":[37],"paper,":[38],"we":[39,50,109,147],"add":[40],"truth":[42],"constant":[43],"t":[44],"but":[47],"more":[48],"importantly":[49],"show":[51],"how":[52],"reshape":[54],"sequent":[56],"calculus":[57,61,85],"as":[58,100,114,116,129],"consecution":[60,84],"containing":[62],"binary":[64],"structural":[65,74],"connective,":[66],"which":[68,146],"permutation":[69],"replaced":[71],"two":[73,96],"rules":[75],"that":[76],"involve":[77],"t.":[78],"This":[79],"calculus,":[80,108],"LT\u2192\u24e3,":[81],"extends":[82],"LT\u2192t":[86],"formalizing":[87],"ticket":[92],"entailment.":[93],"We":[94],"introduce":[95],"other":[97],"new":[98,107],"calculi":[99],"alternative":[101],"formulations":[102],"R\u2192t.":[104,125],"For":[105],"each":[106],"prove":[110],"cut":[112],"theorem":[113],"well":[115],"equivalence":[118],"original":[121],"Hilbert-style":[122],"axiomatization":[123],"These":[126],"results":[127],"serve":[128],"basis":[131],"for":[132],"our":[133],"positive":[134],"solution":[135],"long":[138],"open":[139],"problem":[140],"decidability":[143],"T\u2192,":[145],"present":[148],"another":[150],"paper.":[151]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}