{"id":"https://openalex.org/W1992606256","doi":"https://doi.org/10.1016/s1571-0661(04)80755-2","title":"Eigenvariables, bracketing and the decidability of positive minimal intuitionistic logic","display_name":"Eigenvariables, bracketing and the decidability of positive minimal intuitionistic logic","publication_year":2003,"publication_date":"2003-09-01","ids":{"openalex":"https://openalex.org/W1992606256","doi":"https://doi.org/10.1016/s1571-0661(04)80755-2","mag":"1992606256"},"language":"en","primary_location":{"id":"doi:10.1016/s1571-0661(04)80755-2","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s1571-0661(04)80755-2","pdf_url":null,"source":{"id":"https://openalex.org/S50368787","display_name":"Electronic Notes in Theoretical Computer Science","issn_l":"1571-0661","issn":["1571-0661"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Notes in Theoretical Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.1016/s1571-0661(04)80755-2","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073164575","display_name":"Gilles Dowek","orcid":"https://orcid.org/0000-0001-6253-935X"},"institutions":[{"id":"https://openalex.org/I142476485","display_name":"\u00c9cole Polytechnique","ror":"https://ror.org/05hy3tk52","country_code":"FR","type":"education","lineage":["https://openalex.org/I142476485","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en informatique et en automatique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I4210139461","display_name":"Laboratoire d'Informatique de l'\u00c9cole Polytechnique","ror":"https://ror.org/04afed728","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I142476485","https://openalex.org/I4210139461","https://openalex.org/I4210145102","https://openalex.org/I4210159245"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Gilles Dowek","raw_affiliation_strings":["\u00c9cole polytechnique and INRIA, LIX, \u00c9cole polytechnique, 91128 Palaiseau Cedex, France"],"affiliations":[{"raw_affiliation_string":"\u00c9cole polytechnique and INRIA, LIX, \u00c9cole polytechnique, 91128 Palaiseau Cedex, France","institution_ids":["https://openalex.org/I4210139461","https://openalex.org/I1326498283","https://openalex.org/I142476485"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103120331","display_name":"Ying Jiang","orcid":"https://orcid.org/0000-0003-0524-1818"},"institutions":[{"id":"https://openalex.org/I4210128818","display_name":"Institute of Software","ror":"https://ror.org/033dfsn42","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210128818"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Ying Jiang","raw_affiliation_strings":["Institute of Software, Chinese Academy of Sciences, P.O. Box 100080 Beijing, China"],"affiliations":[{"raw_affiliation_string":"Institute of Software, Chinese Academy of Sciences, P.O. Box 100080 Beijing, China","institution_ids":["https://openalex.org/I4210128818","https://openalex.org/I19820366"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5073164575","https://openalex.org/A5103120331"],"corresponding_institution_ids":["https://openalex.org/I1326498283","https://openalex.org/I142476485","https://openalex.org/I19820366","https://openalex.org/I4210128818","https://openalex.org/I4210139461"],"apc_list":null,"apc_paid":null,"fwci":0.9139,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.80036317,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"85","issue":"7","first_page":"17","last_page":"29"},"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":0.9983000159263611,"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":0.9955999851226807,"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":0.8374238610267639},{"id":"https://openalex.org/keywords/intuitionistic-logic","display_name":"Intuitionistic logic","score":0.7142459154129028},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.631475567817688},{"id":"https://openalex.org/keywords/fragment","display_name":"Fragment (logic)","score":0.5898430347442627},{"id":"https://openalex.org/keywords/proof-theory","display_name":"Proof theory","score":0.553303062915802},{"id":"https://openalex.org/keywords/minimal-logic","display_name":"Minimal logic","score":0.5443347096443176},{"id":"https://openalex.org/keywords/structural-proof-theory","display_name":"Structural proof theory","score":0.539492666721344},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5092929601669312},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5057854652404785},{"id":"https://openalex.org/keywords/type-theory","display_name":"Type theory","score":0.4870310425758362},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.45556309819221497},{"id":"https://openalex.org/keywords/bracketing","display_name":"Bracketing (phenomenology)","score":0.4320109784603119},{"id":"https://openalex.org/keywords/propositional-calculus","display_name":"Propositional calculus","score":0.40975213050842285},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.37472257018089294},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.34868109226226807},{"id":"https://openalex.org/keywords/zeroth-order-logic","display_name":"Zeroth-order logic","score":0.2972247004508972},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2814962565898895},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.26039940118789673},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.2039514183998108},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.16174015402793884},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.0877557098865509},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07916733622550964},{"id":"https://openalex.org/keywords/multimodal-logic","display_name":"Multimodal logic","score":0.05633187294006348},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.05259990692138672}],"concepts":[{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.8374238610267639},{"id":"https://openalex.org/C178421362","wikidata":"https://www.wikidata.org/wiki/Q176786","display_name":"Intuitionistic logic","level":3,"score":0.7142459154129028},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.631475567817688},{"id":"https://openalex.org/C2776235265","wikidata":"https://www.wikidata.org/wiki/Q18392052","display_name":"Fragment (logic)","level":2,"score":0.5898430347442627},{"id":"https://openalex.org/C2318724","wikidata":"https://www.wikidata.org/wiki/Q852732","display_name":"Proof theory","level":3,"score":0.553303062915802},{"id":"https://openalex.org/C171482190","wikidata":"https://www.wikidata.org/wiki/Q3257974","display_name":"Minimal logic","level":5,"score":0.5443347096443176},{"id":"https://openalex.org/C195653647","wikidata":"https://www.wikidata.org/wiki/Q7625047","display_name":"Structural proof theory","level":4,"score":0.539492666721344},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5092929601669312},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5057854652404785},{"id":"https://openalex.org/C93682546","wikidata":"https://www.wikidata.org/wiki/Q1056428","display_name":"Type theory","level":3,"score":0.4870310425758362},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.45556309819221497},{"id":"https://openalex.org/C102944935","wikidata":"https://www.wikidata.org/wiki/Q4953701","display_name":"Bracketing (phenomenology)","level":2,"score":0.4320109784603119},{"id":"https://openalex.org/C69562738","wikidata":"https://www.wikidata.org/wiki/Q200694","display_name":"Propositional calculus","level":2,"score":0.40975213050842285},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.37472257018089294},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.34868109226226807},{"id":"https://openalex.org/C110039528","wikidata":"https://www.wikidata.org/wiki/Q8069651","display_name":"Zeroth-order logic","level":4,"score":0.2972247004508972},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2814962565898895},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.26039940118789673},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2039514183998108},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.16174015402793884},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.0877557098865509},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07916733622550964},{"id":"https://openalex.org/C203659156","wikidata":"https://www.wikidata.org/wiki/Q6934805","display_name":"Multimodal logic","level":3,"score":0.05633187294006348},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.05259990692138672},{"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},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s1571-0661(04)80755-2","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s1571-0661(04)80755-2","pdf_url":null,"source":{"id":"https://openalex.org/S50368787","display_name":"Electronic Notes in Theoretical Computer Science","issn_l":"1571-0661","issn":["1571-0661"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Notes in Theoretical Computer Science","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1016/s1571-0661(04)80755-2","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s1571-0661(04)80755-2","pdf_url":null,"source":{"id":"https://openalex.org/S50368787","display_name":"Electronic Notes in Theoretical Computer Science","issn_l":"1571-0661","issn":["1571-0661"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Notes in Theoretical Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.5600000023841858,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1483568252","https://openalex.org/W1505627668","https://openalex.org/W1975523900","https://openalex.org/W2023145007","https://openalex.org/W2107589331","https://openalex.org/W2131739376","https://openalex.org/W2568721247","https://openalex.org/W3144135223"],"related_works":["https://openalex.org/W4379193094","https://openalex.org/W2620241516","https://openalex.org/W1968027005","https://openalex.org/W20138908","https://openalex.org/W3046415793","https://openalex.org/W3176397990","https://openalex.org/W1992606256","https://openalex.org/W31250260","https://openalex.org/W2009938424","https://openalex.org/W2491263424"],"abstract_inverted_index":{"We":[0,91],"give":[1],"a":[2,6,75,95],"new":[3,96],"proof":[4,24,41,97],"of":[5,8,14,22,62,78,98,101],"theorem":[7],"Mints":[9],"that":[10,48,70],"the":[11,23,28,51,60,63,99],"positive":[12,104],"fragment":[13],"minimal":[15],"intuitionistic":[16],"logic":[17],"is":[18,25,57,67],"decidable.":[19],"The":[20,36],"idea":[21],"to":[26,43,68,74],"replace":[27],"eigenvariable":[29],"condition":[30],"by":[31,39,50],"an":[32],"appropriate":[33],"scoping":[34],"mechanism.":[35],"algorithm":[37],"given":[38,49,58],"this":[40,71,93],"seems":[42],"be":[44],"more":[45],"practical":[46],"than":[47],"original":[52],"proof.":[53],"A":[54],"naive":[55],"implementation":[56],"at":[59],"end":[61],"paper.":[64],"Another":[65],"contribution":[66],"show":[69],"result":[72],"extends":[73],"large":[76],"class":[77],"theories,":[79],"including":[80],"simple":[81],"type":[82],"theory":[83],"(higher-order":[84],"logic)":[85],"and":[86],"second":[87],"order":[88],"propositional":[89],"logic.":[90],"obtain":[92],"way":[94],"decidability":[100],"inhabitation":[102],"for":[103],"types":[105],"in":[106],"system":[107],"F.":[108]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}