{"id":"https://openalex.org/W2472748050","doi":"https://doi.org/10.1002/malq.201400099","title":"Embedding classical in minimal implicational logic","display_name":"Embedding classical in minimal implicational logic","publication_year":2016,"publication_date":"2016-01-19","ids":{"openalex":"https://openalex.org/W2472748050","doi":"https://doi.org/10.1002/malq.201400099","mag":"2472748050"},"language":"en","primary_location":{"id":"doi:10.1002/malq.201400099","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.201400099","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0044-3050","issn":["0044-3050","0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","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/A5016735166","display_name":"Hajime Ishihara","orcid":"https://orcid.org/0000-0001-6074-4579"},"institutions":[{"id":"https://openalex.org/I177738480","display_name":"Japan Advanced Institute of Science and Technology","ror":"https://ror.org/03frj4r98","country_code":"JP","type":"education","lineage":["https://openalex.org/I177738480"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Hajime Ishihara","raw_affiliation_strings":["School of Information Science Japan Advanced Institute of Science and Technoloty 1\u20101 Asahidai Nomi Ishikawa 923\u20101292 Japan","School of Information Science, Japan Advanced Institute of Science and Technoloty, 1-1 Asahidai, Nomi, Ishikawa, 923-1292 Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information Science Japan Advanced Institute of Science and Technoloty 1\u20101 Asahidai Nomi Ishikawa 923\u20101292 Japan","institution_ids":["https://openalex.org/I177738480"]},{"raw_affiliation_string":"School of Information Science, Japan Advanced Institute of Science and Technoloty, 1-1 Asahidai, Nomi, Ishikawa, 923-1292 Japan","institution_ids":["https://openalex.org/I177738480"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112382767","display_name":"Helmut Schwichtenberg","orcid":null},"institutions":[{"id":"https://openalex.org/I8204097","display_name":"Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen","ror":"https://ror.org/05591te55","country_code":"DE","type":"education","lineage":["https://openalex.org/I8204097"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Helmut Schwichtenberg","raw_affiliation_strings":["Mathematisches Institut Ludwig\u2010Maximilians\u2010Universit\u00e4t M\u00fcnchen Theresienstra\u00dfe 39 80333 M\u00fcnchen Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematisches Institut Ludwig\u2010Maximilians\u2010Universit\u00e4t M\u00fcnchen Theresienstra\u00dfe 39 80333 M\u00fcnchen Germany","institution_ids":["https://openalex.org/I8204097"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5112382767"],"corresponding_institution_ids":["https://openalex.org/I8204097"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":0.6245,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.75345009,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"62","issue":"1-2","first_page":"94","last_page":"101"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10258","display_name":"Philosophy and Theoretical Science","score":0.9811999797821045,"subfield":{"id":"https://openalex.org/subfields/3205","display_name":"Experimental and Cognitive Psychology"},"field":{"id":"https://openalex.org/fields/32","display_name":"Psychology"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10258","display_name":"Philosophy and Theoretical Science","score":0.9811999797821045,"subfield":{"id":"https://openalex.org/subfields/3205","display_name":"Experimental and Cognitive Psychology"},"field":{"id":"https://openalex.org/fields/32","display_name":"Psychology"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10778","display_name":"Philosophy and History of Science","score":0.973800003528595,"subfield":{"id":"https://openalex.org/subfields/1207","display_name":"History and Philosophy of Science"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12133","display_name":"Pragmatism in Philosophy and Education","score":0.9725000262260437,"subfield":{"id":"https://openalex.org/subfields/1211","display_name":"Philosophy"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8387757539749146},{"id":"https://openalex.org/keywords/intuitionistic-logic","display_name":"Intuitionistic logic","score":0.6862372159957886},{"id":"https://openalex.org/keywords/propositional-variable","display_name":"Propositional variable","score":0.6443767547607422},{"id":"https://openalex.org/keywords/propositional-calculus","display_name":"Propositional calculus","score":0.5667769312858582},{"id":"https://openalex.org/keywords/corollary","display_name":"Corollary","score":0.5361248254776001},{"id":"https://openalex.org/keywords/classical-logic","display_name":"Classical logic","score":0.5220391750335693},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.5211629867553711},{"id":"https://openalex.org/keywords/intermediate-logic","display_name":"Intermediate logic","score":0.464517742395401},{"id":"https://openalex.org/keywords/zeroth-order-logic","display_name":"Zeroth-order logic","score":0.464344322681427},{"id":"https://openalex.org/keywords/propositional-formula","display_name":"Propositional formula","score":0.43644237518310547},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4182429611682892},{"id":"https://openalex.org/keywords/atomic-formula","display_name":"Atomic formula","score":0.41152215003967285},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3515925407409668},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3054148554801941},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08197131752967834},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06181517243385315},{"id":"https://openalex.org/keywords/multimodal-logic","display_name":"Multimodal logic","score":0.06031790375709534}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8387757539749146},{"id":"https://openalex.org/C178421362","wikidata":"https://www.wikidata.org/wiki/Q176786","display_name":"Intuitionistic logic","level":3,"score":0.6862372159957886},{"id":"https://openalex.org/C14523651","wikidata":"https://www.wikidata.org/wiki/Q3492863","display_name":"Propositional variable","level":4,"score":0.6443767547607422},{"id":"https://openalex.org/C69562738","wikidata":"https://www.wikidata.org/wiki/Q200694","display_name":"Propositional calculus","level":2,"score":0.5667769312858582},{"id":"https://openalex.org/C2780012671","wikidata":"https://www.wikidata.org/wiki/Q1343870","display_name":"Corollary","level":2,"score":0.5361248254776001},{"id":"https://openalex.org/C32241873","wikidata":"https://www.wikidata.org/wiki/Q236975","display_name":"Classical logic","level":2,"score":0.5220391750335693},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.5211629867553711},{"id":"https://openalex.org/C33203268","wikidata":"https://www.wikidata.org/wiki/Q5361594","display_name":"Intermediate logic","level":3,"score":0.464517742395401},{"id":"https://openalex.org/C110039528","wikidata":"https://www.wikidata.org/wiki/Q8069651","display_name":"Zeroth-order logic","level":4,"score":0.464344322681427},{"id":"https://openalex.org/C74640108","wikidata":"https://www.wikidata.org/wiki/Q1372900","display_name":"Propositional formula","level":5,"score":0.43644237518310547},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4182429611682892},{"id":"https://openalex.org/C203264685","wikidata":"https://www.wikidata.org/wiki/Q2328174","display_name":"Atomic formula","level":2,"score":0.41152215003967285},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3515925407409668},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3054148554801941},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08197131752967834},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06181517243385315},{"id":"https://openalex.org/C203659156","wikidata":"https://www.wikidata.org/wiki/Q6934805","display_name":"Multimodal logic","level":3,"score":0.06031790375709534},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/malq.201400099","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.201400099","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0044-3050","issn":["0044-3050","0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":1,"referenced_works":["https://openalex.org/W2081976468"],"related_works":["https://openalex.org/W2055558461","https://openalex.org/W3137333128","https://openalex.org/W4251854500","https://openalex.org/W2081976468","https://openalex.org/W3200682096","https://openalex.org/W1986625420","https://openalex.org/W2441642482","https://openalex.org/W62016554","https://openalex.org/W3020878688","https://openalex.org/W2356894535"],"abstract_inverted_index":{"Consider":[0],"the":[1,38,43,77,87,96,110,116,135],"problem":[2],"which":[3,132],"set":[4,151],"V":[5],"of":[6,42,66,86,95,125,134,152,164],"propositional":[7,40,127],"variables":[8],"suffices":[9,99],"for":[10,37,118],"whenever":[11],",":[12,14],"where":[13],"and":[15,18,25,156],"\u22a2":[16,19],"c":[17],"i":[20],"denote":[21],"derivability":[22,144],"in":[23,145,159],"classical":[24,103,123],"intuitionistic":[26,105],"implicational":[27],"logic,":[28],"respectively.":[29],"We":[30,148],"give":[31,62],"a":[32,50,92,122,126,150],"direct":[33],"proof":[34,65],"that":[35,90,158],"stability":[36,73],"final":[39],"variable":[41],"(implicational)":[44],"formula":[45,79,98,128,137],"A":[46],"is":[47,82,166],"sufficient;":[48],"as":[49,139],"corollary":[51],"one":[52,60,113],"obtains":[53],"Glivenko's":[54,58],"theorem.":[55],"Conversely,":[56],"using":[57],"theorem":[59],"can":[61],"an":[63,70,83,161],"alternative":[64,71],"our":[67],"result.":[68],"As":[69],"to":[72,100,104,142],"we":[74,108],"then":[75],"consider":[76,109],"Peirce":[78,97,136,154],".":[80],"It":[81],"easy":[84],"consequence":[85],"result":[88],"above":[89],"adding":[91],"single":[93],"instance":[94],"move":[101],"from":[102],"derivability.":[106],"Finally":[107],"question":[111],"whether":[112],"could":[114],"do":[115],"same":[117],"minimal":[119,146],"logic.":[120],"Given":[121],"derivation":[124],"not":[129],"involving":[130],"\u22a5,":[131],"instances":[133],"suffice":[138],"additional":[140],"premises":[141],"ensure":[143],"logic?":[147],"define":[149],"such":[153],"formulas,":[155],"show":[157],"general":[160],"unbounded":[162],"number":[163],"them":[165],"necessary.":[167]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
