{"id":"https://openalex.org/W2057714618","doi":"https://doi.org/10.1305/ndjfl/1099238445","title":"LK, LJ, Dual Intuitionistic Logic, and Quantum Logic","display_name":"LK, LJ, Dual Intuitionistic Logic, and Quantum Logic","publication_year":2004,"publication_date":"2004-10-01","ids":{"openalex":"https://openalex.org/W2057714618","doi":"https://doi.org/10.1305/ndjfl/1099238445","mag":"2057714618"},"language":"en","primary_location":{"id":"doi:10.1305/ndjfl/1099238445","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1099238445","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-45/issue-4/LK-LJ-Dual-Intuitionistic-Logic-and-Quantum-Logic/10.1305/ndjfl/1099238445.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-45/issue-4/LK-LJ-Dual-Intuitionistic-Logic-and-Quantum-Logic/10.1305/ndjfl/1099238445.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044264060","display_name":"Hiroshi Aoyama","orcid":null},"institutions":[{"id":"https://openalex.org/I107639228","display_name":"University of Notre Dame","ror":"https://ror.org/00mkhxb43","country_code":"US","type":"education","lineage":["https://openalex.org/I107639228"]},{"id":"https://openalex.org/I175135595","display_name":"Tokai Gakuen University","ror":"https://ror.org/03aet8853","country_code":"JP","type":"education","lineage":["https://openalex.org/I175135595"]}],"countries":["JP","US"],"is_corresponding":true,"raw_author_name":"Hiroshi Aoyama","raw_affiliation_strings":["Tokaigakuen University Nakahira 2-901 Tempaku ward , Nagoya City 468-8514 JAPAN","University of Notre Dame 193 Faculty of Humanities","Faculty of Humanities Tokaigakuen University Nakahira 2-901 Tempaku ward, Nagoya City 468-8514 JAPAN","University of Notre Dame"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tokaigakuen University Nakahira 2-901 Tempaku ward , Nagoya City 468-8514 JAPAN","institution_ids":["https://openalex.org/I175135595"]},{"raw_affiliation_string":"University of Notre Dame 193 Faculty of Humanities","institution_ids":["https://openalex.org/I107639228"]},{"raw_affiliation_string":"Faculty of Humanities Tokaigakuen University Nakahira 2-901 Tempaku ward, Nagoya City 468-8514 JAPAN","institution_ids":["https://openalex.org/I175135595"]},{"raw_affiliation_string":"University of Notre Dame","institution_ids":["https://openalex.org/I107639228"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5044264060"],"corresponding_institution_ids":["https://openalex.org/I107639228","https://openalex.org/I175135595"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":11,"citation_normalized_percentile":{"value":0.15191731,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"45","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9993000030517578,"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":0.9993000030517578,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9990000128746033,"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/T10126","display_name":"Logic, programming, and type systems","score":0.996399998664856,"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/quantum-logic","display_name":"Quantum logic","score":0.7590967416763306},{"id":"https://openalex.org/keywords/intuitionistic-logic","display_name":"Intuitionistic logic","score":0.7310818433761597},{"id":"https://openalex.org/keywords/paraconsistent-logic","display_name":"Paraconsistent logic","score":0.7246221899986267},{"id":"https://openalex.org/keywords/intermediate-logic","display_name":"Intermediate logic","score":0.6685327291488647},{"id":"https://openalex.org/keywords/many-valued-logic","display_name":"Many-valued logic","score":0.6630114912986755},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4820909798145294},{"id":"https://openalex.org/keywords/dynamic-logic","display_name":"Dynamic logic (digital electronics)","score":0.4580146372318268},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.457028329372406},{"id":"https://openalex.org/keywords/higher-order-logic","display_name":"Higher-order logic","score":0.44498422741889954},{"id":"https://openalex.org/keywords/substructural-logic","display_name":"Substructural logic","score":0.4345269203186035},{"id":"https://openalex.org/keywords/classical-logic","display_name":"Classical logic","score":0.43253639340400696},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.378273606300354},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3548840284347534},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3353472352027893},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.26226091384887695},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.23143437504768372},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.2190796136856079},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.20761671662330627},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.1975632905960083},{"id":"https://openalex.org/keywords/propositional-calculus","display_name":"Propositional calculus","score":0.19593071937561035},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.09779044985771179},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08983579277992249},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07865998148918152},{"id":"https://openalex.org/keywords/quantum-computer","display_name":"Quantum computer","score":0.06768813729286194}],"concepts":[{"id":"https://openalex.org/C169460222","wikidata":"https://www.wikidata.org/wiki/Q1206311","display_name":"Quantum logic","level":4,"score":0.7590967416763306},{"id":"https://openalex.org/C178421362","wikidata":"https://www.wikidata.org/wiki/Q176786","display_name":"Intuitionistic logic","level":3,"score":0.7310818433761597},{"id":"https://openalex.org/C16796852","wikidata":"https://www.wikidata.org/wiki/Q426592","display_name":"Paraconsistent logic","level":4,"score":0.7246221899986267},{"id":"https://openalex.org/C33203268","wikidata":"https://www.wikidata.org/wiki/Q5361594","display_name":"Intermediate logic","level":3,"score":0.6685327291488647},{"id":"https://openalex.org/C150889026","wikidata":"https://www.wikidata.org/wiki/Q185502","display_name":"Many-valued logic","level":3,"score":0.6630114912986755},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4820909798145294},{"id":"https://openalex.org/C2777796570","wikidata":"https://www.wikidata.org/wiki/Q2351326","display_name":"Dynamic logic (digital electronics)","level":4,"score":0.4580146372318268},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.457028329372406},{"id":"https://openalex.org/C169896238","wikidata":"https://www.wikidata.org/wiki/Q1644136","display_name":"Higher-order logic","level":3,"score":0.44498422741889954},{"id":"https://openalex.org/C144760519","wikidata":"https://www.wikidata.org/wiki/Q839490","display_name":"Substructural logic","level":4,"score":0.4345269203186035},{"id":"https://openalex.org/C32241873","wikidata":"https://www.wikidata.org/wiki/Q236975","display_name":"Classical logic","level":2,"score":0.43253639340400696},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.378273606300354},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3548840284347534},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3353472352027893},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.26226091384887695},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.23143437504768372},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.2190796136856079},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.20761671662330627},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.1975632905960083},{"id":"https://openalex.org/C69562738","wikidata":"https://www.wikidata.org/wiki/Q200694","display_name":"Propositional calculus","level":2,"score":0.19593071937561035},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.09779044985771179},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08983579277992249},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07865998148918152},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.06768813729286194},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.0},{"id":"https://openalex.org/C172385210","wikidata":"https://www.wikidata.org/wiki/Q5339","display_name":"Transistor","level":3,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1305/ndjfl/1099238445","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1099238445","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-45/issue-4/LK-LJ-Dual-Intuitionistic-Logic-and-Quantum-Logic/10.1305/ndjfl/1099238445.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/1099238445","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.ndjfl/1099238445","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:10.1305/ndjfl/1099238445","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1099238445","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-45/issue-4/LK-LJ-Dual-Intuitionistic-Logic-and-Quantum-Logic/10.1305/ndjfl/1099238445.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":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.4099999964237213}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2057714618.pdf","grobid_xml":"https://content.openalex.org/works/W2057714618.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W245987618","https://openalex.org/W612868514","https://openalex.org/W656700481","https://openalex.org/W996720968","https://openalex.org/W1485574327","https://openalex.org/W1602312920","https://openalex.org/W1838881120","https://openalex.org/W1989314289","https://openalex.org/W2007096790","https://openalex.org/W2058093611","https://openalex.org/W2085057391","https://openalex.org/W2112103497","https://openalex.org/W2126414330","https://openalex.org/W2135986646","https://openalex.org/W3040499212","https://openalex.org/W4240750369","https://openalex.org/W4388313831"],"related_works":["https://openalex.org/W2092293513","https://openalex.org/W2153288022","https://openalex.org/W2140910855","https://openalex.org/W1770974247","https://openalex.org/W1999598455","https://openalex.org/W1873680480","https://openalex.org/W2406515025","https://openalex.org/W2952835335","https://openalex.org/W837246972","https://openalex.org/W3118267960"],"abstract_inverted_index":{"In":[0],"this":[1,42],"paper,":[2],"we":[3],"study":[4,63],"the":[5],"relationship":[6],"among":[7],"classical":[8],"logic,":[9,11],"intuitionistic":[10,55],"and":[12,16,27],"quantum":[13],"logic":[14,56],"(orthologic":[15],"orthomodular":[17],"logic).":[18,61],"These":[19],"logics":[20],"are":[21,28,47],"related":[22,48],"in":[23,41],"an":[24],"interesting":[25],"way":[26],"not":[29],"far":[30],"apart":[31],"from":[32],"each":[33,50],"other,":[34],"as":[35],"is":[36,64],"widely":[37],"believed.":[38],"The":[39],"results":[40],"paper":[43],"show":[44],"how":[45],"they":[46],"with":[49],"other":[51],"through":[52],"a":[53],"dual":[54],"(a":[57],"kind":[58],"of":[59],"paraconsistent":[60],"Our":[62],"completely":[65],"syntactical.":[66]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-10T00:00:00"}