{"id":"https://openalex.org/W1995074720","doi":"https://doi.org/10.1155/2012/259541","title":"A Comparison of Implications in Orthomodular Quantum Logic\u2014Morphological Analysis of Quantum Logic","display_name":"A Comparison of Implications in Orthomodular Quantum Logic\u2014Morphological Analysis of Quantum Logic","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W1995074720","doi":"https://doi.org/10.1155/2012/259541","mag":"1995074720"},"language":"en","primary_location":{"id":"doi:10.1155/2012/259541","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/259541","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2012/259541.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/ijmms/2012/259541.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5114078849","display_name":"Mitsuhiko Fujio","orcid":null},"institutions":[{"id":"https://openalex.org/I207014233","display_name":"Kyushu Institute of Technology","ror":"https://ror.org/02278tr80","country_code":"JP","type":"education","lineage":["https://openalex.org/I207014233"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Mitsuhiko Fujio","raw_affiliation_strings":["Department of Systems Design and Informatics, Faculty of Computer Science and Systems Engineering, Kyushu Institute of Technology, Iizuka-shi 820-8502, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Systems Design and Informatics, Faculty of Computer Science and Systems Engineering, Kyushu Institute of Technology, Iizuka-shi 820-8502, Japan","institution_ids":["https://openalex.org/I207014233"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5114078849"],"corresponding_institution_ids":["https://openalex.org/I207014233"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.08309525,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"2012","issue":"334","first_page":"1","last_page":"8"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9987000226974487,"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":0.9987000226974487,"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":0.9959999918937683,"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/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9649999737739563,"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/mathematics","display_name":"Mathematics","score":0.8012669682502747},{"id":"https://openalex.org/keywords/quantum-logic","display_name":"Quantum logic","score":0.7074755430221558},{"id":"https://openalex.org/keywords/adjunction","display_name":"Adjunction","score":0.5499982237815857},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5018680095672607},{"id":"https://openalex.org/keywords/kripke-semantics","display_name":"Kripke semantics","score":0.47542980313301086},{"id":"https://openalex.org/keywords/\u0142ukasiewicz-logic","display_name":"\u0141ukasiewicz logic","score":0.45901432633399963},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.44508031010627747},{"id":"https://openalex.org/keywords/monoidal-t-norm-logic","display_name":"Monoidal t-norm logic","score":0.4449057877063751},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4443337619304657},{"id":"https://openalex.org/keywords/t-norm-fuzzy-logics","display_name":"T-norm fuzzy logics","score":0.4364001154899597},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3937148451805115},{"id":"https://openalex.org/keywords/intermediate-logic","display_name":"Intermediate logic","score":0.2945077419281006},{"id":"https://openalex.org/keywords/quantum-computer","display_name":"Quantum computer","score":0.21494123339653015},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.1749705672264099},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.12421455979347229},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.11770999431610107},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.11726900935173035},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09448179602622986},{"id":"https://openalex.org/keywords/substructural-logic","display_name":"Substructural logic","score":0.08187329769134521}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8012669682502747},{"id":"https://openalex.org/C169460222","wikidata":"https://www.wikidata.org/wiki/Q1206311","display_name":"Quantum logic","level":4,"score":0.7074755430221558},{"id":"https://openalex.org/C2780580338","wikidata":"https://www.wikidata.org/wiki/Q577835","display_name":"Adjunction","level":2,"score":0.5499982237815857},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5018680095672607},{"id":"https://openalex.org/C160131679","wikidata":"https://www.wikidata.org/wiki/Q2462350","display_name":"Kripke semantics","level":4,"score":0.47542980313301086},{"id":"https://openalex.org/C206321295","wikidata":"https://www.wikidata.org/wiki/Q8080919","display_name":"\u0141ukasiewicz logic","level":5,"score":0.45901432633399963},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.44508031010627747},{"id":"https://openalex.org/C98224912","wikidata":"https://www.wikidata.org/wiki/Q6901647","display_name":"Monoidal t-norm logic","level":5,"score":0.4449057877063751},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4443337619304657},{"id":"https://openalex.org/C86602344","wikidata":"https://www.wikidata.org/wiki/Q7667918","display_name":"T-norm fuzzy logics","level":5,"score":0.4364001154899597},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3937148451805115},{"id":"https://openalex.org/C33203268","wikidata":"https://www.wikidata.org/wiki/Q5361594","display_name":"Intermediate logic","level":3,"score":0.2945077419281006},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.21494123339653015},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.1749705672264099},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.12421455979347229},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.11770999431610107},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.11726900935173035},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09448179602622986},{"id":"https://openalex.org/C144760519","wikidata":"https://www.wikidata.org/wiki/Q839490","display_name":"Substructural logic","level":4,"score":0.08187329769134521},{"id":"https://openalex.org/C5263885","wikidata":"https://www.wikidata.org/wiki/Q1967302","display_name":"Membership function","level":4,"score":0.0},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"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/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.0},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2012/259541","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/259541","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2012/259541.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:jijmms:259541","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/IJMMS/2012/259541.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:0706bda8b64d451cb9376474fa840241","is_oa":true,"landing_page_url":"https://doaj.org/article/0706bda8b64d451cb9376474fa840241","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences, Vol 2012 (2012)","raw_type":"article"},{"id":"mag:2915169533","is_oa":false,"landing_page_url":"https://www.ieice.org/ken/paper/20081205ca7r/eng/","pdf_url":null,"source":{"id":"https://openalex.org/S4306512848","display_name":"IEICE Technical Report; IEICE Tech. Rep.","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"IEICE Technical Report; IEICE Tech. Rep.","raw_type":null}],"best_oa_location":{"id":"doi:10.1155/2012/259541","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/259541","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2012/259541.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1995074720.pdf","grobid_xml":"https://content.openalex.org/works/W1995074720.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W1590218343","https://openalex.org/W1593939129","https://openalex.org/W1963848754","https://openalex.org/W2164741953","https://openalex.org/W2170949105"],"related_works":["https://openalex.org/W4308610738","https://openalex.org/W16267316","https://openalex.org/W4367840777","https://openalex.org/W1578365337","https://openalex.org/W88232665","https://openalex.org/W1968826078","https://openalex.org/W2061319273","https://openalex.org/W2072402123","https://openalex.org/W2482057698","https://openalex.org/W4224275486"],"abstract_inverted_index":{"Morphological":[0],"operators":[1,47,86],"are":[2,109],"generalized":[3],"to":[4,27,53,99,131,152],"lattices":[5,24,117],"as":[6,48,112],"adjunction":[7,50],"pairs":[8],"(Serra,":[9],"1984;":[10],"Ronse,":[11,15],"1990;":[12,16],"Heijmans":[13],"and":[14,36,61,88,119,126,129,136,171],"Heijmans,":[17],"1994).":[18],"In":[19,149],"particular,":[20],"morphology":[21],"for":[22,70,146,159],"set":[23],"is":[25],"applied":[26,98],"analyze":[28],"logics":[29,75,108,169],"through":[30],"Kripke":[31,133],"semantics":[32,134],"(Bloch,":[33],"2002;":[34],"Fujio":[35],"Bloch,":[37,62,89],"2004;":[38,63],"Fujio,":[39,64],"2006).":[40,65],"For":[41],"example,":[42],"a":[43,54,177],"pair":[44],"of":[45,56,68,81,143,156,179],"morphological":[46,82,94,144,157],"an":[49,154],"gives":[51],"rise":[52],"temporalization":[55],"normal":[57],"modal":[58],"logic":[59,72],"(Fujio":[60,87],"Also,":[66],"constructions":[67],"models":[69],"intuitionistic":[71],"or":[73,114],"linear":[74],"can":[76,96],"be":[77,97],"described":[78],"in":[79,167,186],"terms":[80],"interior":[83],"and/or":[84],"closure":[85],"2004).":[90],"This":[91,139],"shows":[92],"that":[93],"analysis":[95,145,158],"various":[100],"non-classical":[101],"logics.":[102,148,188],"On":[103],"the":[104,141,164,180],"other":[105],"hand,":[106],"quantum":[107,147,160,168,187],"algebraically":[110],"formalized":[111],"orhomodular":[113],"modular":[115],"ortho-complemented":[116],"(Birkhoff":[118],"von":[120],"Neumann,":[121],"1936;":[122],"Maeda,":[123],"1980;":[124],"Chiara":[125],"Giuntini,":[127,137,172],"2002),":[128],"shown":[130],"allow":[132],"(Chiara":[135,170],"2002).":[138,173],"suggests":[140],"possibility":[142],"this":[150],"article,":[151],"show":[153],"efficiency":[155],"logic,":[161],"we":[162],"consider":[163],"implication":[165,183],"problem":[166],"We":[174],"will":[175],"give":[176],"comparison":[178],"5":[181],"polynomial":[182],"connectives":[184],"available":[185]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
