{"id":"https://openalex.org/W1986952446","doi":"https://doi.org/10.2307/2266509","title":"On an implication function in many-valued systems of logic","display_name":"On an implication function in many-valued systems of logic","publication_year":1949,"publication_date":"1949-06-23","ids":{"openalex":"https://openalex.org/W1986952446","doi":"https://doi.org/10.2307/2266509","mag":"1986952446"},"language":"en","primary_location":{"id":"doi:10.2307/2266509","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2266509","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","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/A5020287759","display_name":"Zolt\u00e1n Dienes","orcid":"https://orcid.org/0000-0001-7454-3161"},"institutions":[{"id":"https://openalex.org/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Z. P. Dienes","raw_affiliation_strings":["The University of Manchester"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The University of Manchester","institution_ids":["https://openalex.org/I28407311"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5020287759"],"corresponding_institution_ids":["https://openalex.org/I28407311"],"apc_list":{"value":3550,"currency":"USD","value_usd":3550},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":46,"citation_normalized_percentile":{"value":0.08057851,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"14","issue":"2","first_page":"95","last_page":"97"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9890999794006348,"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":0.9890999794006348,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9539999961853027,"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/T10050","display_name":"Multi-Criteria Decision Making","score":0.9211000204086304,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/negation","display_name":"Negation","score":0.8342494964599609},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.7024152278900146},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.531970202922821},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4105977416038513},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3639647364616394},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3307090699672699},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.1297672688961029},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.0882437527179718}],"concepts":[{"id":"https://openalex.org/C2185349","wikidata":"https://www.wikidata.org/wiki/Q190558","display_name":"Negation","level":2,"score":0.8342494964599609},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.7024152278900146},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.531970202922821},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4105977416038513},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3639647364616394},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3307090699672699},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.1297672688961029},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0882437527179718},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"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":2,"locations":[{"id":"doi:10.2307/2266509","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2266509","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1183730617","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183730617","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":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.5400000214576721}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2059922809","https://openalex.org/W2387527986","https://openalex.org/W2479250593","https://openalex.org/W4283261428","https://openalex.org/W2131148043","https://openalex.org/W2092783274","https://openalex.org/W4318829426","https://openalex.org/W4391025849","https://openalex.org/W4384940451","https://openalex.org/W2389908864"],"abstract_inverted_index":{"In":[0,66],"a":[1],"paper":[2],"J.":[3],"\u0141ukasiewicz":[4],"and":[5,27,44,59],"A.":[6],"Tarski":[7],"study":[8],"the":[9,14,28],"systems":[10],"arising":[11],"out":[12],"of":[13],"implication":[15,73],"function":[16,30],"C":[17],"(x,":[18],"y)":[19,26,58],"=":[20,32,52,61,77],"min(1,":[21,53],"1":[22,33,45,54,62],"\u2013":[23,34,55,63],"x":[24,56],"+":[25,57],"negation":[29],"Nx":[31,60],"x,":[35,37],"where":[36],"y":[38],"are":[39],"real":[40],"numbers":[41],"between":[42],"0":[43],"inclusive.":[46],"Let":[47],"us":[48],"then":[49],"write":[50],"\u0421xy":[51],"x.":[64],"(1)":[65],"this":[67],"note":[68],"we":[69],"shall":[70],"consider":[71],"another":[72],"function,":[74],"namely":[75],"\u0421\u2032xy":[76],"\u0421\u0421Nxyy,":[78],"(2)":[79]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}