{"id":"https://openalex.org/W2016676818","doi":"https://doi.org/10.2307/2267133","title":"Axiom schemes for m-valued functional calculi of first order. Part I. Definition of axiom schemes and proof of plausibility","display_name":"Axiom schemes for m-valued functional calculi of first order. Part I. Definition of axiom schemes and proof of plausibility","publication_year":1948,"publication_date":"1948-12-01","ids":{"openalex":"https://openalex.org/W2016676818","doi":"https://doi.org/10.2307/2267133","mag":"2016676818"},"language":"en","primary_location":{"id":"doi:10.2307/2267133","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2267133","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/A5112814928","display_name":"J. Barkley Rosser","orcid":null},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]},{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. B. Rosser","raw_affiliation_strings":["Cornell University and University of Illinois"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Cornell University and University of Illinois","institution_ids":["https://openalex.org/I157725225","https://openalex.org/I205783295"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000783137","display_name":"A. R. Turquette","orcid":null},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]},{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"A. R. Turquette","raw_affiliation_strings":["Cornell University and University of Illinois"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Cornell University and University of Illinois","institution_ids":["https://openalex.org/I157725225","https://openalex.org/I205783295"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3550,"currency":"USD","value_usd":3550},"apc_paid":null,"fwci":3.1794,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.89945862,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"13","issue":"4","first_page":"177","last_page":"192"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.963100016117096,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.963100016117096,"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":0.9442999958992004,"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/T11106","display_name":"Data Management and Algorithms","score":0.9199000000953674,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/axiom","display_name":"Axiom","score":0.7435628175735474},{"id":"https://openalex.org/keywords/truth-function","display_name":"Truth function","score":0.7015950679779053},{"id":"https://openalex.org/keywords/truth-value","display_name":"Truth value","score":0.603935956954956},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5523322224617004},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.5083701014518738},{"id":"https://openalex.org/keywords/axiom-of-choice","display_name":"Axiom of choice","score":0.46320831775665283},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.43221503496170044},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3312067985534668},{"id":"https://openalex.org/keywords/set-theory","display_name":"Set theory","score":0.1547570824623108},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.12407734990119934},{"id":"https://openalex.org/keywords/propositional-calculus","display_name":"Propositional calculus","score":0.10363394021987915}],"concepts":[{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.7435628175735474},{"id":"https://openalex.org/C37754750","wikidata":"https://www.wikidata.org/wiki/Q913874","display_name":"Truth function","level":3,"score":0.7015950679779053},{"id":"https://openalex.org/C46274116","wikidata":"https://www.wikidata.org/wiki/Q185521","display_name":"Truth value","level":2,"score":0.603935956954956},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5523322224617004},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.5083701014518738},{"id":"https://openalex.org/C151797676","wikidata":"https://www.wikidata.org/wiki/Q179692","display_name":"Axiom of choice","level":4,"score":0.46320831775665283},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43221503496170044},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3312067985534668},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.1547570824623108},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.12407734990119934},{"id":"https://openalex.org/C69562738","wikidata":"https://www.wikidata.org/wiki/Q200694","display_name":"Propositional calculus","level":2,"score":0.10363394021987915},{"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/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2307/2267133","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2267133","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"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.46000000834465027,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":1,"referenced_works":["https://openalex.org/W2320688134"],"related_works":["https://openalex.org/W2116215193","https://openalex.org/W1745965678","https://openalex.org/W2145181205","https://openalex.org/W150180408","https://openalex.org/W4386544825","https://openalex.org/W4236665418","https://openalex.org/W2028283249","https://openalex.org/W2133220150","https://openalex.org/W2124620155","https://openalex.org/W2369394266"],"abstract_inverted_index":{"A":[0],"calculus,":[1],"or":[2],"its":[3,8],"formalization,":[4],"is":[5,21,43],"m-valued":[6],"when":[7],"truth-functions":[9],"are":[10,29,34,39,73,81,104],"allowed":[11],"to":[12,23,88],"take":[13,56],"truth-values":[14,27,58,69,77],"ranging":[15],"from":[16],"1":[17],"through":[18],"m.":[19],"It":[20],"customary":[22],"divide":[24],"the":[25,68,76,89],"m":[26,80],"that":[28,33,38,49,67],"possible":[30],"into":[31],"those":[32,37],"\u201cdesignated\u201d":[35],"and":[36,52,75],"\u201cundesignated.\u201d":[40],"Furthermore,":[41],"it":[42],"usually":[44],"desired":[45],"of":[46,91],"a":[47],"formalization":[48],"provable":[50,54],"formulas":[51,55],"only":[53],"designated":[57,74,93],"exclusively.":[59],"For":[60],"our":[61],"present":[62],"purposes,":[63],"we":[64,95],"shall":[65,96],"suppose":[66],"1,":[70],"\u2026,":[71,79],"8":[72],"8+1,":[78],"undesignated.":[82],"When":[83],"calculi":[84],"differ":[85],"in":[86],"respect":[87],"number":[90],"their":[92],"truth-values,":[94],"consider":[97],"them":[98],"different":[99],"calculi,":[100],"even":[101],"if":[102],"they":[103],"otherwise":[105],"similar.":[106]},"counts_by_year":[],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}
