{"id":"https://openalex.org/W2037678188","doi":"https://doi.org/10.1305/ndjfl/1107220676","title":"The Expressive Unary Truth Functions of n-valued Logic","display_name":"The Expressive Unary Truth Functions of n-valued Logic","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2037678188","doi":"https://doi.org/10.1305/ndjfl/1107220676","mag":"2037678188"},"language":"en","primary_location":{"id":"doi:10.1305/ndjfl/1107220676","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1107220676","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-46/issue-1/The-Expressive-Unary-Truth-Functions-of-n-valued-Logic/10.1305/ndjfl/1107220676.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-46/issue-1/The-Expressive-Unary-Truth-Functions-of-n-valued-Logic/10.1305/ndjfl/1107220676.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064440308","display_name":"Stephen Pollard","orcid":"https://orcid.org/0000-0002-0292-2928"},"institutions":[{"id":"https://openalex.org/I199639920","display_name":"Truman State University","ror":"https://ror.org/0396bvs97","country_code":"US","type":"education","lineage":["https://openalex.org/I199639920"]},{"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"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Stephen Pollard","raw_affiliation_strings":["Division of Social Science Truman State University Kirksville MO 63501","University of Notre Dame"],"affiliations":[{"raw_affiliation_string":"Division of Social Science Truman State University Kirksville MO 63501","institution_ids":["https://openalex.org/I199639920"]},{"raw_affiliation_string":"University of Notre Dame","institution_ids":["https://openalex.org/I107639228"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5064440308"],"corresponding_institution_ids":["https://openalex.org/I107639228","https://openalex.org/I199639920"],"apc_list":null,"apc_paid":null,"fwci":0.35008268,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.57743623,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"46","issue":"1","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":0.9936000108718872,"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":0.9936000108718872,"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":0.9478999972343445,"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":0.9101999998092651,"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/unary-operation","display_name":"Unary operation","score":0.9377893209457397},{"id":"https://openalex.org/keywords/truth-function","display_name":"Truth function","score":0.8894332647323608},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.5873674154281616},{"id":"https://openalex.org/keywords/truth-value","display_name":"Truth value","score":0.5201523900032043},{"id":"https://openalex.org/keywords/intermediate-logic","display_name":"Intermediate logic","score":0.49036478996276855},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49006974697113037},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38804492354393005},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36831918358802795},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.30035966634750366},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.23770827054977417},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.2333914041519165}],"concepts":[{"id":"https://openalex.org/C78023250","wikidata":"https://www.wikidata.org/wiki/Q657596","display_name":"Unary operation","level":2,"score":0.9377893209457397},{"id":"https://openalex.org/C37754750","wikidata":"https://www.wikidata.org/wiki/Q913874","display_name":"Truth function","level":3,"score":0.8894332647323608},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.5873674154281616},{"id":"https://openalex.org/C46274116","wikidata":"https://www.wikidata.org/wiki/Q185521","display_name":"Truth value","level":2,"score":0.5201523900032043},{"id":"https://openalex.org/C33203268","wikidata":"https://www.wikidata.org/wiki/Q5361594","display_name":"Intermediate logic","level":3,"score":0.49036478996276855},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49006974697113037},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38804492354393005},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36831918358802795},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.30035966634750366},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.23770827054977417},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.2333914041519165},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1305/ndjfl/1107220676","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1107220676","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-46/issue-1/The-Expressive-Unary-Truth-Functions-of-n-valued-Logic/10.1305/ndjfl/1107220676.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/1107220676","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.ndjfl/1107220676","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/1107220676","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1107220676","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-46/issue-1/The-Expressive-Unary-Truth-Functions-of-n-valued-Logic/10.1305/ndjfl/1107220676.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":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.550000011920929}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2037678188.pdf","grobid_xml":"https://content.openalex.org/works/W2037678188.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W1490829364","https://openalex.org/W1547615865","https://openalex.org/W1984210212","https://openalex.org/W2020989430","https://openalex.org/W2023254732","https://openalex.org/W2059362200","https://openalex.org/W2313326893"],"related_works":["https://openalex.org/W2116215193","https://openalex.org/W2037678188","https://openalex.org/W2145181205","https://openalex.org/W2020097426","https://openalex.org/W2391208245","https://openalex.org/W2356894535","https://openalex.org/W2348536727","https://openalex.org/W2347850088","https://openalex.org/W2355076697","https://openalex.org/W2792126174"],"abstract_inverted_index":{"The":[0],"expressive":[1,19],"truth":[2,20],"functions":[3,21,31],"of":[4,16,22],"two-valued":[5],"logic":[6,24],"have":[7,32],"all":[8],"been":[9],"identified.":[10],"This":[11],"paper":[12],"begins":[13],"the":[14,18,27],"task":[15],"identifying":[17],"n-valued":[23],"by":[25],"characterizing":[26],"unary":[28],"ones.":[29],"These":[30],"distinctive":[33],"algebraic,":[34],"semantic,":[35],"and":[36],"closure-theoretic":[37],"properties.":[38]},"counts_by_year":[{"year":2014,"cited_by_count":1}],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}
