{"id":"https://openalex.org/W2089488392","doi":"https://doi.org/10.1080/11663081.1998.10510951","title":"An Algebraic Method to Decide the Deduction Problem in Many-Valued Logics","display_name":"An Algebraic Method to Decide the Deduction Problem in Many-Valued Logics","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W2089488392","doi":"https://doi.org/10.1080/11663081.1998.10510951","mag":"2089488392"},"language":"en","primary_location":{"id":"doi:10.1080/11663081.1998.10510951","is_oa":false,"landing_page_url":"https://doi.org/10.1080/11663081.1998.10510951","pdf_url":null,"source":{"id":"https://openalex.org/S93822064","display_name":"Journal of Applied Non-Classical Logics","issn_l":"1166-3081","issn":["1166-3081","1958-5780"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Non-Classical Logics","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/A5102894562","display_name":"Jinzhao Wu","orcid":"https://orcid.org/0000-0002-0272-7487"},"institutions":[{"id":"https://openalex.org/I149899117","display_name":"Max Planck Society","ror":"https://ror.org/01hhn8329","country_code":"DE","type":"nonprofit","lineage":["https://openalex.org/I149899117"]},{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]},{"id":"https://openalex.org/I4210109712","display_name":"Max Planck Institute for Informatics","ror":"https://ror.org/01w19ak89","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210109712"]}],"countries":["CN","DE"],"is_corresponding":false,"raw_author_name":"Jinzhao Wu","raw_affiliation_strings":["School of Mathematical Sciences, Peking University , Beijing , 100871 , China","Programming Logics, MPI for Informatics, Max Planck Society"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Peking University , Beijing , 100871 , China","institution_ids":["https://openalex.org/I20231570"]},{"raw_affiliation_string":"Programming Logics, MPI for Informatics, Max Planck Society","institution_ids":["https://openalex.org/I4210109712","https://openalex.org/I149899117"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066657313","display_name":"Hong-yan Tan","orcid":null},"institutions":[{"id":"https://openalex.org/I76214153","display_name":"Lanzhou University","ror":"https://ror.org/01mkqqe32","country_code":"CN","type":"education","lineage":["https://openalex.org/I76214153"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongyan Tan","raw_affiliation_strings":["Department of Computer Science , Lanzhou University , Lanzhou , 730000 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science , Lanzhou University , Lanzhou , 730000 , China","institution_ids":["https://openalex.org/I76214153"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024786747","display_name":"Yongli Li","orcid":null},"institutions":[{"id":"https://openalex.org/I76214153","display_name":"Lanzhou University","ror":"https://ror.org/01mkqqe32","country_code":"CN","type":"education","lineage":["https://openalex.org/I76214153"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yongli Li","raw_affiliation_strings":["Department of Computer Science , Lanzhou University , Lanzhou , 730000 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science , Lanzhou University , Lanzhou , 730000 , China","institution_ids":["https://openalex.org/I76214153"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.6498,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.87062511,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"8","issue":"4","first_page":"353","last_page":"360"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9997000098228455,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9997000098228455,"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/T10142","display_name":"Formal Methods in Verification","score":0.9994000196456909,"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":0.9980000257492065,"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":0.7099940776824951},{"id":"https://openalex.org/keywords/propositional-calculus","display_name":"Propositional calculus","score":0.6679495573043823},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.614269495010376},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4988977909088135},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.441177099943161},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4324072003364563},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4273136258125305},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4192828834056854},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35591262578964233},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.21050405502319336},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2048826515674591},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.05871838331222534}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7099940776824951},{"id":"https://openalex.org/C69562738","wikidata":"https://www.wikidata.org/wiki/Q200694","display_name":"Propositional calculus","level":2,"score":0.6679495573043823},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.614269495010376},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4988977909088135},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.441177099943161},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4324072003364563},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4273136258125305},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4192828834056854},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35591262578964233},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.21050405502319336},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2048826515674591},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.05871838331222534},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"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":3,"locations":[{"id":"doi:10.1080/11663081.1998.10510951","is_oa":false,"landing_page_url":"https://doi.org/10.1080/11663081.1998.10510951","pdf_url":null,"source":{"id":"https://openalex.org/S93822064","display_name":"Journal of Applied Non-Classical Logics","issn_l":"1166-3081","issn":["1166-3081","1958-5780"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Non-Classical Logics","raw_type":"journal-article"},{"id":"pmh:oai:edoc.mpg.de:519666","is_oa":false,"landing_page_url":"http://edoc.mpg.de/519666","pdf_url":null,"source":{"id":"https://openalex.org/S4406922265","display_name":"Max Planck Institute for Plasma Physics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Non-Classical Logics, v.8, 353-360 (1998)","raw_type":"Article"},{"id":"pmh:oai:pure.mpg.de:item_1331395","is_oa":false,"landing_page_url":"http://hdl.handle.net/11858/00-001M-0000-000F-3813-C","pdf_url":null,"source":{"id":"https://openalex.org/S4306400654","display_name":"MPG.PuRe (Max Planck Society)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149899117","host_organization_name":"Max Planck Society","host_organization_lineage":["https://openalex.org/I149899117"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Non-Classical Logics","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W61450922","https://openalex.org/W1483568252","https://openalex.org/W1577951736","https://openalex.org/W2017890624","https://openalex.org/W2019751493","https://openalex.org/W4388218653"],"related_works":["https://openalex.org/W2032233321","https://openalex.org/W3121970507","https://openalex.org/W2110028391","https://openalex.org/W54497855","https://openalex.org/W217960748","https://openalex.org/W3125814499","https://openalex.org/W2090827041","https://openalex.org/W2094012830","https://openalex.org/W187246281","https://openalex.org/W2079194830"],"abstract_inverted_index":{"ABSTRACT":[0],"We":[1],"show":[2],"that":[3],"there":[4],"is":[5,63],"a":[6,19,26,33,47],"polynomial":[7,48],"over":[8],"the":[9],"rational":[10],"number":[11],"field":[12],"corresponding":[13],"to":[14,44],"each":[15],"propositional":[16,27],"formula":[17,28],"in":[18],"given":[20],"many-valued":[21],"logic.":[22],"To":[23],"decide":[24,45],"whether":[25,46],"can":[29],"be":[30],"deduced":[31],"from":[32],"finite":[34],"set":[35],"of":[36],"such":[37],"formulas":[38],"(deduction":[39],"problem),":[40],"we":[41],"only":[42],"need":[43],"vanishes":[49],"on":[50],"an":[51,58],"algebraic":[52],"variety.":[53],"By":[54],"using":[55],"Wu's":[56],"method,":[57],"algorithm":[59],"for":[60],"this":[61],"problem":[62],"presented.":[64]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
