{"id":"https://openalex.org/W2480359299","doi":"https://doi.org/10.1080/11663081.2016.1153930","title":"The logic determined by Smiley\u2019s matrix for Anderson and Belnap\u2019s first-degree entailment logic","display_name":"The logic determined by Smiley\u2019s matrix for Anderson and Belnap\u2019s first-degree entailment logic","publication_year":2016,"publication_date":"2016-01-02","ids":{"openalex":"https://openalex.org/W2480359299","doi":"https://doi.org/10.1080/11663081.2016.1153930","mag":"2480359299"},"language":"en","primary_location":{"id":"doi:10.1080/11663081.2016.1153930","is_oa":false,"landing_page_url":"https://doi.org/10.1080/11663081.2016.1153930","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/A5056276034","display_name":"Jos\u00e9 M. M\u00e9ndez","orcid":"https://orcid.org/0000-0002-9560-3327"},"institutions":[{"id":"https://openalex.org/I184999862","display_name":"Universidad de Salamanca","ror":"https://ror.org/02f40zc51","country_code":"ES","type":"education","lineage":["https://openalex.org/I184999862"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Jos\u00e9 M. M\u00e9ndez","raw_affiliation_strings":["University of Salamanca, Salamanca, Spain"],"affiliations":[{"raw_affiliation_string":"University of Salamanca, Salamanca, Spain","institution_ids":["https://openalex.org/I184999862"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035778877","display_name":"Gemma Robles","orcid":"https://orcid.org/0000-0001-6495-0388"},"institutions":[{"id":"https://openalex.org/I8833935","display_name":"Universidad de Le\u00f3n","ror":"https://ror.org/02tzt0b78","country_code":"ES","type":"education","lineage":["https://openalex.org/I8833935"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Gemma Robles","raw_affiliation_strings":["Department of Psychology, Sociology and Philosophy, University of Le\u00f3n, Le\u00f3n, Spain"],"affiliations":[{"raw_affiliation_string":"Department of Psychology, Sociology and Philosophy, University of Le\u00f3n, Le\u00f3n, Spain","institution_ids":["https://openalex.org/I8833935"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5056276034"],"corresponding_institution_ids":["https://openalex.org/I184999862"],"apc_list":null,"apc_paid":null,"fwci":1.0454,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.79624269,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":97},"biblio":{"volume":"26","issue":"1","first_page":"47","last_page":"68"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9991000294685364,"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":0.9987999796867371,"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/logical-consequence","display_name":"Logical consequence","score":0.6624276041984558},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5613535642623901},{"id":"https://openalex.org/keywords/truth-value","display_name":"Truth value","score":0.5313257575035095},{"id":"https://openalex.org/keywords/paraconsistent-logic","display_name":"Paraconsistent logic","score":0.4940236210823059},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4884032607078552},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.4685576558113098},{"id":"https://openalex.org/keywords/smiley","display_name":"Smiley","score":0.46130993962287903},{"id":"https://openalex.org/keywords/accessibility-relation","display_name":"Accessibility relation","score":0.41296103596687317},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.380281925201416},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3373640775680542},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3285145163536072},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.25399869680404663},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.25093376636505127},{"id":"https://openalex.org/keywords/higher-order-logic","display_name":"Higher-order logic","score":0.23916587233543396},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.22071245312690735},{"id":"https://openalex.org/keywords/multimodal-logic","display_name":"Multimodal logic","score":0.2070850431919098},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.12411409616470337}],"concepts":[{"id":"https://openalex.org/C134752490","wikidata":"https://www.wikidata.org/wiki/Q374182","display_name":"Logical consequence","level":2,"score":0.6624276041984558},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5613535642623901},{"id":"https://openalex.org/C46274116","wikidata":"https://www.wikidata.org/wiki/Q185521","display_name":"Truth value","level":2,"score":0.5313257575035095},{"id":"https://openalex.org/C16796852","wikidata":"https://www.wikidata.org/wiki/Q426592","display_name":"Paraconsistent logic","level":4,"score":0.4940236210823059},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4884032607078552},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4685576558113098},{"id":"https://openalex.org/C2781455918","wikidata":"https://www.wikidata.org/wiki/Q11241","display_name":"Smiley","level":2,"score":0.46130993962287903},{"id":"https://openalex.org/C11191006","wikidata":"https://www.wikidata.org/wiki/Q2663311","display_name":"Accessibility relation","level":4,"score":0.41296103596687317},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.380281925201416},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3373640775680542},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3285145163536072},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.25399869680404663},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.25093376636505127},{"id":"https://openalex.org/C169896238","wikidata":"https://www.wikidata.org/wiki/Q1644136","display_name":"Higher-order logic","level":3,"score":0.23916587233543396},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.22071245312690735},{"id":"https://openalex.org/C203659156","wikidata":"https://www.wikidata.org/wiki/Q6934805","display_name":"Multimodal logic","level":3,"score":0.2070850431919098},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.12411409616470337},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/11663081.2016.1153930","is_oa":false,"landing_page_url":"https://doi.org/10.1080/11663081.2016.1153930","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"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.44999998807907104,"display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G7248430182","display_name":null,"funder_award_id":"FFI2014-53919-P","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"}],"funders":[{"id":"https://openalex.org/F4320321837","display_name":"Ministerio de Econom\u00eda y Competitividad","ror":"https://ror.org/034900433"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1015949428","https://openalex.org/W1487409515","https://openalex.org/W1505359507","https://openalex.org/W1531571632","https://openalex.org/W1559874856","https://openalex.org/W1593617641","https://openalex.org/W1995375207","https://openalex.org/W2005521738","https://openalex.org/W2023605209","https://openalex.org/W2027379370","https://openalex.org/W2050498009","https://openalex.org/W2055800745","https://openalex.org/W2067557144","https://openalex.org/W2076222411","https://openalex.org/W2592837392","https://openalex.org/W2738657924","https://openalex.org/W3128976560"],"related_works":["https://openalex.org/W2179819924","https://openalex.org/W1525107372","https://openalex.org/W1982424558","https://openalex.org/W4245886362","https://openalex.org/W2996981141","https://openalex.org/W1608287","https://openalex.org/W4313642989","https://openalex.org/W4313047649","https://openalex.org/W996997567","https://openalex.org/W2489508701"],"abstract_inverted_index":{"The":[0,32],"aim":[1],"of":[2,16,25,27,37,43,52,72,78,83,95,99,108],"this":[3],"paper":[4],"is":[5,48,61],"to":[6,76],"define":[7],"the":[8,14,22,41,50,96],"logical":[9,73],"system":[10],"Sm4":[11,60,87],"characterised":[12],"by":[13],"degree":[15],"truth-preserving":[17],"consequence":[18],"relation":[19],"defined":[20],"on":[21],"ordered":[23],"set":[24],"values":[26],"Smiley\u2019s":[28],"four-element":[29],"matrix":[30,33],"MSm4.":[31],"MSm4":[34],"has":[35],"been":[36],"considerable":[38],"importance":[39],"in":[40],"development":[42],"relevant":[44],"logics":[45],"and":[46,80],"it":[47],"at":[49],"origin":[51],"bilattice":[53],"logics.":[54],"It":[55],"will":[56],"be":[57,89],"shown":[58],"that":[59,77],"a":[62,69,92,105],"most":[63],"interesting":[64],"paraconsistent":[65],"logic":[66,82],"which":[67],"encloses":[68],"sound":[70],"theory":[71],"necessity":[74],"similar":[75],"Anderson":[79],"Belnap\u2019s":[81],"entailment":[84],"E.":[85],"Intuitively,":[86],"can":[88],"described":[90],"as":[91,104],"four-valued":[93,106],"expansion":[94],"positive":[97],"fragment":[98],"Lewis\u2019":[100],"S5":[101],"or,":[102],"alternatively,":[103],"version":[107],"S5.":[109]},"counts_by_year":[{"year":2023,"cited_by_count":3},{"year":2021,"cited_by_count":3},{"year":2019,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
