{"id":"https://openalex.org/W2915692292","doi":"https://doi.org/10.1017/s1755020319000121","title":"BELNAP\u2013DUNN MODAL LOGICS: TRUTH CONSTANTS VS. TRUTH VALUES","display_name":"BELNAP\u2013DUNN MODAL LOGICS: TRUTH CONSTANTS VS. TRUTH VALUES","publication_year":2019,"publication_date":"2019-02-22","ids":{"openalex":"https://openalex.org/W2915692292","doi":"https://doi.org/10.1017/s1755020319000121","mag":"2915692292"},"language":"en","primary_location":{"id":"doi:10.1017/s1755020319000121","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s1755020319000121","pdf_url":null,"source":{"id":"https://openalex.org/S24077076","display_name":"The Review of Symbolic Logic","issn_l":"1755-0203","issn":["1755-0203","1755-0211"],"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":"The Review 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/A5086810812","display_name":"Sergei P. Odintsov","orcid":"https://orcid.org/0000-0003-3115-1293"},"institutions":[{"id":"https://openalex.org/I4210096862","display_name":"Sobolev Institute of Mathematics","ror":"https://ror.org/00shc0s02","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I1313323035","https://openalex.org/I4210096862","https://openalex.org/I4210124601","https://openalex.org/I4210127387"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"SERGEI P. ODINTSOV","raw_affiliation_strings":["Sobolev Institute of Mathematics"],"affiliations":[{"raw_affiliation_string":"Sobolev Institute of Mathematics","institution_ids":["https://openalex.org/I4210096862"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006401614","display_name":"Stanislav O. Speranski","orcid":"https://orcid.org/0000-0001-6386-5632"},"institutions":[{"id":"https://openalex.org/I172901346","display_name":"St Petersburg University","ror":"https://ror.org/023znxa73","country_code":"RU","type":"education","lineage":["https://openalex.org/I172901346"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"STANISLAV O. SPERANSKI","raw_affiliation_strings":["St. Petersburg State University"],"affiliations":[{"raw_affiliation_string":"St. Petersburg State University","institution_ids":["https://openalex.org/I172901346"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5006401614","https://openalex.org/A5086810812"],"corresponding_institution_ids":["https://openalex.org/I172901346","https://openalex.org/I4210096862"],"apc_list":null,"apc_paid":null,"fwci":1.3989,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.82903142,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"13","issue":"2","first_page":"416","last_page":"435"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9990000128746033,"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":0.9990000128746033,"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":0.9976999759674072,"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":0.98580002784729,"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/truth-value","display_name":"Truth value","score":0.7157230973243713},{"id":"https://openalex.org/keywords/negation","display_name":"Negation","score":0.7045286893844604},{"id":"https://openalex.org/keywords/falsity","display_name":"Falsity","score":0.6912602782249451},{"id":"https://openalex.org/keywords/modal-logic","display_name":"Modal logic","score":0.6524942517280579},{"id":"https://openalex.org/keywords/modal","display_name":"Modal","score":0.5621673464775085},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5276581048965454},{"id":"https://openalex.org/keywords/kripke-semantics","display_name":"Kripke semantics","score":0.5167707204818726},{"id":"https://openalex.org/keywords/accessibility-relation","display_name":"Accessibility relation","score":0.4995243549346924},{"id":"https://openalex.org/keywords/monoidal-t-norm-logic","display_name":"Monoidal t-norm logic","score":0.4572983682155609},{"id":"https://openalex.org/keywords/t-norm-fuzzy-logics","display_name":"T-norm fuzzy logics","score":0.4370567798614502},{"id":"https://openalex.org/keywords/normal-modal-logic","display_name":"Normal modal logic","score":0.41453009843826294},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3815660774707794},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3265228569507599},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32229453325271606},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.26289284229278564},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.19337621331214905},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.13190650939941406},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.07759106159210205}],"concepts":[{"id":"https://openalex.org/C46274116","wikidata":"https://www.wikidata.org/wiki/Q185521","display_name":"Truth value","level":2,"score":0.7157230973243713},{"id":"https://openalex.org/C2185349","wikidata":"https://www.wikidata.org/wiki/Q190558","display_name":"Negation","level":2,"score":0.7045286893844604},{"id":"https://openalex.org/C2777685122","wikidata":"https://www.wikidata.org/wiki/Q170028","display_name":"Falsity","level":2,"score":0.6912602782249451},{"id":"https://openalex.org/C27508121","wikidata":"https://www.wikidata.org/wiki/Q210841","display_name":"Modal logic","level":3,"score":0.6524942517280579},{"id":"https://openalex.org/C71139939","wikidata":"https://www.wikidata.org/wiki/Q910194","display_name":"Modal","level":2,"score":0.5621673464775085},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5276581048965454},{"id":"https://openalex.org/C160131679","wikidata":"https://www.wikidata.org/wiki/Q2462350","display_name":"Kripke semantics","level":4,"score":0.5167707204818726},{"id":"https://openalex.org/C11191006","wikidata":"https://www.wikidata.org/wiki/Q2663311","display_name":"Accessibility relation","level":4,"score":0.4995243549346924},{"id":"https://openalex.org/C98224912","wikidata":"https://www.wikidata.org/wiki/Q6901647","display_name":"Monoidal t-norm logic","level":5,"score":0.4572983682155609},{"id":"https://openalex.org/C86602344","wikidata":"https://www.wikidata.org/wiki/Q7667918","display_name":"T-norm fuzzy logics","level":5,"score":0.4370567798614502},{"id":"https://openalex.org/C114092440","wikidata":"https://www.wikidata.org/wiki/Q840226","display_name":"Normal modal logic","level":4,"score":0.41453009843826294},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3815660774707794},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3265228569507599},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32229453325271606},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.26289284229278564},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.19337621331214905},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.13190650939941406},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.07759106159210205},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.0},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.0},{"id":"https://openalex.org/C188027245","wikidata":"https://www.wikidata.org/wiki/Q750446","display_name":"Polymer chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C5263885","wikidata":"https://www.wikidata.org/wiki/Q1967302","display_name":"Membership function","level":4,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s1755020319000121","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s1755020319000121","pdf_url":null,"source":{"id":"https://openalex.org/S24077076","display_name":"The Review of Symbolic Logic","issn_l":"1755-0203","issn":["1755-0203","1755-0211"],"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":"The Review of Symbolic Logic","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.46000000834465027,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W87187940","https://openalex.org/W641245508","https://openalex.org/W1503075583","https://openalex.org/W1603162778","https://openalex.org/W1985443719","https://openalex.org/W1992888677","https://openalex.org/W1995375207","https://openalex.org/W2000140686","https://openalex.org/W2007838222","https://openalex.org/W2007853381","https://openalex.org/W2027379370","https://openalex.org/W2027816834","https://openalex.org/W2071180427","https://openalex.org/W2102134079","https://openalex.org/W2153536416","https://openalex.org/W2401565604","https://openalex.org/W2407046521","https://openalex.org/W2415383613","https://openalex.org/W2529466265","https://openalex.org/W2557563739","https://openalex.org/W2758805975","https://openalex.org/W4251158426","https://openalex.org/W4251538115","https://openalex.org/W6712933353"],"related_works":["https://openalex.org/W2207182393","https://openalex.org/W2072402123","https://openalex.org/W127748980","https://openalex.org/W1996474321","https://openalex.org/W4287372193","https://openalex.org/W2002969096","https://openalex.org/W369161646","https://openalex.org/W4224275486","https://openalex.org/W1558962892","https://openalex.org/W2002305610"],"abstract_inverted_index":{"Abstract":[0],"We":[1,58],"shall":[2],"be":[3,19,80,118],"concerned":[4],"with":[5],"the":[6,13,25,51,62,89,93,97,110],"modal":[7,28,125],"logic":[8,29],"BK\u2014which":[9],"is":[10],"based":[11],"on":[12],"Belnap\u2013Dunn":[14],"four-valued":[15],"matrix,":[16],"and":[17,42],"can":[18],"viewed":[20],"as":[21,56],"being":[22],"obtained":[23],"from":[24],"least":[26],"normal":[27,124],"K":[30],"by":[31],"adding":[32,83],"\u2018strong":[33],"negation\u2019.":[34],"Though":[35],"all":[36],"four":[37],"values":[38],"\u2018truth\u2019,":[39],"\u2018falsity\u2019,":[40],"\u2018neither\u2019":[41,71],"\u2018both\u2019":[43,73],"are":[44,54],"employed":[45],"in":[46],"its":[47],"Kripke":[48],"semantics,":[49],"only":[50],"first":[52],"two":[53],"expressible":[55],"terms.":[57],"show":[59],"that":[60,121],"expanding":[61],"original":[63],"language":[64],"of":[65,85,91,99,107,113,122],"BK":[66],"to":[67,75,117,120],"include":[68],"constants":[69,87],"for":[70],"or/and":[72],"leads":[74],"quite":[76],"unexpected":[77],"results.":[78],"To":[79],"more":[81],"precise,":[82],"one":[84,104],"these":[86],"has":[88],"effect":[90],"eliminating":[92],"respective":[94],"value":[95],"at":[96],"level":[98],"BK-extensions.":[100],"In":[101],"particular,":[102],"if":[103],"adds":[105],"both":[106],"these,":[108],"then":[109],"corresponding":[111],"lattice":[112],"extensions":[114],"turns":[115],"out":[116],"isomorphic":[119],"ordinary":[123],"logics.":[126]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}