{"id":"https://openalex.org/W2276796001","doi":"https://doi.org/10.1093/logcom/exv038","title":"Four-valued modal logic: Kripke semantics and duality","display_name":"Four-valued modal logic: Kripke semantics and duality","publication_year":2015,"publication_date":"2015-06-15","ids":{"openalex":"https://openalex.org/W2276796001","doi":"https://doi.org/10.1093/logcom/exv038","mag":"2276796001"},"language":"en","primary_location":{"id":"doi:10.1093/logcom/exv038","is_oa":false,"landing_page_url":"https://doi.org/10.1093/logcom/exv038","pdf_url":null,"source":{"id":"https://openalex.org/S47057106","display_name":"Journal of Logic and Computation","issn_l":"0955-792X","issn":["0955-792X","1465-363X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Logic and Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://research.birmingham.ac.uk/en/publications/2d16f5f2-33cf-41fd-a790-4a5cbe6c2ac5","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008197317","display_name":"Umberto Rivieccio","orcid":"https://orcid.org/0000-0003-1364-5003"},"institutions":[{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Umberto Rivieccio","raw_affiliation_strings":["Faculty of Technology, Policy and Management, Delft University of Technology, Delft, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Faculty of Technology, Policy and Management, Delft University of Technology, Delft, The Netherlands","institution_ids":["https://openalex.org/I98358874"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112275796","display_name":"Achim Jung","orcid":null},"institutions":[{"id":"https://openalex.org/I79619799","display_name":"University of Birmingham","ror":"https://ror.org/03angcq70","country_code":"GB","type":"education","lineage":["https://openalex.org/I79619799"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Achim Jung","raw_affiliation_strings":["School of Computer Science, University of Birmingham, Edgbaston, Birmingham, United Kingdom"],"affiliations":[{"raw_affiliation_string":"School of Computer Science, University of Birmingham, Edgbaston, Birmingham, United Kingdom","institution_ids":["https://openalex.org/I79619799"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076924750","display_name":"Ram\u00f3n Jansana","orcid":"https://orcid.org/0000-0003-4191-5699"},"institutions":[{"id":"https://openalex.org/I71999127","display_name":"Universitat de Barcelona","ror":"https://ror.org/021018s57","country_code":"ES","type":"education","lineage":["https://openalex.org/I71999127"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Ramon Jansana","raw_affiliation_strings":["Department of Logic, History and Philosophy of Science, University of Barcelona, Barcelona, Spain"],"affiliations":[{"raw_affiliation_string":"Department of Logic, History and Philosophy of Science, University of Barcelona, Barcelona, Spain","institution_ids":["https://openalex.org/I71999127"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5008197317"],"corresponding_institution_ids":["https://openalex.org/I98358874"],"apc_list":{"value":4151,"currency":"USD","value_usd":4151},"apc_paid":null,"fwci":2.8041,"has_fulltext":false,"cited_by_count":45,"citation_normalized_percentile":{"value":0.91304205,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"27","issue":"1","first_page":"155","last_page":"199"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9983999729156494,"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":0.991599977016449,"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/modal-logic","display_name":"Modal logic","score":0.730280876159668},{"id":"https://openalex.org/keywords/accessibility-relation","display_name":"Accessibility relation","score":0.6975399255752563},{"id":"https://openalex.org/keywords/normal-modal-logic","display_name":"Normal modal logic","score":0.6726398468017578},{"id":"https://openalex.org/keywords/multimodal-logic","display_name":"Multimodal logic","score":0.6659572720527649},{"id":"https://openalex.org/keywords/algebraic-semantics","display_name":"Algebraic semantics","score":0.6210678815841675},{"id":"https://openalex.org/keywords/s5","display_name":"S5","score":0.5868257880210876},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5832033157348633},{"id":"https://openalex.org/keywords/kripke-semantics","display_name":"Kripke semantics","score":0.5668050050735474},{"id":"https://openalex.org/keywords/dynamic-logic","display_name":"Dynamic logic (digital electronics)","score":0.5587418079376221},{"id":"https://openalex.org/keywords/modal-\u03bc-calculus","display_name":"Modal \u03bc-calculus","score":0.5527054667472839},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5221403241157532},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.5196646451950073},{"id":"https://openalex.org/keywords/intermediate-logic","display_name":"Intermediate logic","score":0.4400986433029175},{"id":"https://openalex.org/keywords/modal","display_name":"Modal","score":0.35837456583976746},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.3061317205429077},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2866908311843872},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2683719992637634},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.22657451033592224},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.18166294693946838},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0674588680267334}],"concepts":[{"id":"https://openalex.org/C27508121","wikidata":"https://www.wikidata.org/wiki/Q210841","display_name":"Modal logic","level":3,"score":0.730280876159668},{"id":"https://openalex.org/C11191006","wikidata":"https://www.wikidata.org/wiki/Q2663311","display_name":"Accessibility relation","level":4,"score":0.6975399255752563},{"id":"https://openalex.org/C114092440","wikidata":"https://www.wikidata.org/wiki/Q840226","display_name":"Normal modal logic","level":4,"score":0.6726398468017578},{"id":"https://openalex.org/C203659156","wikidata":"https://www.wikidata.org/wiki/Q6934805","display_name":"Multimodal logic","level":3,"score":0.6659572720527649},{"id":"https://openalex.org/C2779729104","wikidata":"https://www.wikidata.org/wiki/Q4724013","display_name":"Algebraic semantics","level":3,"score":0.6210678815841675},{"id":"https://openalex.org/C192609573","wikidata":"https://www.wikidata.org/wiki/Q7388341","display_name":"S5","level":5,"score":0.5868257880210876},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5832033157348633},{"id":"https://openalex.org/C160131679","wikidata":"https://www.wikidata.org/wiki/Q2462350","display_name":"Kripke semantics","level":4,"score":0.5668050050735474},{"id":"https://openalex.org/C2777796570","wikidata":"https://www.wikidata.org/wiki/Q2351326","display_name":"Dynamic logic (digital electronics)","level":4,"score":0.5587418079376221},{"id":"https://openalex.org/C173125200","wikidata":"https://www.wikidata.org/wiki/Q5275729","display_name":"Modal \u03bc-calculus","level":5,"score":0.5527054667472839},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5221403241157532},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.5196646451950073},{"id":"https://openalex.org/C33203268","wikidata":"https://www.wikidata.org/wiki/Q5361594","display_name":"Intermediate logic","level":3,"score":0.4400986433029175},{"id":"https://openalex.org/C71139939","wikidata":"https://www.wikidata.org/wiki/Q910194","display_name":"Modal","level":2,"score":0.35837456583976746},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.3061317205429077},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2866908311843872},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2683719992637634},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.22657451033592224},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.18166294693946838},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0674588680267334},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C172385210","wikidata":"https://www.wikidata.org/wiki/Q5339","display_name":"Transistor","level":3,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1093/logcom/exv038","is_oa":false,"landing_page_url":"https://doi.org/10.1093/logcom/exv038","pdf_url":null,"source":{"id":"https://openalex.org/S47057106","display_name":"Journal of Logic and Computation","issn_l":"0955-792X","issn":["0955-792X","1465-363X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Logic and Computation","raw_type":"journal-article"},{"id":"pmh:oai:open-archive.highwire.org:logcom:27/1/155","is_oa":false,"landing_page_url":"http://logcom.oxfordjournals.org/cgi/content/short/27/1/155","pdf_url":null,"source":{"id":"https://openalex.org/S4406923041","display_name":"HighWire Press Open Archive","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":"","raw_type":"TEXT"},{"id":"pmh:oai:pure.atira.dk:Publications/2d16f5f2-33cf-41fd-a790-4a5cbe6c2ac5","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306402634","display_name":"University of Birmingham Research Portal (University of Birmingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79619799","host_organization_name":"University of Birmingham","host_organization_lineage":["https://openalex.org/I79619799"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/2d16f5f2-33cf-41fd-a790-4a5cbe6c2ac5","is_oa":true,"landing_page_url":"https://research.birmingham.ac.uk/en/publications/2d16f5f2-33cf-41fd-a790-4a5cbe6c2ac5","pdf_url":null,"source":{"id":"https://openalex.org/S4306402634","display_name":"University of Birmingham Research Portal (University of Birmingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79619799","host_organization_name":"University of Birmingham","host_organization_lineage":["https://openalex.org/I79619799"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Rivieccio, U, Jung, A & Jansana, R 2015, 'Four-valued modal logic: Kripke semantics and duality', Journal of Logic and Computation. https://doi.org/10.1093/logcom/exv038","raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/2d16f5f2-33cf-41fd-a790-4a5cbe6c2ac5","is_oa":true,"landing_page_url":"https://research.birmingham.ac.uk/en/publications/2d16f5f2-33cf-41fd-a790-4a5cbe6c2ac5","pdf_url":null,"source":{"id":"https://openalex.org/S4306402634","display_name":"University of Birmingham Research Portal (University of Birmingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79619799","host_organization_name":"University of Birmingham","host_organization_lineage":["https://openalex.org/I79619799"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Rivieccio, U, Jung, A & Jansana, R 2015, 'Four-valued modal logic: Kripke semantics and duality', Journal of Logic and Computation. https://doi.org/10.1093/logcom/exv038","raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W26682242","https://openalex.org/W130537534","https://openalex.org/W1487409515","https://openalex.org/W1503075583","https://openalex.org/W1602405256","https://openalex.org/W1603162778","https://openalex.org/W1650095214","https://openalex.org/W1964591144","https://openalex.org/W1969724379","https://openalex.org/W1979275301","https://openalex.org/W1992888677","https://openalex.org/W2001805670","https://openalex.org/W2004776947","https://openalex.org/W2007853381","https://openalex.org/W2023812928","https://openalex.org/W2027379370","https://openalex.org/W2028965700","https://openalex.org/W2029455106","https://openalex.org/W2038185098","https://openalex.org/W2039232530","https://openalex.org/W2041418362","https://openalex.org/W2043835012","https://openalex.org/W2055054170","https://openalex.org/W2069762673","https://openalex.org/W2071180427","https://openalex.org/W2077395144","https://openalex.org/W2090633591","https://openalex.org/W2117459082","https://openalex.org/W2138601456","https://openalex.org/W2150425213","https://openalex.org/W2153536416","https://openalex.org/W2169921622","https://openalex.org/W2286396437","https://openalex.org/W2914384061","https://openalex.org/W4211144022","https://openalex.org/W4251158426","https://openalex.org/W4251538115","https://openalex.org/W4252113473","https://openalex.org/W4388311772","https://openalex.org/W6660028835"],"related_works":["https://openalex.org/W2077061463","https://openalex.org/W2101793126","https://openalex.org/W2278216746","https://openalex.org/W102788636","https://openalex.org/W2352549085","https://openalex.org/W2766759918","https://openalex.org/W2910112965","https://openalex.org/W2554822349","https://openalex.org/W2276796001","https://openalex.org/W1527720545"],"abstract_inverted_index":{"We":[0,59],"introduce":[1],"a":[2],"family":[3],"of":[4,7,41,55,64,73,89],"modal":[5,29,46,93],"expansions":[6],"Belnap\u2013Dunn":[8],"four-valued":[9,92],"logic":[10,23,47,94],"and":[11,14,25,31,53,86,100],"related":[12],"systems,":[13,66],"interpret":[15],"them":[16,68],"in":[17],"many-valued":[18],"Kripke":[19],"structures.":[20],"Using":[21],"algebraic":[22,62,71],"techniques":[24],"topological":[26],"duality":[27],"for":[28],"algebras,":[30],"generalizing":[32],"the":[33,44,49,61,70,90,96],"so-called":[34],"twist-structure":[35],"representation,":[36],"we":[37],"axiomatize":[38],"by":[39],"means":[40],"Hilbert-style":[42],"calculi":[43],"least":[45,91],"over":[48],"four-element":[50],"Belnap":[51],"lattice":[52],"some":[54],"its":[56],"axiomatic":[57],"extensions.":[58],"study":[60],"models":[63],"these":[65],"relating":[67],"to":[69,81],"semantics":[72],"classical":[74],"multi-modal":[75],"logic.":[76],"This":[77],"link":[78],"allows":[79],"us":[80],"prove":[82],"that":[83],"both":[84],"local":[85],"global":[87],"consequence":[88],"enjoy":[95],"finite":[97],"model":[98],"property":[99],"are":[101],"therefore":[102],"decidable.":[103]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
