{"id":"https://openalex.org/W2040640762","doi":"https://doi.org/10.1145/2817825","title":"On the Decidability of Elementary Modal Logics","display_name":"On the Decidability of Elementary Modal Logics","publication_year":2015,"publication_date":"2015-09-23","ids":{"openalex":"https://openalex.org/W2040640762","doi":"https://doi.org/10.1145/2817825","mag":"2040640762"},"language":"en","primary_location":{"id":"doi:10.1145/2817825","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2817825","pdf_url":null,"source":{"id":"https://openalex.org/S117153874","display_name":"ACM Transactions on Computational Logic","issn_l":"1529-3785","issn":["1529-3785","1557-945X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Computational 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/A5015610041","display_name":"Jakub Michaliszyn","orcid":"https://orcid.org/0000-0002-5053-0347"},"institutions":[{"id":"https://openalex.org/I219388962","display_name":"University of Wroc\u0142aw","ror":"https://ror.org/00yae6e25","country_code":"PL","type":"education","lineage":["https://openalex.org/I219388962"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Jakub Michaliszyn","raw_affiliation_strings":["Imperial College London and University of Wroc\u0142aw, Wroc\u0142aw, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Imperial College London and University of Wroc\u0142aw, Wroc\u0142aw, Poland","institution_ids":["https://openalex.org/I219388962"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089075636","display_name":"Jan Otop","orcid":"https://orcid.org/0000-0002-8804-8011"},"institutions":[{"id":"https://openalex.org/I157556583","display_name":"Institute of Science and Technology Austria","ror":"https://ror.org/03gnh5541","country_code":"AT","type":"education","lineage":["https://openalex.org/I157556583"]},{"id":"https://openalex.org/I219388962","display_name":"University of Wroc\u0142aw","ror":"https://ror.org/00yae6e25","country_code":"PL","type":"education","lineage":["https://openalex.org/I219388962"]}],"countries":["AT","PL"],"is_corresponding":false,"raw_author_name":"Jan Otop","raw_affiliation_strings":["IST Austria and University of Wroc\u0142aw, Wroc\u0142aw, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IST Austria and University of Wroc\u0142aw, Wroc\u0142aw, Poland","institution_ids":["https://openalex.org/I219388962","https://openalex.org/I157556583"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090488658","display_name":"Emanuel Kiero\u0144ski","orcid":"https://orcid.org/0000-0002-8538-8221"},"institutions":[{"id":"https://openalex.org/I219388962","display_name":"University of Wroc\u0142aw","ror":"https://ror.org/00yae6e25","country_code":"PL","type":"education","lineage":["https://openalex.org/I219388962"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Emanuel Kiero\u0144ski","raw_affiliation_strings":["University of Wroc\u0142aw, Wroc\u0142aw, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Wroc\u0142aw, Wroc\u0142aw, Poland","institution_ids":["https://openalex.org/I219388962"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4452,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.76799853,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"17","issue":"1","first_page":"1","last_page":"47"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9962000250816345,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9962000250816345,"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/T11567","display_name":"semigroups and automata theory","score":0.9951000213623047,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9933000206947327,"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/decidability","display_name":"Decidability","score":0.8559802770614624},{"id":"https://openalex.org/keywords/satisfiability","display_name":"Satisfiability","score":0.7977659702301025},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7673614025115967},{"id":"https://openalex.org/keywords/undecidable-problem","display_name":"Undecidable problem","score":0.7156178951263428},{"id":"https://openalex.org/keywords/modal-logic","display_name":"Modal logic","score":0.6327919960021973},{"id":"https://openalex.org/keywords/normal-modal-logic","display_name":"Normal modal logic","score":0.6298068761825562},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5740478038787842},{"id":"https://openalex.org/keywords/boolean-satisfiability-problem","display_name":"Boolean satisfiability problem","score":0.520107626914978},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4229475259780884},{"id":"https://openalex.org/keywords/dynamic-logic","display_name":"Dynamic logic (digital electronics)","score":0.41273033618927},{"id":"https://openalex.org/keywords/horn-clause","display_name":"Horn clause","score":0.41168704628944397},{"id":"https://openalex.org/keywords/modal","display_name":"Modal","score":0.372717022895813},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14854559302330017},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.11874446272850037},{"id":"https://openalex.org/keywords/logic-programming","display_name":"Logic programming","score":0.09603515267372131}],"concepts":[{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.8559802770614624},{"id":"https://openalex.org/C168773769","wikidata":"https://www.wikidata.org/wiki/Q1350299","display_name":"Satisfiability","level":2,"score":0.7977659702301025},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7673614025115967},{"id":"https://openalex.org/C192034797","wikidata":"https://www.wikidata.org/wiki/Q3502995","display_name":"Undecidable problem","level":3,"score":0.7156178951263428},{"id":"https://openalex.org/C27508121","wikidata":"https://www.wikidata.org/wiki/Q210841","display_name":"Modal logic","level":3,"score":0.6327919960021973},{"id":"https://openalex.org/C114092440","wikidata":"https://www.wikidata.org/wiki/Q840226","display_name":"Normal modal logic","level":4,"score":0.6298068761825562},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5740478038787842},{"id":"https://openalex.org/C6943359","wikidata":"https://www.wikidata.org/wiki/Q875276","display_name":"Boolean satisfiability problem","level":2,"score":0.520107626914978},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4229475259780884},{"id":"https://openalex.org/C2777796570","wikidata":"https://www.wikidata.org/wiki/Q2351326","display_name":"Dynamic logic (digital electronics)","level":4,"score":0.41273033618927},{"id":"https://openalex.org/C189790780","wikidata":"https://www.wikidata.org/wiki/Q933932","display_name":"Horn clause","level":3,"score":0.41168704628944397},{"id":"https://openalex.org/C71139939","wikidata":"https://www.wikidata.org/wiki/Q910194","display_name":"Modal","level":2,"score":0.372717022895813},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14854559302330017},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.11874446272850037},{"id":"https://openalex.org/C128838566","wikidata":"https://www.wikidata.org/wiki/Q275603","display_name":"Logic programming","level":2,"score":0.09603515267372131},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2817825","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2817825","pdf_url":null,"source":{"id":"https://openalex.org/S117153874","display_name":"ACM Transactions on Computational Logic","issn_l":"1529-3785","issn":["1529-3785","1557-945X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Computational Logic","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W9225573","https://openalex.org/W352853685","https://openalex.org/W1483892218","https://openalex.org/W1488636480","https://openalex.org/W1527720545","https://openalex.org/W1608125757","https://openalex.org/W1982129592","https://openalex.org/W1986667059","https://openalex.org/W1997817571","https://openalex.org/W2008070102","https://openalex.org/W2017025480","https://openalex.org/W2017112542","https://openalex.org/W2018462672","https://openalex.org/W2073491323","https://openalex.org/W2086470346","https://openalex.org/W2099081288","https://openalex.org/W2104419987","https://openalex.org/W2161518325","https://openalex.org/W2166108892","https://openalex.org/W2246583867","https://openalex.org/W2404506531","https://openalex.org/W2610670723","https://openalex.org/W2914576081","https://openalex.org/W3121437753","https://openalex.org/W4206871748"],"related_works":["https://openalex.org/W2398566420","https://openalex.org/W2057232741","https://openalex.org/W2028452607","https://openalex.org/W1498755214","https://openalex.org/W176661328","https://openalex.org/W3108798275","https://openalex.org/W2260113151","https://openalex.org/W3126675290","https://openalex.org/W2795425183","https://openalex.org/W1550258874"],"abstract_inverted_index":{"We":[0,14,35,88],"consider":[1,139],"the":[2,16,46,49,59,92,108,127,140],"satisfiability":[3,51,66,76,94,141],"problem":[4,95,142],"for":[5,58,96],"modal":[6,24,97,133],"logic":[7,25,98,134,145],"over":[8,28,99,131,146],"first-order":[9],"definable":[10,30,101,148],"classes":[11,29,102,149],"of":[12,40,48,62,103,114,129,143,150],"frames.":[13],"confirm":[15],"conjecture":[17],"from":[18],"Hemaspaandra":[19],"and":[20,74,152],"Schnoor":[21],"[2008]":[22],"that":[23,56,91],"is":[26,67,77,105,135],"decidable":[27],"by":[31],"universal":[32,123],"Horn":[33,41,100,147],"formulae.":[34],"provide":[36],"a":[37,121,155],"full":[38],"classification":[39],"formulae":[42],"with":[43],"respect":[44],"to":[45,158],"complexity":[47],"corresponding":[50],"problem.":[52],"It":[53],"turns":[54],"out,":[55],"except":[57],"trivial":[60],"case":[61],"inconsistent":[63],"formulae,":[64],"local":[65],"either":[68],"NP-complete":[69],"or":[70,82],"PS":[71,79],"pace":[72,80],"-complete,":[73,81],"global":[75],"NP-complete,":[78],"E":[83],"xp":[84],"T":[85],"ime":[86],"-complete.":[87],"also":[89,153],"show":[90,112],"finite":[93],"frames":[104,130],"decidable.":[106],"On":[107],"negative":[109],"side,":[110],"we":[111,119,138],"undecidability":[113],"two":[115],"related":[116],"problems.":[117],"First,":[118],"exhibit":[120],"simple":[122],"three-variable":[124],"formula":[125,156],"defining":[126],"class":[128],"which":[132],"undecidable.":[136],"Second,":[137],"bimodal":[144],"frames,":[151],"present":[154],"leading":[157],"undecidability.":[159]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
