{"id":"https://openalex.org/W2950450725","doi":"https://doi.org/10.2168/lmcs-2(1:5)2006","title":"Algorithmic correspondence and completeness in modal logic. I. The core algorithm SQEMA","display_name":"Algorithmic correspondence and completeness in modal logic. I. The core algorithm SQEMA","publication_year":2006,"publication_date":"2006-03-07","ids":{"openalex":"https://openalex.org/W2950450725","doi":"https://doi.org/10.2168/lmcs-2(1:5)2006","mag":"2950450725"},"language":"en","primary_location":{"id":"doi:10.2168/lmcs-2(1:5)2006","is_oa":true,"landing_page_url":"https://doi.org/10.2168/lmcs-2(1:5)2006","pdf_url":"https://lmcs.episciences.org/2259/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://lmcs.episciences.org/2259/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037378549","display_name":"Willem Conradie","orcid":"https://orcid.org/0000-0001-9906-4132"},"institutions":[{"id":"https://openalex.org/I192619145","display_name":"University of the Witwatersrand","ror":"https://ror.org/03rp50x72","country_code":"ZA","type":"education","lineage":["https://openalex.org/I192619145"]},{"id":"https://openalex.org/I24027795","display_name":"University of Johannesburg","ror":"https://ror.org/04z6c2n17","country_code":"ZA","type":"education","lineage":["https://openalex.org/I24027795"]}],"countries":["ZA"],"is_corresponding":false,"raw_author_name":"Willem Conradie","raw_affiliation_strings":["Department of Mathematics, University of Johannesburg, and","School of Mathematics, University of the Witwatersrand, Johannesburg"],"raw_orcid":"https://orcid.org/0000-0001-9906-4132","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Johannesburg, and","institution_ids":["https://openalex.org/I24027795"]},{"raw_affiliation_string":"School of Mathematics, University of the Witwatersrand, Johannesburg","institution_ids":["https://openalex.org/I192619145"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066665696","display_name":"Valentin Goranko","orcid":"https://orcid.org/0000-0002-0157-1644"},"institutions":[{"id":"https://openalex.org/I192619145","display_name":"University of the Witwatersrand","ror":"https://ror.org/03rp50x72","country_code":"ZA","type":"education","lineage":["https://openalex.org/I192619145"]}],"countries":["ZA"],"is_corresponding":true,"raw_author_name":"Valentin Goranko","raw_affiliation_strings":["School of Mathematics, University of the Witwatersrand, Johannesburg"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, University of the Witwatersrand, Johannesburg","institution_ids":["https://openalex.org/I192619145"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076246494","display_name":"Dimiter Vakarelov","orcid":null},"institutions":[{"id":"https://openalex.org/I58918642","display_name":"Sofia University \"St. Kliment Ohridski\"","ror":"https://ror.org/02jv3k292","country_code":"BG","type":"education","lineage":["https://openalex.org/I58918642"]}],"countries":["BG"],"is_corresponding":false,"raw_author_name":"Dimiter Vakarelov","raw_affiliation_strings":["Faculty of Mathematics and Computer Science, Sofia University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, Sofia University","institution_ids":["https://openalex.org/I58918642"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5066665696"],"corresponding_institution_ids":["https://openalex.org/I192619145"],"apc_list":null,"apc_paid":null,"fwci":7.8024,"has_fulltext":true,"cited_by_count":96,"citation_normalized_percentile":{"value":0.970577,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"Volume 2, Issue 1","issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9995999932289124,"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":0.9995999932289124,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9939000010490417,"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/modal-logic","display_name":"Modal logic","score":0.8044863343238831},{"id":"https://openalex.org/keywords/ackermann-function","display_name":"Ackermann function","score":0.7699987888336182},{"id":"https://openalex.org/keywords/normal-modal-logic","display_name":"Normal modal logic","score":0.6596006751060486},{"id":"https://openalex.org/keywords/modal","display_name":"Modal","score":0.625533938407898},{"id":"https://openalex.org/keywords/correctness","display_name":"Correctness","score":0.5922456383705139},{"id":"https://openalex.org/keywords/accessibility-relation","display_name":"Accessibility relation","score":0.5900993347167969},{"id":"https://openalex.org/keywords/completeness","display_name":"Completeness (order theory)","score":0.5512139797210693},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49939966201782227},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4944577217102051},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.48874664306640625},{"id":"https://openalex.org/keywords/dynamic-logic","display_name":"Dynamic logic (digital electronics)","score":0.4833238124847412},{"id":"https://openalex.org/keywords/multimodal-logic","display_name":"Multimodal logic","score":0.46108266711235046},{"id":"https://openalex.org/keywords/automated-theorem-proving","display_name":"Automated theorem proving","score":0.4412544369697571},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38365867733955383},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3833966553211212},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.23560801148414612},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.12671273946762085}],"concepts":[{"id":"https://openalex.org/C27508121","wikidata":"https://www.wikidata.org/wiki/Q210841","display_name":"Modal logic","level":3,"score":0.8044863343238831},{"id":"https://openalex.org/C33436860","wikidata":"https://www.wikidata.org/wiki/Q341835","display_name":"Ackermann function","level":3,"score":0.7699987888336182},{"id":"https://openalex.org/C114092440","wikidata":"https://www.wikidata.org/wiki/Q840226","display_name":"Normal modal logic","level":4,"score":0.6596006751060486},{"id":"https://openalex.org/C71139939","wikidata":"https://www.wikidata.org/wiki/Q910194","display_name":"Modal","level":2,"score":0.625533938407898},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.5922456383705139},{"id":"https://openalex.org/C11191006","wikidata":"https://www.wikidata.org/wiki/Q2663311","display_name":"Accessibility relation","level":4,"score":0.5900993347167969},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.5512139797210693},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49939966201782227},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4944577217102051},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.48874664306640625},{"id":"https://openalex.org/C2777796570","wikidata":"https://www.wikidata.org/wiki/Q2351326","display_name":"Dynamic logic (digital electronics)","level":4,"score":0.4833238124847412},{"id":"https://openalex.org/C203659156","wikidata":"https://www.wikidata.org/wiki/Q6934805","display_name":"Multimodal logic","level":3,"score":0.46108266711235046},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.4412544369697571},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38365867733955383},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3833966553211212},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.23560801148414612},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.12671273946762085},{"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},{"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/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","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/C172385210","wikidata":"https://www.wikidata.org/wiki/Q5339","display_name":"Transistor","level":3,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"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":6,"locations":[{"id":"doi:10.2168/lmcs-2(1:5)2006","is_oa":true,"landing_page_url":"https://doi.org/10.2168/lmcs-2(1:5)2006","pdf_url":"https://lmcs.episciences.org/2259/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:cs/0602024","is_oa":true,"landing_page_url":"http://arxiv.org/abs/cs/0602024","pdf_url":"https://arxiv.org/pdf/cs/0602024","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.341.4790","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.341.4790","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/cs/0602024v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.342.3386","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.342.3386","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/cs/0602024v3.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.342.5820","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.342.5820","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/cs/0602024v2.pdf","raw_type":"text"},{"id":"pmh:oai:doaj.org/article:67ebddc3e8534066a406b34e5ea097a2","is_oa":true,"landing_page_url":"https://doaj.org/article/67ebddc3e8534066a406b34e5ea097a2","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Logical Methods in Computer Science, Vol Volume 2, Issue 1 (2006)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.2168/lmcs-2(1:5)2006","is_oa":true,"landing_page_url":"https://doi.org/10.2168/lmcs-2(1:5)2006","pdf_url":"https://lmcs.episciences.org/2259/pdf","source":{"id":"https://openalex.org/S114379355","display_name":"Logical Methods in Computer Science","issn_l":"1860-5974","issn":["1860-5974"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310313916","host_organization_name":"Logical Methods in Computer Science e.V.","host_organization_lineage":["https://openalex.org/P4310313916"],"host_organization_lineage_names":["Logical Methods in Computer Science e.V."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logical Methods in Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320291","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27"},{"id":"https://openalex.org/F4320320671","display_name":"National Research Foundation","ror":"https://ror.org/05s0g1g46"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2950450725.pdf","grobid_xml":"https://content.openalex.org/works/W2950450725.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W4147469","https://openalex.org/W57599773","https://openalex.org/W285264636","https://openalex.org/W1522802449","https://openalex.org/W1527720545","https://openalex.org/W1536469384","https://openalex.org/W1558518027","https://openalex.org/W1572523058","https://openalex.org/W1582039021","https://openalex.org/W1728675562","https://openalex.org/W1981936535","https://openalex.org/W1987652121","https://openalex.org/W1989151171","https://openalex.org/W1998532035","https://openalex.org/W2008621787","https://openalex.org/W2048154108","https://openalex.org/W2051649506","https://openalex.org/W2057503265","https://openalex.org/W2111082593","https://openalex.org/W2126382654","https://openalex.org/W2144185328","https://openalex.org/W2610670723","https://openalex.org/W2950450725","https://openalex.org/W3103855201","https://openalex.org/W4211144022","https://openalex.org/W4285719527","https://openalex.org/W6600166751"],"related_works":["https://openalex.org/W142011187","https://openalex.org/W3108798275","https://openalex.org/W2795425183","https://openalex.org/W2534562289","https://openalex.org/W2175984923","https://openalex.org/W1528547703","https://openalex.org/W4318188140","https://openalex.org/W2028312452","https://openalex.org/W176661328","https://openalex.org/W1909183225"],"abstract_inverted_index":{"Modal":[0],"formulae":[1,36,156],"express":[2],"monadic":[3],"second-order":[4,62,70],"properties":[5],"on":[6,75,81,123,157,169,175],"Kripke":[7],"frames,":[8],"but":[9,173],"in":[10,183,198,202,212],"many":[11],"important":[12,22],"cases":[13],"these":[14],"have":[15,66],"first-order":[16,52,99],"equivalents.":[17],"Computing":[18,50],"such":[19],"equivalents":[20,100],"is":[21,37],"for":[23,69,97,110],"both":[24],"logical":[25,83],"and":[26,78,118,129,140,151],"computational":[27],"reasons.":[28],"On":[29],"the":[30,130,137,152,159,176,207],"other":[31],"hand,":[32],"canonicity":[33,112,153],"of":[34,44,54,61,105,113,133,154,179,206],"modal":[35,56,103,114,124,199,213],"important,":[38],"too,":[39],"because":[40],"it":[41,120,142,165],"implies":[42],"frame-completeness":[43],"logics":[45],"axiomatized":[46],"with":[47,143],"canonical":[48,196],"formulae.":[49,115],"a":[51,55,82,93,102,190],"equivalent":[53],"formula":[57],"amounts":[58],"to":[59,194],"elimination":[60],"quantifiers.":[63],"Two":[64],"algorithms":[65],"been":[67],"developed":[68],"quantifier":[71],"elimination:":[72],"SCAN,":[73],"based":[74,80],"constraint":[76],"resolution,":[77],"DLS,":[79,119],"equivalence":[84],"established":[85],"by":[86],"Ackermann.":[87],"In":[88],"this":[89],"paper":[90],"we":[91,188],"introduce":[92],"new":[94],"algorithm,":[95],"SQEMA,":[96],"computing":[98],"(using":[101],"version":[104],"Ackermann's":[106],"lemma)":[107],"and,":[108,201],"moreover,":[109],"proving":[111,195],"Unlike":[116],"SCAN":[117],"works":[121],"directly":[122],"formulae,":[125,172,181],"thus":[126],"avoiding":[127],"Skolemization":[128],"subsequent":[131],"problem":[132],"unskolemization.":[134],"We":[135,146,162],"present":[136],"core":[138],"algorithm":[139,160],"illustrate":[141],"some":[144],"examples.":[145],"then":[147],"prove":[148],"its":[149],"correctness":[150],"all":[155,170],"which":[158],"succeeds.":[161],"show":[163],"that":[164],"succeeds":[166],"not":[167],"only":[168],"Sahlqvist":[171],"also":[174],"larger":[177],"class":[178],"inductive":[180],"introduced":[182],"our":[184],"earlier":[185],"papers.":[186],"Thus,":[187],"develop":[189],"purely":[191],"algorithmic":[192],"approach":[193],"completeness":[197,210],"logic":[200,214],"particular,":[203],"establish":[204],"one":[205],"most":[208],"general":[209],"results":[211],"so":[215],"far.":[216]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":15},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}
