{"id":"https://openalex.org/W2887080569","doi":"https://doi.org/10.1093/jigpal/jzaa068","title":"Frame-validity Games and Lower Bounds on the Complexity of Modal Axioms","display_name":"Frame-validity Games and Lower Bounds on the Complexity of Modal Axioms","publication_year":2020,"publication_date":"2020-11-15","ids":{"openalex":"https://openalex.org/W2887080569","doi":"https://doi.org/10.1093/jigpal/jzaa068","mag":"2887080569"},"language":"en","primary_location":{"id":"doi:10.1093/jigpal/jzaa068","is_oa":false,"landing_page_url":"http://doi.org/10.1093/jigpal/jzaa068","pdf_url":null,"source":{"id":"https://openalex.org/S2734381524","display_name":"Logic Journal of IGPL","issn_l":"1367-0751","issn":["1367-0751","1368-9894"],"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":"Logic Journal of the IGPL","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1808.05051","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043349795","display_name":"Philippe Balbiani","orcid":"https://orcid.org/0000-0002-3569-9160"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I134560555","display_name":"Universit\u00e9 Toulouse III - Paul Sabatier","ror":"https://ror.org/02v6kpv12","country_code":"FR","type":"education","lineage":["https://openalex.org/I134560555"]},{"id":"https://openalex.org/I3131550300","display_name":"Universit\u00e9 Toulouse-I-Capitole","ror":"https://ror.org/0443n9e75","country_code":"FR","type":"education","lineage":["https://openalex.org/I3131550300"]},{"id":"https://openalex.org/I4210119061","display_name":"Institut de Recherche en Informatique de Toulouse","ror":"https://ror.org/01rx4qw44","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I205747304","https://openalex.org/I205747304","https://openalex.org/I4210119061","https://openalex.org/I4210152422","https://openalex.org/I4387153255","https://openalex.org/I4405258862","https://openalex.org/I4405259414"]},{"id":"https://openalex.org/I4210152422","display_name":"Universit\u00e9 Toulouse - Jean Jaur\u00e8s","ror":"https://ror.org/04ezk3x31","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210152422"]},{"id":"https://openalex.org/I4210160189","display_name":"Institut Polytechnique de Bordeaux","ror":"https://ror.org/054qv7y42","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210160189"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Philippe Balbiani","raw_affiliation_strings":["IRIT, CNRS Toulouse University, F-31062 Toulouse, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IRIT, CNRS Toulouse University, F-31062 Toulouse, France","institution_ids":["https://openalex.org/I134560555","https://openalex.org/I3131550300","https://openalex.org/I4210160189","https://openalex.org/I4210152422","https://openalex.org/I1294671590","https://openalex.org/I4210119061"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080309379","display_name":"David Fern\u00e1ndez\u2013Duque","orcid":"https://orcid.org/0000-0001-8604-4183"},"institutions":[{"id":"https://openalex.org/I32597200","display_name":"Ghent University","ror":"https://ror.org/00cv9y106","country_code":"BE","type":"education","lineage":["https://openalex.org/I32597200"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"David Fern\u00e1ndez-Duque","raw_affiliation_strings":["Department of Mathematics, Ghent University Department of Mathematics, Ghent University, B 9000 Gent, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Ghent University Department of Mathematics, Ghent University, B 9000 Gent, Belgium","institution_ids":["https://openalex.org/I32597200"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004332415","display_name":"Andreas Herzig","orcid":"https://orcid.org/0000-0003-0833-2782"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I134560555","display_name":"Universit\u00e9 Toulouse III - Paul Sabatier","ror":"https://ror.org/02v6kpv12","country_code":"FR","type":"education","lineage":["https://openalex.org/I134560555"]},{"id":"https://openalex.org/I3131550300","display_name":"Universit\u00e9 Toulouse-I-Capitole","ror":"https://ror.org/0443n9e75","country_code":"FR","type":"education","lineage":["https://openalex.org/I3131550300"]},{"id":"https://openalex.org/I4210119061","display_name":"Institut de Recherche en Informatique de Toulouse","ror":"https://ror.org/01rx4qw44","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I205747304","https://openalex.org/I205747304","https://openalex.org/I4210119061","https://openalex.org/I4210152422","https://openalex.org/I4387153255","https://openalex.org/I4405258862","https://openalex.org/I4405259414"]},{"id":"https://openalex.org/I4210152422","display_name":"Universit\u00e9 Toulouse - Jean Jaur\u00e8s","ror":"https://ror.org/04ezk3x31","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210152422"]},{"id":"https://openalex.org/I4210160189","display_name":"Institut Polytechnique de Bordeaux","ror":"https://ror.org/054qv7y42","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210160189"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Andreas Herzig","raw_affiliation_strings":["IRIT, CNRS Toulouse University, F-31062 Toulouse, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IRIT, CNRS Toulouse University, F-31062 Toulouse, France","institution_ids":["https://openalex.org/I134560555","https://openalex.org/I3131550300","https://openalex.org/I4210160189","https://openalex.org/I4210152422","https://openalex.org/I1294671590","https://openalex.org/I4210119061"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045194736","display_name":"Petar Iliev","orcid":null},"institutions":[{"id":"https://openalex.org/I24768866","display_name":"Bulgarian Academy of Sciences","ror":"https://ror.org/01x8hew03","country_code":"BG","type":"government","lineage":["https://openalex.org/I24768866"]},{"id":"https://openalex.org/I4210110320","display_name":"Institute of Philosophy and Sociology","ror":"https://ror.org/023t1e924","country_code":"BG","type":"facility","lineage":["https://openalex.org/I24768866","https://openalex.org/I4210110320"]}],"countries":["BG"],"is_corresponding":false,"raw_author_name":"Petar Iliev","raw_affiliation_strings":["Institute of Philosophy and Sociology, Bulgarian Academy of Sciences, Sofia 1000, Bulgaria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Philosophy and Sociology, Bulgarian Academy of Sciences, Sofia 1000, Bulgaria","institution_ids":["https://openalex.org/I24768866","https://openalex.org/I4210110320"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":4151,"currency":"USD","value_usd":4151},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01076021,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"30","issue":"1","first_page":"155","last_page":"185"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9462000131607056,"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":0.9462000131607056,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.8786317110061646},{"id":"https://openalex.org/keywords/modal","display_name":"Modal","score":0.7666187286376953},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6285643577575684},{"id":"https://openalex.org/keywords/frame","display_name":"Frame (networking)","score":0.6071605682373047},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5940835475921631},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.530756950378418},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.5239137411117554},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3851687014102936},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.343576580286026},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24686390161514282},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08856534957885742},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07938644289970398}],"concepts":[{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.8786317110061646},{"id":"https://openalex.org/C71139939","wikidata":"https://www.wikidata.org/wiki/Q910194","display_name":"Modal","level":2,"score":0.7666187286376953},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6285643577575684},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.6071605682373047},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5940835475921631},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.530756950378418},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5239137411117554},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3851687014102936},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.343576580286026},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24686390161514282},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08856534957885742},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07938644289970398},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C188027245","wikidata":"https://www.wikidata.org/wiki/Q750446","display_name":"Polymer chemistry","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1093/jigpal/jzaa068","is_oa":false,"landing_page_url":"http://doi.org/10.1093/jigpal/jzaa068","pdf_url":null,"source":{"id":"https://openalex.org/S2734381524","display_name":"Logic Journal of IGPL","issn_l":"1367-0751","issn":["1367-0751","1368-9894"],"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":"Logic Journal of the IGPL","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1808.05051","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1808.05051","pdf_url":"https://arxiv.org/pdf/1808.05051","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"","raw_type":"text"},{"id":"mag:2887080569","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1808.05051.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:HAL:hal-02936458v1","is_oa":true,"landing_page_url":"https://hal.science/hal-02936458","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"https://academic.oup.com/jigpal/article-abstract/30/1/155/6039977?redirectedFrom=fulltext&login=true","raw_type":"Journal articles"},{"id":"doi:10.48550/arxiv.1808.05051","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1808.05051","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1808.05051","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1808.05051","pdf_url":"https://arxiv.org/pdf/1808.05051","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1489366126","https://openalex.org/W1555138513","https://openalex.org/W1985255932","https://openalex.org/W1991755574","https://openalex.org/W1995365759","https://openalex.org/W2033743662","https://openalex.org/W2042590814","https://openalex.org/W2094001511","https://openalex.org/W2175748456","https://openalex.org/W2339697109","https://openalex.org/W2399173794","https://openalex.org/W2490907619","https://openalex.org/W2749335491","https://openalex.org/W2996136717","https://openalex.org/W4210350201","https://openalex.org/W4236835455","https://openalex.org/W4245713184","https://openalex.org/W6610398787","https://openalex.org/W6629463652","https://openalex.org/W6636445471","https://openalex.org/W6656780288","https://openalex.org/W6684469001","https://openalex.org/W6704348348","https://openalex.org/W6713702496","https://openalex.org/W6760878036"],"related_works":["https://openalex.org/W3114768102","https://openalex.org/W2045225747","https://openalex.org/W2118915359","https://openalex.org/W3198194642","https://openalex.org/W311063083","https://openalex.org/W1522855049","https://openalex.org/W3008129045","https://openalex.org/W2405691245","https://openalex.org/W4389421","https://openalex.org/W3029800901","https://openalex.org/W2531234554","https://openalex.org/W2520158987","https://openalex.org/W2403171661","https://openalex.org/W225390579","https://openalex.org/W2460611553","https://openalex.org/W2169150716","https://openalex.org/W2788272802","https://openalex.org/W2121683501","https://openalex.org/W2255083403","https://openalex.org/W1979438158"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"introduce":[2],"frame-equivalence":[3],"games":[4],"tailored":[5],"for":[6,43,53],"reasoning":[7],"about":[8],"the":[9,40,56,65,68],"size,":[10],"modal":[11,25,48],"depth,":[12],"number":[13,19,45],"of":[14,16,20,24,46,55,71],"occurrences":[15],"symbols":[17],"and":[18],"different":[21],"propositional":[22],"variables":[23],"formulae":[26,66],"defining":[27,67],"a":[28,44],"given":[29],"frame":[30],"property.":[31],"Using":[32],"these":[33],"games,":[34],"we":[35,58],"prove":[36],"lower":[37],"bounds":[38],"on":[39],"above":[41],"measures":[42],"well-known":[47],"axioms;":[49],"what":[50],"is":[51],"more,":[52],"some":[54],"axioms,":[57],"show":[59],"that":[60],"they":[61],"are":[62],"optimal":[63],"among":[64],"respective":[69],"class":[70],"frames.":[72]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
