{"id":"https://openalex.org/W2233161159","doi":"https://doi.org/10.1093/jigpal/jzy012","title":"A many-sorted variant of Japaridze\u2019s polymodal provability logic","display_name":"A many-sorted variant of Japaridze\u2019s polymodal provability logic","publication_year":2018,"publication_date":"2018-04-06","ids":{"openalex":"https://openalex.org/W2233161159","doi":"https://doi.org/10.1093/jigpal/jzy012","mag":"2233161159"},"language":"en","primary_location":{"id":"doi:10.1093/jigpal/jzy012","is_oa":false,"landing_page_url":"https://doi.org/10.1093/jigpal/jzy012","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":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1601.02857","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Gerald Berger","orcid":null},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Gerald Berger","raw_affiliation_strings":["Institute of Logic and Computation, TU Wien, Favoritenstra\u00dfe, Austria"],"affiliations":[{"raw_affiliation_string":"Institute of Logic and Computation, TU Wien, Favoritenstra\u00dfe, Austria","institution_ids":["https://openalex.org/I145847075"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Lev D Beklemishev","orcid":null},"institutions":[{"id":"https://openalex.org/I2801160905","display_name":"Steklov Mathematical Institute","ror":"https://ror.org/03zeg8w71","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I2801160905","https://openalex.org/I4210124601"]},{"id":"https://openalex.org/I1313323035","display_name":"Russian Academy of Sciences","ror":"https://ror.org/05qrfxd25","country_code":"RU","type":"funder","lineage":["https://openalex.org/I1313323035"]},{"id":"https://openalex.org/I118501908","display_name":"National Research University Higher School of Economics","ror":"https://ror.org/055f7t516","country_code":"RU","type":"education","lineage":["https://openalex.org/I118501908"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Lev D Beklemishev","raw_affiliation_strings":["National Research University Higher School of Economics, Moscow, Russia","Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia"],"affiliations":[{"raw_affiliation_string":"National Research University Higher School of Economics, Moscow, Russia","institution_ids":["https://openalex.org/I118501908"]},{"raw_affiliation_string":"Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia","institution_ids":["https://openalex.org/I2801160905","https://openalex.org/I1313323035"]}]},{"author_position":"last","author":{"id":null,"display_name":"Hans Tompits","orcid":null},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Hans Tompits","raw_affiliation_strings":["Institute of Logic and Computation, TU Wien, Favoritenstra\u00dfe, Austria"],"affiliations":[{"raw_affiliation_string":"Institute of Logic and Computation, TU Wien, Favoritenstra\u00dfe, Austria","institution_ids":["https://openalex.org/I145847075"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I145847075"],"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":0.00394904,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"26","issue":"5","first_page":"505","last_page":"538"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.724399983882904,"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":0.724399983882904,"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":0.17839999496936798,"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/T10142","display_name":"Formal Methods in Verification","score":0.04470000043511391,"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/arithmetic-function","display_name":"Arithmetic function","score":0.7318999767303467},{"id":"https://openalex.org/keywords/sort","display_name":"sort","score":0.6297000050544739},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.5177000164985657},{"id":"https://openalex.org/keywords/interpretation","display_name":"Interpretation (philosophy)","score":0.5041000247001648},{"id":"https://openalex.org/keywords/propositional-variable","display_name":"Propositional variable","score":0.487199991941452},{"id":"https://openalex.org/keywords/propositional-calculus","display_name":"Propositional calculus","score":0.46860000491142273},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.40560001134872437},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.39169999957084656},{"id":"https://openalex.org/keywords/reflection","display_name":"Reflection (computer programming)","score":0.38499999046325684}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8533999919891357},{"id":"https://openalex.org/C112343008","wikidata":"https://www.wikidata.org/wiki/Q140744","display_name":"Arithmetic function","level":2,"score":0.7318999767303467},{"id":"https://openalex.org/C88548561","wikidata":"https://www.wikidata.org/wiki/Q347599","display_name":"sort","level":2,"score":0.6297000050544739},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.5177000164985657},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.5041000247001648},{"id":"https://openalex.org/C14523651","wikidata":"https://www.wikidata.org/wiki/Q3492863","display_name":"Propositional variable","level":4,"score":0.487199991941452},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4717000126838684},{"id":"https://openalex.org/C69562738","wikidata":"https://www.wikidata.org/wiki/Q200694","display_name":"Propositional calculus","level":2,"score":0.46860000491142273},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.40560001134872437},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.39169999957084656},{"id":"https://openalex.org/C65682993","wikidata":"https://www.wikidata.org/wiki/Q1056451","display_name":"Reflection (computer programming)","level":2,"score":0.38499999046325684},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.3822999894618988},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3806999921798706},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.36809998750686646},{"id":"https://openalex.org/C110039528","wikidata":"https://www.wikidata.org/wiki/Q8069651","display_name":"Zeroth-order logic","level":4,"score":0.3610000014305115},{"id":"https://openalex.org/C178421362","wikidata":"https://www.wikidata.org/wiki/Q176786","display_name":"Intuitionistic logic","level":3,"score":0.35830000042915344},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.32690000534057617},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.32519999146461487},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2856000065803528},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.27810001373291016},{"id":"https://openalex.org/C171988527","wikidata":"https://www.wikidata.org/wiki/Q188276","display_name":"Pigeonhole principle","level":2,"score":0.2734000086784363},{"id":"https://openalex.org/C65880906","wikidata":"https://www.wikidata.org/wiki/Q1771121","display_name":"Sequent calculus","level":3,"score":0.2703000009059906},{"id":"https://openalex.org/C97489613","wikidata":"https://www.wikidata.org/wiki/Q842755","display_name":"Peano axioms","level":2,"score":0.2702000141143799},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.2644999921321869},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.26030001044273376},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.2531000077724457}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1093/jigpal/jzy012","is_oa":false,"landing_page_url":"https://doi.org/10.1093/jigpal/jzy012","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:1601.02857","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1601.02857","pdf_url":"https://arxiv.org/pdf/1601.02857","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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1601.02857","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1601.02857","pdf_url":"https://arxiv.org/pdf/1601.02857","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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1975729292","display_name":null,"funder_award_id":"W1255-N23","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G7590453568","display_name":null,"funder_award_id":"15-01-09218","funder_id":"https://openalex.org/F4320321004","funder_display_name":"\u00d6sterreichischen Akademie der Wissenschaften"}],"funders":[{"id":"https://openalex.org/F4320321004","display_name":"\u00d6sterreichischen Akademie der Wissenschaften","ror":"https://ror.org/03anc3s24"},{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1569545587","https://openalex.org/W1574162351","https://openalex.org/W1982073522","https://openalex.org/W1994332324","https://openalex.org/W2010855309","https://openalex.org/W2017621431","https://openalex.org/W2034453867","https://openalex.org/W2059933820","https://openalex.org/W2065285281","https://openalex.org/W2163960919","https://openalex.org/W2225896778","https://openalex.org/W2596960772","https://openalex.org/W2607208118","https://openalex.org/W2726060486","https://openalex.org/W3136553163","https://openalex.org/W6676125690","https://openalex.org/W6683279979","https://openalex.org/W6685292077"],"related_works":[],"abstract_inverted_index":{"We":[0,56,99,144],"consider":[1],"a":[2,102,134],"many-sorted":[3],"variant":[4,104,149],"of":[5,30,42,48,88,105,133,150],"Japaridze\u2019s":[6],"polymodal":[7],"provability":[8],"logic":[9],"(\u2060|$\\textsf{GLP}$|\u2060).":[10],"In":[11],"this":[12,67],"variant,":[13],"which":[14],"is":[15,61,153],"denoted":[16],"|$\\textsf{GLP}^\\ast":[17,59,72,106,151],"$|\u2060,":[18,27],"propositional":[19],"variables":[20,29],"are":[21,37,116],"assigned":[22],"sorts":[23],"|$\\alpha":[24],"\\leq":[25],"\\omega":[26,35],"where":[28],"finite":[31],"sort":[32,49],"|$n":[33],"<":[34],"$|":[36,51,60,73,107,152],"interpreted":[38],"as":[39],"|$\\varPi":[40],"_{n+1}$|-sentences":[41],"the":[43,82,89,131,139],"arithmetical":[44,114],"hierarchy,":[45],"while":[46],"those":[47],"|$\\omega":[50],"range":[52,119],"over":[53,120],"arbitrary":[54],"ones.":[55],"prove":[57,80],"that":[58,81,108,136,146],"arithmetically":[62,154],"complete":[63],"with":[64],"respect":[65],"to":[66,74,118,138],"interpretation.":[68],"Moreover,":[69],"we":[70],"relate":[71],"its":[75],"one-sorted":[76],"counterpart":[77],"|$\\textsf{GLP}$|":[78],"and":[79,94],"former":[83],"inherits":[84],"some":[85],"well-known":[86],"properties":[87],"latter,":[90],"like":[91],"Craig":[92],"interpolation":[93],"polynomial":[95],"space":[96],"(PSpace)":[97],"decidability.":[98],"also":[100],"study":[101],"positive":[103,148],"allows":[109,130],"for":[110],"an":[111],"even":[112],"richer":[113],"interpretation\u2014variables":[115],"permitted":[117],"theories":[121],"rather":[122],"than":[123],"single":[124],"sentences.":[125],"This":[126],"interpretation":[127],"in":[128],"turn":[129],"introduction":[132],"modality":[135],"corresponds":[137],"full":[140],"uniform":[141],"reflection":[142],"principle.":[143],"show":[145],"our":[147],"complete.":[155]},"counts_by_year":[],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2016-06-24T00:00:00"}