{"id":"https://openalex.org/W4416026854","doi":"https://doi.org/10.4230/lipics.lics.2026.26","title":"The Size of Interpolants in Modal Logics","display_name":"The Size of Interpolants in Modal Logics","publication_year":2025,"publication_date":"2025-11-06","ids":{"openalex":"https://openalex.org/W4416026854","doi":"https://doi.org/10.4230/lipics.lics.2026.26"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2511.04577","is_oa":true,"landing_page_url":"https://arxiv.org/abs/2511.04577","pdf_url":"https://arxiv.org/pdf/2511.04577","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":null,"raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2511.04577","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080220262","display_name":"Balder ten Cate","orcid":"https://orcid.org/0000-0002-2538-5846"},"institutions":[{"id":"https://openalex.org/I887064364","display_name":"University of Amsterdam","ror":"https://ror.org/04dkp9463","country_code":"NL","type":"education","lineage":["https://openalex.org/I887064364"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"ten Cate, Balder","raw_affiliation_strings":["University of Amsterdam, The Netherlands"],"raw_orcid":"https://orcid.org/0000-0002-2538-5846","affiliations":[{"raw_affiliation_string":"University of Amsterdam, The Netherlands","institution_ids":["https://openalex.org/I887064364"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091303743","display_name":"Louwe B. Kuijer","orcid":"https://orcid.org/0000-0001-6696-9023"},"institutions":[{"id":"https://openalex.org/I146655781","display_name":"University of Liverpool","ror":"https://ror.org/04xs57h96","country_code":"GB","type":"education","lineage":["https://openalex.org/I146655781"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Kuijer, Louwe B.","raw_affiliation_strings":["University of Liverpool, UK"],"raw_orcid":"https://orcid.org/0000-0001-6696-9023","affiliations":[{"raw_affiliation_string":"University of Liverpool, UK","institution_ids":["https://openalex.org/I146655781"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010967150","display_name":"Frank Wolter","orcid":"https://orcid.org/0000-0002-4470-606X"},"institutions":[{"id":"https://openalex.org/I146655781","display_name":"University of Liverpool","ror":"https://ror.org/04xs57h96","country_code":"GB","type":"education","lineage":["https://openalex.org/I146655781"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Wolter, Frank","raw_affiliation_strings":["University of Liverpool, UK"],"raw_orcid":"https://orcid.org/0000-0002-4470-606X","affiliations":[{"raw_affiliation_string":"University of Liverpool, UK","institution_ids":["https://openalex.org/I146655781"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"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":0.8668000102043152,"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":0.8668000102043152,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.05050000175833702,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.04340000078082085,"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/modal","display_name":"Modal","score":0.7414000034332275},{"id":"https://openalex.org/keywords/modal-logic","display_name":"Modal logic","score":0.6190999746322632},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.6043000221252441},{"id":"https://openalex.org/keywords/normal-modal-logic","display_name":"Normal modal logic","score":0.5853000283241272},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5835000276565552},{"id":"https://openalex.org/keywords/accessibility-relation","display_name":"Accessibility relation","score":0.5295000076293945},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.49939998984336853},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.46380001306533813}],"concepts":[{"id":"https://openalex.org/C71139939","wikidata":"https://www.wikidata.org/wiki/Q910194","display_name":"Modal","level":2,"score":0.7414000034332275},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7335000038146973},{"id":"https://openalex.org/C27508121","wikidata":"https://www.wikidata.org/wiki/Q210841","display_name":"Modal logic","level":3,"score":0.6190999746322632},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.6043000221252441},{"id":"https://openalex.org/C114092440","wikidata":"https://www.wikidata.org/wiki/Q840226","display_name":"Normal modal logic","level":4,"score":0.5853000283241272},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5835000276565552},{"id":"https://openalex.org/C11191006","wikidata":"https://www.wikidata.org/wiki/Q2663311","display_name":"Accessibility relation","level":4,"score":0.5295000076293945},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.49939998984336853},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.46380001306533813},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4625999927520752},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4341999888420105},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.3853999972343445},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35929998755455017},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3458999991416931},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34540000557899475},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33090001344680786},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3260999917984009},{"id":"https://openalex.org/C173125200","wikidata":"https://www.wikidata.org/wiki/Q5275729","display_name":"Modal \u03bc-calculus","level":5,"score":0.325300008058548},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.30469998717308044},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.29109999537467957},{"id":"https://openalex.org/C192609573","wikidata":"https://www.wikidata.org/wiki/Q7388341","display_name":"S5","level":5,"score":0.2872999906539917},{"id":"https://openalex.org/C86602344","wikidata":"https://www.wikidata.org/wiki/Q7667918","display_name":"T-norm fuzzy logics","level":5,"score":0.28439998626708984},{"id":"https://openalex.org/C69562738","wikidata":"https://www.wikidata.org/wiki/Q200694","display_name":"Propositional calculus","level":2,"score":0.27459999918937683},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.26080000400543213},{"id":"https://openalex.org/C16221470","wikidata":"https://www.wikidata.org/wiki/Q846564","display_name":"Conjunctive normal form","level":2,"score":0.25459998846054077}],"mesh":[],"locations_count":5,"locations":[{"id":"pmh:oai:arXiv.org:2511.04577","is_oa":true,"landing_page_url":"https://arxiv.org/abs/2511.04577","pdf_url":"https://arxiv.org/pdf/2511.04577","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":null,"raw_type":"text"},{"id":"pmh:oai:drops-oai.dagstuhl.de:26813","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.LICS.2026.26","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol380-lics2026/LIPIcs.LICS.2026.26/LIPIcs.LICS.2026.26.pdf","source":{"id":"https://openalex.org/S4306402524","display_name":"Leibniz-Zentrum f\u00fcr Informatik (Schloss Dagstuhl)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"InProceedings"},{"id":"pmh:doi:10.4230/lipics.lics.2026.26","is_oa":true,"landing_page_url":"http://www.cambridge.org/catalogue/catalogue.asp?isbn=9780521424264","pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"ConferencePaper"},{"id":"doi:10.48550/arxiv.2511.04577","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2511.04577","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":"Preprint"},{"id":"doi:10.4230/lipics.lics.2026.26","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.lics.2026.26","pdf_url":null,"source":{"id":"https://openalex.org/S7407052059","display_name":"Dagstuhl Research Online Publication Server","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","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"ConferencePaper"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2511.04577","is_oa":true,"landing_page_url":"https://arxiv.org/abs/2511.04577","pdf_url":"https://arxiv.org/pdf/2511.04577","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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4416026854.pdf","grobid_xml":"https://content.openalex.org/works/W4416026854.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"start":[1],"a":[2],"systematic":[3],"investigation":[4],"of":[5,8,32,52,91],"the":[6,30,69,74,89,118],"size":[7,90],"Craig":[9,66,75,92],"interpolants,":[10,12],"uniform":[11,42],"and":[13,94],"strongest":[14,33,95],"implicates":[15,34,96],"for":[16,26,65,128],"(quasi-)normal":[17],"modal":[18,28,71,103,107],"logics.":[19,104],"Our":[20,78],"main":[21,79],"upper":[22],"bound":[23,81,87,135],"states":[24],"that":[25],"tabular":[27,70,121],"logics,":[29],"computation":[31,44],"can":[35],"be":[36],"reduced":[37],"in":[38,45,59,110],"polynomial":[39,53],"time":[40],"to":[41],"interpolant":[43],"classical":[46],"propositional":[47],"logic.":[48],"Hence":[49],"they":[50],"are":[51],"dag-size":[54],"iff":[55],"NP":[56],"is":[57],"included":[58],"P/poly.":[60],"The":[61],"reduction":[62],"also":[63],"holds":[64],"interpolants":[67,93,126],"if":[68],"logic":[72],"has":[73],"interpolation":[76],"property.":[77],"lower":[80,86,134],"shows":[82],"an":[83,131],"unconditional":[84,132],"exponential":[85,133],"on":[88],"covering":[97],"almost":[98],"all":[99],"non-tabular":[100,129],"standard":[101],"normal":[102,106],"For":[105],"logics":[108,122,130],"contained":[109],"or":[111,114],"containing":[112],"S4":[113],"GL":[115],"we":[116],"obtain":[117],"following":[119],"dichotomy:":[120],"have":[123],"\"propositionally":[124],"sized\"":[125],"while":[127],"holds.":[136]},"counts_by_year":[],"updated_date":"2026-07-18T07:39:51.176621","created_date":"2025-11-08T00:00:00"}
