{"id":"https://openalex.org/W7167813166","doi":"https://doi.org/10.4230/lipics.lics.2026.46","title":"The Logic of Bunched Implications Is Undecidable","display_name":"The Logic of Bunched Implications Is Undecidable","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W7167813166","doi":"https://doi.org/10.4230/lipics.lics.2026.46"},"language":"en","primary_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:26833","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.LICS.2026.46","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol380-lics2026/LIPIcs.LICS.2026.46/LIPIcs.LICS.2026.46.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","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"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol380-lics2026/LIPIcs.LICS.2026.46/LIPIcs.LICS.2026.46.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5006796466","display_name":"Nikolaos Galatos","orcid":"https://orcid.org/0000-0001-8707-8844"},"institutions":[{"id":"https://openalex.org/I131651094","display_name":"University of Denver","ror":"https://ror.org/04w7skc03","country_code":"US","type":"education","lineage":["https://openalex.org/I131651094"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Galatos, Nikolaos","raw_affiliation_strings":["University of Denver, CO, USA"],"raw_orcid":"https://orcid.org/0000-0001-8707-8844","affiliations":[{"raw_affiliation_string":"University of Denver, CO, USA","institution_ids":["https://openalex.org/I131651094"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004708077","display_name":"Peter Jipsen","orcid":"https://orcid.org/0000-0001-8608-808X"},"institutions":[{"id":"https://openalex.org/I185071736","display_name":"Chapman University","ror":"https://ror.org/0452jzg20","country_code":"US","type":"education","lineage":["https://openalex.org/I185071736"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jipsen, Peter","raw_affiliation_strings":["Chapman University, Orange, CA, USA"],"raw_orcid":"https://orcid.org/0000-0001-8608-808X","affiliations":[{"raw_affiliation_string":"Chapman University, Orange, CA, USA","institution_ids":["https://openalex.org/I185071736"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5093489179","display_name":"S\u00f8ren Brinck Knudstorp","orcid":"https://orcid.org/0009-0008-9835-4195"},"institutions":[{"id":"https://openalex.org/I13089092","display_name":"Amsterdam University College","ror":"https://ror.org/03dpjfc73","country_code":"NL","type":"education","lineage":["https://openalex.org/I13089092"]},{"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":"Knudstorp, S\u00f8ren Brinck","raw_affiliation_strings":["ILLC and Philosophy, University of Amsterdam, The Netherlands"],"raw_orcid":"https://orcid.org/0009-0008-9835-4195","affiliations":[{"raw_affiliation_string":"ILLC and Philosophy, University of Amsterdam, The Netherlands","institution_ids":["https://openalex.org/I13089092","https://openalex.org/I887064364"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001826398","display_name":"Revantha Ramanayake","orcid":"https://orcid.org/0000-0002-7940-9065"},"institutions":[{"id":"https://openalex.org/I169381384","display_name":"University of Groningen","ror":"https://ror.org/012p63287","country_code":"NL","type":"education","lineage":["https://openalex.org/I169381384"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Ramanayake, Revantha","raw_affiliation_strings":["University of Groningen, The Netherlands"],"raw_orcid":"https://orcid.org/0000-0002-7940-9065","affiliations":[{"raw_affiliation_string":"University of Groningen, The Netherlands","institution_ids":["https://openalex.org/I169381384"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.8437364,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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":0.35519999265670776,"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":0.35519999265670776,"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/T10258","display_name":"Philosophy and Theoretical Science","score":0.2249000072479248,"subfield":{"id":"https://openalex.org/subfields/3205","display_name":"Experimental and Cognitive Psychology"},"field":{"id":"https://openalex.org/fields/32","display_name":"Psychology"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.21320000290870667,"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/undecidable-problem","display_name":"Undecidable problem","score":0.9265000224113464},{"id":"https://openalex.org/keywords/negation","display_name":"Negation","score":0.7718999981880188},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.5726000070571899},{"id":"https://openalex.org/keywords/fragment","display_name":"Fragment (logic)","score":0.5465999841690063},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.5422000288963318},{"id":"https://openalex.org/keywords/propositional-calculus","display_name":"Propositional calculus","score":0.4878000020980835},{"id":"https://openalex.org/keywords/conjunction","display_name":"Conjunction (astronomy)","score":0.48429998755455017},{"id":"https://openalex.org/keywords/linear-logic","display_name":"Linear logic","score":0.46160000562667847},{"id":"https://openalex.org/keywords/decidability","display_name":"Decidability","score":0.41920000314712524},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.3889000117778778}],"concepts":[{"id":"https://openalex.org/C192034797","wikidata":"https://www.wikidata.org/wiki/Q3502995","display_name":"Undecidable problem","level":3,"score":0.9265000224113464},{"id":"https://openalex.org/C2185349","wikidata":"https://www.wikidata.org/wiki/Q190558","display_name":"Negation","level":2,"score":0.7718999981880188},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6179999709129333},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.5726000070571899},{"id":"https://openalex.org/C2776235265","wikidata":"https://www.wikidata.org/wiki/Q18392052","display_name":"Fragment (logic)","level":2,"score":0.5465999841690063},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.5422000288963318},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5047000050544739},{"id":"https://openalex.org/C69562738","wikidata":"https://www.wikidata.org/wiki/Q200694","display_name":"Propositional calculus","level":2,"score":0.4878000020980835},{"id":"https://openalex.org/C59656382","wikidata":"https://www.wikidata.org/wiki/Q191536","display_name":"Conjunction (astronomy)","level":2,"score":0.48429998755455017},{"id":"https://openalex.org/C28077239","wikidata":"https://www.wikidata.org/wiki/Q841728","display_name":"Linear logic","level":2,"score":0.46160000562667847},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.41920000314712524},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.3889000117778778},{"id":"https://openalex.org/C178421362","wikidata":"https://www.wikidata.org/wiki/Q176786","display_name":"Intuitionistic logic","level":3,"score":0.3513999879360199},{"id":"https://openalex.org/C39685927","wikidata":"https://www.wikidata.org/wiki/Q173183","display_name":"Boolean algebra","level":2,"score":0.35010001063346863},{"id":"https://openalex.org/C33203268","wikidata":"https://www.wikidata.org/wiki/Q5361594","display_name":"Intermediate logic","level":3,"score":0.34769999980926514},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.34529998898506165},{"id":"https://openalex.org/C136726353","wikidata":"https://www.wikidata.org/wiki/Q903789","display_name":"Disjunctive normal form","level":2,"score":0.3418000042438507},{"id":"https://openalex.org/C14523651","wikidata":"https://www.wikidata.org/wiki/Q3492863","display_name":"Propositional variable","level":4,"score":0.335999995470047},{"id":"https://openalex.org/C144760519","wikidata":"https://www.wikidata.org/wiki/Q839490","display_name":"Substructural logic","level":4,"score":0.3264999985694885},{"id":"https://openalex.org/C3845977","wikidata":"https://www.wikidata.org/wiki/Q4826262","display_name":"Autoepistemic logic","level":4,"score":0.3122999966144562},{"id":"https://openalex.org/C150889026","wikidata":"https://www.wikidata.org/wiki/Q185502","display_name":"Many-valued logic","level":3,"score":0.30709999799728394},{"id":"https://openalex.org/C2318724","wikidata":"https://www.wikidata.org/wiki/Q852732","display_name":"Proof theory","level":3,"score":0.30550000071525574},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.3043999969959259},{"id":"https://openalex.org/C74640108","wikidata":"https://www.wikidata.org/wiki/Q1372900","display_name":"Propositional formula","level":5,"score":0.30390000343322754},{"id":"https://openalex.org/C46274116","wikidata":"https://www.wikidata.org/wiki/Q185521","display_name":"Truth value","level":2,"score":0.30329999327659607},{"id":"https://openalex.org/C197115733","wikidata":"https://www.wikidata.org/wiki/Q1003136","display_name":"Forcing (mathematics)","level":2,"score":0.29600000381469727},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.29429998993873596},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2711000144481659},{"id":"https://openalex.org/C2780432614","wikidata":"https://www.wikidata.org/wiki/Q864213","display_name":"Conservative extension","level":2,"score":0.2709999978542328},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.2549000084400177},{"id":"https://openalex.org/C125411270","wikidata":"https://www.wikidata.org/wiki/Q18653","display_name":"Encoding (memory)","level":2,"score":0.25119999051094055}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:drops-oai.dagstuhl.de:26833","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.LICS.2026.46","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol380-lics2026/LIPIcs.LICS.2026.46/LIPIcs.LICS.2026.46.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","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":"doi:10.4230/lipics.lics.2026.46","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.lics.2026.46","pdf_url":null,"source":null,"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:drops-oai.dagstuhl.de:26833","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.LICS.2026.46","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol380-lics2026/LIPIcs.LICS.2026.46/LIPIcs.LICS.2026.46.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","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"},"sustainable_development_goals":[{"score":0.6033225655555725,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G2198898644","display_name":null,"funder_award_id":"H2020-MSCA-RISE-2020","funder_id":"https://openalex.org/F4320332999","funder_display_name":"Horizon 2020 Framework Programme"},{"id":"https://openalex.org/G3223141065","display_name":null,"funder_award_id":"101007627","funder_id":"https://openalex.org/F4320332999","funder_display_name":"Horizon 2020 Framework Programme"},{"id":"https://openalex.org/G3345895242","display_name":null,"funder_award_id":"H2020-MSCA","funder_id":"https://openalex.org/F4320332999","funder_display_name":"Horizon 2020 Framework Programme"},{"id":"https://openalex.org/G3477743816","display_name":null,"funder_award_id":"H2020-MSCA-RISE","funder_id":"https://openalex.org/F4320332999","funder_display_name":"Horizon 2020 Framework Programme"},{"id":"https://openalex.org/G3921594597","display_name":"Complexities of Well-quasi-order-based logics through Proof Theory (COMWELT)","funder_award_id":"OCENW.M.22.258","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G5866100518","display_name":null,"funder_award_id":"406.21","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G6388471989","display_name":"Nothing is Logical (NihiL): Neglect-zero effects in reasoning and interpretation","funder_award_id":"406.21.CTW.023","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"}],"funders":[{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"},{"id":"https://openalex.org/F4320332999","display_name":"Horizon 2020 Framework Programme","ror":"https://ror.org/00k4n6c32"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7167813166.pdf","grobid_xml":"https://content.openalex.org/works/W7167813166.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0],"logic":[1,115],"of":[2,31,57,61,76],"bunched":[3],"implications":[4],"(BI),":[5],"introduced":[6],"by":[7,43],"O\u2019Hearn":[8],"and":[9,24,78,88,117],"Pym":[10],"(1999),":[11],"has":[12],"attracted":[13],"significant":[14],"attention":[15],"due":[16],"to":[17,27,70,85,125],"its":[18,48],"elegant":[19],"proof":[20],"calculus,":[21],"varied":[22],"semantics,":[23],"close":[25],"connections":[26],"the":[28,55,58,71,81,89,113,121,143,146],"propositional":[29],"fragment":[30],"separation":[32],"logic.":[33],"We":[34,140],"show":[35],"here":[36],"that":[37,110,135],"provability":[38],"in":[39,145],"BI":[40,119,136],"is":[41,65],"undecidable":[42],"encoding":[44],"Wang":[45],"tilings":[46],"into":[47,99],"ternary":[49],"relational":[50],"semantics.":[51],"Equivalently,":[52],"this":[53],"yields":[54],"undecidability":[56],"equational":[59],"theory":[60],"BI-algebras.":[62],"Our":[63],"result":[64,106,129],"much":[66],"more":[67],"general,":[68],"applying":[69],"{\u2227,":[72],"\u2228,":[73],"\u00ac,":[74],"-*}-fragment":[75],"stronger":[77],"weaker":[79],"logics:":[80],"negation":[82],"simply":[83],"needs":[84],"be":[86,94,126,138],"disjointive,":[87],"multiplicative":[90],"conjunction":[91],"need":[92],"not":[93],"commutative":[95],"(then":[96],"-*":[97],"splits":[98],"two":[100],"divisions":[101],"\u29f5,":[102],"\u2215).":[103],"Consequently,":[104],"our":[105],"covers":[107],"an":[108],"interval":[109],"includes":[111],"BI,":[112],"non-commutative":[114],"GBI,":[116],"Boolean":[118],"(BBI),":[120],"latter":[122],"already":[123],"known":[124],"undecidable.":[127],"This":[128],"contrasts":[130],"with":[131],"a":[132],"long-standing":[133],"expectation":[134],"might":[137],"decidable.":[139],"also":[141],"identify":[142],"gaps":[144],"publications":[147],"claiming":[148],"decidability.":[149]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-07-10T00:00:00"}