{"id":"https://openalex.org/W2075419333","doi":"https://doi.org/10.1145/1071596.1071598","title":"On the complexity of the disjunction property in intuitionistic and modal logics","display_name":"On the complexity of the disjunction property in intuitionistic and modal logics","publication_year":2005,"publication_date":"2005-07-01","ids":{"openalex":"https://openalex.org/W2075419333","doi":"https://doi.org/10.1145/1071596.1071598","mag":"2075419333"},"language":"en","primary_location":{"id":"doi:10.1145/1071596.1071598","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1071596.1071598","pdf_url":null,"source":{"id":"https://openalex.org/S117153874","display_name":"ACM Transactions on Computational Logic","issn_l":"1529-3785","issn":["1529-3785","1557-945X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Computational Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/2434/4800","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102948163","display_name":"Mauro Ferrari","orcid":"https://orcid.org/0000-0002-7904-1125"},"institutions":[{"id":"https://openalex.org/I189158943","display_name":"University of Milan","ror":"https://ror.org/00wjc7c48","country_code":"IT","type":"education","lineage":["https://openalex.org/I189158943"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Mauro Ferrari","raw_affiliation_strings":["Universit\u00e0 degli Studi di Milano, Milan, Italy"],"affiliations":[{"raw_affiliation_string":"Universit\u00e0 degli Studi di Milano, Milan, Italy","institution_ids":["https://openalex.org/I189158943"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011583391","display_name":"Camillo Fiorentini","orcid":"https://orcid.org/0000-0003-2152-7488"},"institutions":[{"id":"https://openalex.org/I189158943","display_name":"University of Milan","ror":"https://ror.org/00wjc7c48","country_code":"IT","type":"education","lineage":["https://openalex.org/I189158943"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Camillo Fiorentini","raw_affiliation_strings":["Universit\u00e0 degli Studi di Milano, Milan, Italy"],"affiliations":[{"raw_affiliation_string":"Universit\u00e0 degli Studi di Milano, Milan, Italy","institution_ids":["https://openalex.org/I189158943"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090594213","display_name":"Guido Fiorino","orcid":"https://orcid.org/0000-0002-0556-0723"},"institutions":[{"id":"https://openalex.org/I66752286","display_name":"University of Milano-Bicocca","ror":"https://ror.org/01ynf4891","country_code":"IT","type":"education","lineage":["https://openalex.org/I66752286"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Guido Fiorino","raw_affiliation_strings":["Universit\u00e0 degli Studi di Milano-Bicocca, Milan, Italy"],"affiliations":[{"raw_affiliation_string":"Universit\u00e0 degli Studi di Milano-Bicocca, Milan, Italy","institution_ids":["https://openalex.org/I66752286"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5102948163"],"corresponding_institution_ids":["https://openalex.org/I189158943"],"apc_list":null,"apc_paid":null,"fwci":1.755,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.86991302,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"6","issue":"3","first_page":"519","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":0.9998999834060669,"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":0.9998999834060669,"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":0.9990000128746033,"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":0.9987000226974487,"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/normal-modal-logic","display_name":"Normal modal logic","score":0.7168428897857666},{"id":"https://openalex.org/keywords/intuitionistic-logic","display_name":"Intuitionistic logic","score":0.6839606761932373},{"id":"https://openalex.org/keywords/modal-logic","display_name":"Modal logic","score":0.6809173822402954},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6729482412338257},{"id":"https://openalex.org/keywords/s5","display_name":"S5","score":0.6071091890335083},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.5295102596282959},{"id":"https://openalex.org/keywords/accessibility-relation","display_name":"Accessibility relation","score":0.5087071061134338},{"id":"https://openalex.org/keywords/modal","display_name":"Modal","score":0.5077039003372192},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.48005354404449463},{"id":"https://openalex.org/keywords/intermediate-logic","display_name":"Intermediate logic","score":0.47821447253227234},{"id":"https://openalex.org/keywords/normalization","display_name":"Normalization (sociology)","score":0.4736165702342987},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.4711008667945862},{"id":"https://openalex.org/keywords/kripke-semantics","display_name":"Kripke semantics","score":0.4334265887737274},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.40004920959472656},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.36094802618026733},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3022058606147766},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19990235567092896},{"id":"https://openalex.org/keywords/linear-logic","display_name":"Linear logic","score":0.15710806846618652},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.1558467447757721},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.11036211252212524}],"concepts":[{"id":"https://openalex.org/C114092440","wikidata":"https://www.wikidata.org/wiki/Q840226","display_name":"Normal modal logic","level":4,"score":0.7168428897857666},{"id":"https://openalex.org/C178421362","wikidata":"https://www.wikidata.org/wiki/Q176786","display_name":"Intuitionistic logic","level":3,"score":0.6839606761932373},{"id":"https://openalex.org/C27508121","wikidata":"https://www.wikidata.org/wiki/Q210841","display_name":"Modal logic","level":3,"score":0.6809173822402954},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6729482412338257},{"id":"https://openalex.org/C192609573","wikidata":"https://www.wikidata.org/wiki/Q7388341","display_name":"S5","level":5,"score":0.6071091890335083},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.5295102596282959},{"id":"https://openalex.org/C11191006","wikidata":"https://www.wikidata.org/wiki/Q2663311","display_name":"Accessibility relation","level":4,"score":0.5087071061134338},{"id":"https://openalex.org/C71139939","wikidata":"https://www.wikidata.org/wiki/Q910194","display_name":"Modal","level":2,"score":0.5077039003372192},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.48005354404449463},{"id":"https://openalex.org/C33203268","wikidata":"https://www.wikidata.org/wiki/Q5361594","display_name":"Intermediate logic","level":3,"score":0.47821447253227234},{"id":"https://openalex.org/C136886441","wikidata":"https://www.wikidata.org/wiki/Q926129","display_name":"Normalization (sociology)","level":2,"score":0.4736165702342987},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.4711008667945862},{"id":"https://openalex.org/C160131679","wikidata":"https://www.wikidata.org/wiki/Q2462350","display_name":"Kripke semantics","level":4,"score":0.4334265887737274},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.40004920959472656},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.36094802618026733},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3022058606147766},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19990235567092896},{"id":"https://openalex.org/C28077239","wikidata":"https://www.wikidata.org/wiki/Q841728","display_name":"Linear logic","level":2,"score":0.15710806846618652},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.1558467447757721},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.11036211252212524},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C19165224","wikidata":"https://www.wikidata.org/wiki/Q23404","display_name":"Anthropology","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/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"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":4,"locations":[{"id":"doi:10.1145/1071596.1071598","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1071596.1071598","pdf_url":null,"source":{"id":"https://openalex.org/S117153874","display_name":"ACM Transactions on Computational Logic","issn_l":"1529-3785","issn":["1529-3785","1557-945X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Computational Logic","raw_type":"journal-article"},{"id":"pmh:oai:air.unimi.it:2434/4800","is_oa":true,"landing_page_url":"http://hdl.handle.net/2434/4800","pdf_url":null,"source":{"id":"https://openalex.org/S4306400516","display_name":"Archivio Istituzionale della Ricerca (Universita Degli Studi Di Milano)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I189158943","host_organization_name":"University of Milan","host_organization_lineage":["https://openalex.org/I189158943"],"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":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:boa.unimib.it:10281/997","is_oa":false,"landing_page_url":"http://hdl.handle.net/10281/997","pdf_url":null,"source":{"id":"https://openalex.org/S4306401259","display_name":"BOA (University of Milano-Bicocca)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66752286","host_organization_name":"University of Milano-Bicocca","host_organization_lineage":["https://openalex.org/I66752286"],"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":"info:eu-repo/semantics/article"},{"id":"pmh:oai:irinsubria.uninsubria.it:11383/1504070","is_oa":false,"landing_page_url":"http://hdl.handle.net/11383/1504070","pdf_url":null,"source":{"id":"https://openalex.org/S4377196351","display_name":"IrInSubria (University of Insubria)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I115752224","host_organization_name":"University of Insubria","host_organization_lineage":["https://openalex.org/I115752224"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:air.unimi.it:2434/4800","is_oa":true,"landing_page_url":"http://hdl.handle.net/2434/4800","pdf_url":null,"source":{"id":"https://openalex.org/S4306400516","display_name":"Archivio Istituzionale della Ricerca (Universita Degli Studi Di Milano)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I189158943","host_organization_name":"University of Milan","host_organization_lineage":["https://openalex.org/I189158943"],"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":"","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W33157876","https://openalex.org/W1487291494","https://openalex.org/W1530106163","https://openalex.org/W1562163515","https://openalex.org/W1607926272","https://openalex.org/W1795577507","https://openalex.org/W1972606747","https://openalex.org/W1979622965","https://openalex.org/W2005236741","https://openalex.org/W2042899834","https://openalex.org/W2052270606","https://openalex.org/W2058973858","https://openalex.org/W2095477479","https://openalex.org/W2492280620","https://openalex.org/W2970205057","https://openalex.org/W4388311772"],"related_works":["https://openalex.org/W2403418519","https://openalex.org/W3111905456","https://openalex.org/W2278216746","https://openalex.org/W3128849256","https://openalex.org/W2554822349","https://openalex.org/W2004665970","https://openalex.org/W2039904055","https://openalex.org/W2963628981","https://openalex.org/W1995638481","https://openalex.org/W1785615301"],"abstract_inverted_index":{"In":[0],"this":[1],"article":[2],"we":[3,36,44,56],"study":[4],"the":[5,13,25,29,39,50,65,71,75],"complexity":[6],"of":[7,28,52,64,83],"disjunction":[8],"property":[9],"for":[10,49,93],"intuitionistic":[11,26],"logic,":[12,21,23],"modal":[14,30],"logics":[15,92],"S4":[16,35],",":[17,19],"S4.1":[18],"Grzegorczyk":[20],"G\u00f6del-L\u00f6b":[22],"and":[24,43],"counterpart":[27],"logic":[31],"K":[32],".":[33],"For":[34],"even":[37],"prove":[38],"feasible":[40],"interpolation":[41],"theorem":[42,73],"provide":[45],"a":[46,80],"lower":[47],"bound":[48],"length":[51],"proofs.":[53],"The":[54],"techniques":[55],"use":[57],"do":[58],"not":[59],"require":[60],"proving":[61],"structural":[62],"properties":[63],"calculi":[66],"in":[67],"hand,":[68],"such":[69],"as":[70],"cut-elimination":[72],"or":[74],"normalization":[76],"theorem.":[77],"This":[78],"is":[79],"key":[81],"point":[82],"our":[84],"approach,":[85],"since":[86],"it":[87],"allows":[88],"us":[89],"to":[90],"treat":[91],"which":[94],"only":[95],"Hilbert-style":[96],"characterizations":[97],"are":[98],"known.":[99]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}