{"id":"https://openalex.org/W4391167623","doi":"https://doi.org/10.3390/axioms13020076","title":"Boolean Subtypes of the U4 Hexagon of Opposition","display_name":"Boolean Subtypes of the U4 Hexagon of Opposition","publication_year":2024,"publication_date":"2024-01-24","ids":{"openalex":"https://openalex.org/W4391167623","doi":"https://doi.org/10.3390/axioms13020076"},"language":"en","primary_location":{"id":"doi:10.3390/axioms13020076","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13020076","pdf_url":"https://www.mdpi.com/2075-1680/13/2/76/pdf?version=1706091161","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/13/2/76/pdf?version=1706091161","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051081904","display_name":"Lorenz Demey","orcid":"https://orcid.org/0000-0002-0176-1958"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"Lorenz Demey","raw_affiliation_strings":["Center for Logic and Philosophy of Science, KU Leuven, 3000 Leuven, Belgium","KU Leuven Institute for Artificial Intelligence, KU Leuven, 3000 Leuven, Belgium"],"raw_orcid":"https://orcid.org/0000-0002-0176-1958","affiliations":[{"raw_affiliation_string":"Center for Logic and Philosophy of Science, KU Leuven, 3000 Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]},{"raw_affiliation_string":"KU Leuven Institute for Artificial Intelligence, KU Leuven, 3000 Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5093776885","display_name":"Atahan Erbas","orcid":"https://orcid.org/0000-0003-1863-8777"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Atahan Erbas","raw_affiliation_strings":["Center for Logic and Philosophy of Science, KU Leuven, 3000 Leuven, Belgium"],"raw_orcid":"https://orcid.org/0000-0003-1863-8777","affiliations":[{"raw_affiliation_string":"Center for Logic and Philosophy of Science, KU Leuven, 3000 Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5051081904"],"corresponding_institution_ids":["https://openalex.org/I99464096"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":1.0276,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.76228482,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":97},"biblio":{"volume":"13","issue":"2","first_page":"76","last_page":"76"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9940000176429749,"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":0.9940000176429749,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9891999959945679,"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":0.9495000243186951,"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/opposition","display_name":"Opposition (politics)","score":0.7835768461227417},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.3416966199874878},{"id":"https://openalex.org/keywords/political-science","display_name":"Political science","score":0.34156662225723267},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.21219363808631897},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.07949221134185791},{"id":"https://openalex.org/keywords/politics","display_name":"Politics","score":0.05840033292770386}],"concepts":[{"id":"https://openalex.org/C2780668109","wikidata":"https://www.wikidata.org/wiki/Q192852","display_name":"Opposition (politics)","level":3,"score":0.7835768461227417},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.3416966199874878},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.34156662225723267},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.21219363808631897},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.07949221134185791},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.05840033292770386}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms13020076","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13020076","pdf_url":"https://www.mdpi.com/2075-1680/13/2/76/pdf?version=1706091161","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:lirias2repo.kuleuven.be:20.500.12942/735665","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/20.500.12942/735665","pdf_url":"https://lirias.kuleuven.be/retrieve/33b9fd24-574d-4686-b962-c8609f5851f7","source":{"id":"https://openalex.org/S7407055369","display_name":"Lirias","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":"Axioms, vol. 13 (2), Art.No. 76, (1-20)","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:doaj.org/article:25e24e0adbb54330843092b4cf30d46d","is_oa":true,"landing_page_url":"https://doaj.org/article/25e24e0adbb54330843092b4cf30d46d","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 13, Iss 2, p 76 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms13020076","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13020076","pdf_url":"https://www.mdpi.com/2075-1680/13/2/76/pdf?version=1706091161","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1857803026","display_name":null,"funder_award_id":"IDN-19-009","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"},{"id":"https://openalex.org/G2291634242","display_name":null,"funder_award_id":"101040049","funder_id":"https://openalex.org/F4320322308","funder_display_name":"KU Leuven"},{"id":"https://openalex.org/G3322763786","display_name":null,"funder_award_id":"IDN-19-009","funder_id":"https://openalex.org/F4320322308","funder_display_name":"KU Leuven"},{"id":"https://openalex.org/G5227081768","display_name":"Towards a Systematic Theory of Aristotelian Diagrams in Logical Geometry","funder_award_id":"101040049","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G7195515175","display_name":null,"funder_award_id":"101040049","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320322308","display_name":"KU Leuven","ror":"https://ror.org/05f950310"},{"id":"https://openalex.org/F4320334678","display_name":"European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4391167623.pdf"},"referenced_works_count":56,"referenced_works":["https://openalex.org/W193908926","https://openalex.org/W217221060","https://openalex.org/W1500029195","https://openalex.org/W1930345655","https://openalex.org/W1963972041","https://openalex.org/W1969081181","https://openalex.org/W1989242467","https://openalex.org/W1999963832","https://openalex.org/W2000136482","https://openalex.org/W2001457416","https://openalex.org/W2005586845","https://openalex.org/W2022007219","https://openalex.org/W2023429459","https://openalex.org/W2023667931","https://openalex.org/W2037730906","https://openalex.org/W2044926618","https://openalex.org/W2049004042","https://openalex.org/W2083863362","https://openalex.org/W2089336371","https://openalex.org/W2089525093","https://openalex.org/W2089907006","https://openalex.org/W2133551789","https://openalex.org/W2179211458","https://openalex.org/W2219204552","https://openalex.org/W2264275978","https://openalex.org/W2314679416","https://openalex.org/W2331920816","https://openalex.org/W2332639719","https://openalex.org/W2335736099","https://openalex.org/W2345009590","https://openalex.org/W2346447115","https://openalex.org/W2476283206","https://openalex.org/W2592067820","https://openalex.org/W2614826371","https://openalex.org/W2750030610","https://openalex.org/W2789132423","https://openalex.org/W2800845814","https://openalex.org/W2804436922","https://openalex.org/W2899169730","https://openalex.org/W2945492887","https://openalex.org/W3177269891","https://openalex.org/W4232781137","https://openalex.org/W4234138073","https://openalex.org/W4238138617","https://openalex.org/W4243638179","https://openalex.org/W4251340532","https://openalex.org/W4253025657","https://openalex.org/W4292714226","https://openalex.org/W4294837972","https://openalex.org/W4317206684","https://openalex.org/W4376611709","https://openalex.org/W4387419996","https://openalex.org/W4388695632","https://openalex.org/W4399977702","https://openalex.org/W6671664196","https://openalex.org/W6964286790"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W182058443","https://openalex.org/W2490768301","https://openalex.org/W3171504412","https://openalex.org/W2490610300","https://openalex.org/W4361003648","https://openalex.org/W39094661","https://openalex.org/W3040061915","https://openalex.org/W4240920334","https://openalex.org/W4386380567"],"abstract_inverted_index":{"This":[0],"paper":[1],"investigates":[2],"the":[3,15,24,29,33,59,75,84,107,135],"so-called":[4,60],"\u2018unconnectedness-4":[5],"(U4)":[6],"hexagons":[7,112],"of":[8,18,32,35,52,70,77,99,110,126,138,143],"opposition\u2019,":[9],"which":[10,146],"have":[11],"various":[12,156],"applications":[13],"across":[14],"broad":[16],"field":[17],"philosophical":[19],"logic.":[20,79],"We":[21,80],"first":[22],"study":[23,65],"oldest":[25],"known":[26],"U4":[27,46,68,97,111,120],"hexagon,":[28],"conversion":[30],"closure":[31,93],"square":[34,86],"opposition":[36],"for":[37],"categorical":[38,85],"statements.":[39],"In":[40],"particular,":[41],"we":[42,64,104],"show":[43,88],"that":[44,89,106],"this":[45],"hexagon":[47,69,98,121],"has":[48,113,122],"a":[49,66,123,140],"Boolean":[50,71,100,116,124,160],"complexity":[51,72,101,125],"5,":[53],"and":[54,87,159],"discuss":[55],"its":[56],"connection":[57],"with":[58],"\u2018Gergonne":[61],"relations\u2019.":[62],"Next,":[63],"simple":[67],"4,":[73],"in":[74],"context":[76],"propositional":[78],"then":[81],"return":[82],"to":[83,134,150],"another":[90,96],"(quite":[91],"subtle)":[92],"operation":[94],"yields":[95],"4.":[102],"Finally,":[103],"prove":[105],"Aristotelian":[108,144,157],"family":[109],"no":[114],"other":[115],"subtypes,":[117],"i.e.,":[118],"every":[119],"either":[127],"4":[128],"or":[129],"5.":[130],"These":[131],"results":[132],"contribute":[133],"overarching":[136],"goal":[137],"developing":[139],"comprehensive":[141],"typology":[142],"diagrams,":[145],"will":[147],"allow":[148],"us":[149],"systematically":[151],"classify":[152],"these":[153],"diagrams":[154],"into":[155],"families":[158],"subfamilies.":[161]},"counts_by_year":[{"year":2024,"cited_by_count":3}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}