{"id":"https://openalex.org/W2760099783","doi":"https://doi.org/10.3390/sym9100204","title":"Logical and Geometrical Distance in Polyhedral Aristotelian Diagrams in Knowledge Representation","display_name":"Logical and Geometrical Distance in Polyhedral Aristotelian Diagrams in Knowledge Representation","publication_year":2017,"publication_date":"2017-09-29","ids":{"openalex":"https://openalex.org/W2760099783","doi":"https://doi.org/10.3390/sym9100204","mag":"2760099783"},"language":"en","primary_location":{"id":"doi:10.3390/sym9100204","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym9100204","pdf_url":"https://www.mdpi.com/2073-8994/9/10/204/pdf?version=1506686806","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/9/10/204/pdf?version=1506686806","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 Analytic Philosophy, KU Leuven, 3000 Leuven, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Logic and Analytic Philosophy, KU Leuven, 3000 Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032155501","display_name":"Hans Smessaert","orcid":"https://orcid.org/0000-0002-8186-0170"},"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":"Hans Smessaert","raw_affiliation_strings":["Research Group on Formal and Computational Linguistics, KU Leuven, 3000 Leuven, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Research Group on Formal and Computational Linguistics, 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":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.1955,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.81546105,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"9","issue":"10","first_page":"204","last_page":"204"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9713000059127808,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9713000059127808,"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":0.910099983215332,"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/T13083","display_name":"Advanced Text Analysis Techniques","score":0.9042999744415283,"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/tetrahedron","display_name":"Tetrahedron","score":0.7214337587356567},{"id":"https://openalex.org/keywords/dodecahedron","display_name":"Dodecahedron","score":0.6301291584968567},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.5762240886688232},{"id":"https://openalex.org/keywords/rotation-formalisms-in-three-dimensions","display_name":"Rotation formalisms in three dimensions","score":0.4867089092731476},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4429699182510376},{"id":"https://openalex.org/keywords/diagram","display_name":"Diagram","score":0.4177471697330475},{"id":"https://openalex.org/keywords/hexahedron","display_name":"Hexahedron","score":0.41401153802871704},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.39612337946891785},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.38618388772010803},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1011914610862732}],"concepts":[{"id":"https://openalex.org/C105239961","wikidata":"https://www.wikidata.org/wiki/Q160003","display_name":"Tetrahedron","level":2,"score":0.7214337587356567},{"id":"https://openalex.org/C94239619","wikidata":"https://www.wikidata.org/wiki/Q178296","display_name":"Dodecahedron","level":2,"score":0.6301291584968567},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.5762240886688232},{"id":"https://openalex.org/C171018156","wikidata":"https://www.wikidata.org/wiki/Q7370306","display_name":"Rotation formalisms in three dimensions","level":2,"score":0.4867089092731476},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4429699182510376},{"id":"https://openalex.org/C186399060","wikidata":"https://www.wikidata.org/wiki/Q959962","display_name":"Diagram","level":2,"score":0.4177471697330475},{"id":"https://openalex.org/C22411076","wikidata":"https://www.wikidata.org/wiki/Q668113","display_name":"Hexahedron","level":3,"score":0.41401153802871704},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39612337946891785},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.38618388772010803},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1011914610862732},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/sym9100204","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym9100204","pdf_url":"https://www.mdpi.com/2073-8994/9/10/204/pdf?version=1506686806","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/594264","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/123456789/594264","pdf_url":null,"source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Symmetry, vol. 9 (10), Art.No. 204","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:doaj.org/article:9a1479306a2e4666ae408c832cc23d68","is_oa":true,"landing_page_url":"https://doaj.org/article/9a1479306a2e4666ae408c832cc23d68","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":"Symmetry, Vol 9, Iss 10, p 204 (2017)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/9/10/204/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym9100204","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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":"Symmetry; Volume 9; Issue 10; Pages: 204","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym9100204","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym9100204","pdf_url":"https://www.mdpi.com/2073-8994/9/10/204/pdf?version=1506686806","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321730","display_name":"Fonds Wetenschappelijk Onderzoek","ror":"https://ror.org/03qtxy027"},{"id":"https://openalex.org/F4320327336","display_name":"Vlaamse regering","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2760099783.pdf","grobid_xml":"https://content.openalex.org/works/W2760099783.grobid-xml"},"referenced_works_count":107,"referenced_works":["https://openalex.org/W25412590","https://openalex.org/W46773933","https://openalex.org/W52313798","https://openalex.org/W89358548","https://openalex.org/W156379767","https://openalex.org/W206347215","https://openalex.org/W217221060","https://openalex.org/W266013613","https://openalex.org/W432400243","https://openalex.org/W623468948","https://openalex.org/W626407659","https://openalex.org/W1162524868","https://openalex.org/W1500029195","https://openalex.org/W1533381840","https://openalex.org/W1554939770","https://openalex.org/W1559666492","https://openalex.org/W1588388544","https://openalex.org/W1600589698","https://openalex.org/W1617290740","https://openalex.org/W1676982517","https://openalex.org/W1912497050","https://openalex.org/W1966710300","https://openalex.org/W1984656613","https://openalex.org/W1988046476","https://openalex.org/W1990100773","https://openalex.org/W1991650963","https://openalex.org/W1999273320","https://openalex.org/W2001457416","https://openalex.org/W2002093268","https://openalex.org/W2005586845","https://openalex.org/W2006941876","https://openalex.org/W2012074478","https://openalex.org/W2023727797","https://openalex.org/W2037730906","https://openalex.org/W2048545227","https://openalex.org/W2048748334","https://openalex.org/W2049004042","https://openalex.org/W2052154979","https://openalex.org/W2054204410","https://openalex.org/W2057761151","https://openalex.org/W2060314224","https://openalex.org/W2062388094","https://openalex.org/W2086796727","https://openalex.org/W2093397547","https://openalex.org/W2114669639","https://openalex.org/W2136224062","https://openalex.org/W2179211458","https://openalex.org/W2179956734","https://openalex.org/W2215856917","https://openalex.org/W2216040752","https://openalex.org/W2219204552","https://openalex.org/W2253255956","https://openalex.org/W2264275978","https://openalex.org/W2288821240","https://openalex.org/W2294374137","https://openalex.org/W2294851585","https://openalex.org/W2314679416","https://openalex.org/W2321236795","https://openalex.org/W2329972104","https://openalex.org/W2341415563","https://openalex.org/W2345474136","https://openalex.org/W2476283206","https://openalex.org/W2476954248","https://openalex.org/W2478931886","https://openalex.org/W2492656955","https://openalex.org/W2493277499","https://openalex.org/W2494268181","https://openalex.org/W2495014012","https://openalex.org/W2496035556","https://openalex.org/W2499258114","https://openalex.org/W2519758866","https://openalex.org/W2522916568","https://openalex.org/W2526877385","https://openalex.org/W2531452992","https://openalex.org/W2549731080","https://openalex.org/W2551440050","https://openalex.org/W2581369044","https://openalex.org/W2592067820","https://openalex.org/W2593074971","https://openalex.org/W2600077159","https://openalex.org/W2750030610","https://openalex.org/W2751198190","https://openalex.org/W2789483438","https://openalex.org/W2800845814","https://openalex.org/W2895239415","https://openalex.org/W2995102019","https://openalex.org/W3125217621","https://openalex.org/W3133654369","https://openalex.org/W4210492164","https://openalex.org/W4232040330","https://openalex.org/W4232781137","https://openalex.org/W4233906803","https://openalex.org/W4234138073","https://openalex.org/W4236119664","https://openalex.org/W4236216294","https://openalex.org/W4237494933","https://openalex.org/W4240494126","https://openalex.org/W4242916057","https://openalex.org/W4245218903","https://openalex.org/W4252208286","https://openalex.org/W4299811907","https://openalex.org/W4300958603","https://openalex.org/W4317650629","https://openalex.org/W6601877606","https://openalex.org/W6636303861","https://openalex.org/W6662685679","https://openalex.org/W6819340455"],"related_works":["https://openalex.org/W2750377778","https://openalex.org/W2281645065","https://openalex.org/W2037812407","https://openalex.org/W4231057703","https://openalex.org/W2330661319","https://openalex.org/W2383759168","https://openalex.org/W2109770908","https://openalex.org/W2962853751","https://openalex.org/W2290010570","https://openalex.org/W3144317966"],"abstract_inverted_index":{"Aristotelian":[0,46,62,125,174],"diagrams":[1,13,47,63],"visualize":[2],"the":[3,43,65,72,75,78,81,89,100,124,132,142,147,151,166,179],"logical":[4,106,138],"relations":[5],"among":[6],"a":[7],"finite":[8],"set":[9],"of":[10,88,94,114,119,135,154,171],"objects.":[11],"These":[12],"originated":[14],"in":[15,25,28,112],"philosophy,":[16],"but":[17],"recently,":[18],"they":[19],"have":[20],"also":[21],"been":[22],"used":[23,160],"extensively":[24],"artificial":[26],"intelligence,":[27],"order":[29],"to":[30,161,178],"study":[31],"(connections":[32],"between)":[33],"various":[34],"knowledge":[35],"representation":[36],"formalisms.":[37],"In":[38,55],"this":[39,120],"paper,":[40],"we":[41,57,98],"develop":[42],"idea":[44],"that":[45,123],"can":[48],"be":[49],"fruitfully":[50],"studied":[51],"as":[52],"geometrical":[53,90,109,140],"entities.":[54],"particular,":[56],"focus":[58],"on":[59,165,185],"four":[60],"polyhedral":[61,96,173],"for":[64],"Boolean":[66],"algebra":[67],"B":[68],"4":[69],",":[70],"viz.":[71],"rhombic":[73,126],"dodecahedron,":[74],"tetrakis":[76,129],"hexahedron,":[77],"tetraicosahedron":[79,143],"and":[80,92,108,128,139,146,169],"nested":[82,148],"tetrahedron.":[83],"After":[84],"an":[85],"in-depth":[86],"investigation":[87],"properties":[91],"interrelationships":[93],"these":[95,115,157,172],"diagrams,":[97,175],"analyze":[99],"correlation":[101,136],"(or":[102],"lack":[103],"thereof)":[104],"between":[105,137],"(Hamming)":[107],"(Euclidean)":[110],"distance":[111],"each":[113],"diagrams.":[116],"The":[117],"outcome":[118],"analysis":[121],"is":[122],"dodecahedron":[127],"hexahedron":[130],"exhibit":[131],"strongest":[133],"degree":[134,153],"distance;":[141],"performs":[144],"worse;":[145],"tetrahedron":[149],"has":[150],"lowest":[152],"correlation.":[155],"Finally,":[156],"results":[158],"are":[159],"shed":[162],"new":[163],"light":[164],"relative":[167],"strengths":[168],"weaknesses":[170],"by":[176],"appealing":[177],"congruence":[180],"principle":[181],"from":[182],"cognitive":[183],"research":[184],"diagram":[186],"design.":[187]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2017-10-06T00:00:00"}
