{"id":"https://openalex.org/W2140371133","doi":"https://doi.org/10.1080/13875860801944887","title":"On Embedding a Qualitative Representation in a Two-Dimensional Plane","display_name":"On Embedding a Qualitative Representation in a Two-Dimensional Plane","publication_year":2008,"publication_date":"2008-05-22","ids":{"openalex":"https://openalex.org/W2140371133","doi":"https://doi.org/10.1080/13875860801944887","mag":"2140371133"},"language":"en","primary_location":{"id":"doi:10.1080/13875860801944887","is_oa":false,"landing_page_url":"https://doi.org/10.1080/13875860801944887","pdf_url":null,"source":{"id":"https://openalex.org/S4121042","display_name":"Spatial Cognition and Computation","issn_l":"1387-5868","issn":["1387-5868","1542-7633","1573-9252"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Spatial Cognition & Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100892549","display_name":"Kazuko Takahashi","orcid":null},"institutions":[{"id":"https://openalex.org/I206011266","display_name":"Kwansei Gakuin University","ror":"https://ror.org/02qf2tx24","country_code":"JP","type":"education","lineage":["https://openalex.org/I206011266"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Kazuko Takahashi","raw_affiliation_strings":["a  Kwansei Gakuin University","Kwansei Gakuin University"],"affiliations":[{"raw_affiliation_string":"a  Kwansei Gakuin University","institution_ids":["https://openalex.org/I206011266"]},{"raw_affiliation_string":"Kwansei Gakuin University","institution_ids":["https://openalex.org/I206011266"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047757989","display_name":"Takao Sumitomo","orcid":null},"institutions":[{"id":"https://openalex.org/I206011266","display_name":"Kwansei Gakuin University","ror":"https://ror.org/02qf2tx24","country_code":"JP","type":"education","lineage":["https://openalex.org/I206011266"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Takao Sumitomo","raw_affiliation_strings":["a  Kwansei Gakuin University","Kwansei Gakuin University"],"affiliations":[{"raw_affiliation_string":"a  Kwansei Gakuin University","institution_ids":["https://openalex.org/I206011266"]},{"raw_affiliation_string":"Kwansei Gakuin University","institution_ids":["https://openalex.org/I206011266"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000908442","display_name":"Izumi Takeuti","orcid":"https://orcid.org/0000-0001-7235-2281"},"institutions":[{"id":"https://openalex.org/I73613424","display_name":"National Institute of Advanced Industrial Science and Technology","ror":"https://ror.org/01703db54","country_code":"JP","type":"government","lineage":["https://openalex.org/I73613424"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Izumi Takeuti","raw_affiliation_strings":["b  National Institute of Advanced Industrial Science and Technology","National Institute of Advanced Industrial Science and Technology"],"affiliations":[{"raw_affiliation_string":"b  National Institute of Advanced Industrial Science and Technology","institution_ids":["https://openalex.org/I73613424"]},{"raw_affiliation_string":"National Institute of Advanced Industrial Science and Technology","institution_ids":["https://openalex.org/I73613424"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100892549"],"corresponding_institution_ids":["https://openalex.org/I206011266"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.16318615,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"8","issue":"1-2","first_page":"4","last_page":"26"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T11106","display_name":"Data Management and Algorithms","score":0.9944999814033508,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9832000136375427,"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/expression","display_name":"Expression (computer science)","score":0.8208993673324585},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.7207989692687988},{"id":"https://openalex.org/keywords/correctness","display_name":"Correctness","score":0.717274010181427},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.711869478225708},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.6196189522743225},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5265089869499207},{"id":"https://openalex.org/keywords/realizability","display_name":"Realizability","score":0.5197758078575134},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42955532670021057},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4258395731449127},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.38849252462387085},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2789660096168518},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.24340349435806274}],"concepts":[{"id":"https://openalex.org/C90559484","wikidata":"https://www.wikidata.org/wiki/Q778379","display_name":"Expression (computer science)","level":2,"score":0.8208993673324585},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.7207989692687988},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.717274010181427},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.711869478225708},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.6196189522743225},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5265089869499207},{"id":"https://openalex.org/C2776378722","wikidata":"https://www.wikidata.org/wiki/Q3454417","display_name":"Realizability","level":2,"score":0.5197758078575134},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42955532670021057},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4258395731449127},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38849252462387085},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2789660096168518},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.24340349435806274},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/13875860801944887","is_oa":false,"landing_page_url":"https://doi.org/10.1080/13875860801944887","pdf_url":null,"source":{"id":"https://openalex.org/S4121042","display_name":"Spatial Cognition and Computation","issn_l":"1387-5868","issn":["1387-5868","1542-7633","1573-9252"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Spatial Cognition & Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320325302","display_name":"Shanghai Ocean University","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W852874","https://openalex.org/W145918469","https://openalex.org/W186516023","https://openalex.org/W228803548","https://openalex.org/W582967230","https://openalex.org/W1486682191","https://openalex.org/W1542039873","https://openalex.org/W1871668702","https://openalex.org/W2089868779","https://openalex.org/W2132112596","https://openalex.org/W2207098507","https://openalex.org/W2269814849","https://openalex.org/W2346933546","https://openalex.org/W2612978016","https://openalex.org/W2626914210","https://openalex.org/W2913012755","https://openalex.org/W4214494916"],"related_works":["https://openalex.org/W1603488308","https://openalex.org/W4298120007","https://openalex.org/W2136737082","https://openalex.org/W2321910655","https://openalex.org/W3173554384","https://openalex.org/W1517224694","https://openalex.org/W1857750633","https://openalex.org/W2051968535","https://openalex.org/W2033443491","https://openalex.org/W2963559218"],"abstract_inverted_index":{"Abstract":[0],"This":[1],"paper":[2],"discusses":[3],"embedding":[4],"in":[5,50,53,80,112],"a":[6,9,33,37,42,51,68,81,113,123],"two-dimensional":[7,65,114],"plane":[8,115],"symbolic":[10],"representation":[11],"for":[12,36,64,100],"spatial":[13,39],"data":[14],"using":[15],"the":[16,45,56,62,73,76,91,102,105],"simple":[17],"objects,":[18],"points":[19],"(P),":[20],"lines":[21],"(L),":[22],"circuits":[23],"(C),":[24],"and":[25,71,116],"areas":[26],"(A).":[27],"We":[28,60,95],"have":[29],"proposed":[30],"PLCA":[31,43,69,82,106],"as":[32],"new":[34],"framework":[35],"qualitative":[38,127],"reasoning.":[40],"In":[41,86],"expression,":[44,70],"entire":[46],"figure":[47,103],"is":[48],"represented":[49],"form":[52],"which":[54],"all":[55],"objects":[57,79],"are":[58],"related.":[59],"investigate":[61],"conditions":[63],"realizability":[66],"of":[67,78,104],"derive":[72],"relation":[74],"that":[75,108],"numbers":[77],"expression":[83,107,125],"should":[84],"have.":[85],"this":[87,110],"process,":[88],"we":[89],"use":[90],"well-known":[92],"Euler's":[93],"formula.":[94],"also":[96],"give":[97],"an":[98],"algorithm":[99,121],"drawing":[101],"satisfies":[109],"condition":[111],"prove":[117],"its":[118],"correctness.":[119],"The":[120],"generates":[122],"quantitative":[124],"from":[126],"expression.":[128]},"counts_by_year":[{"year":2015,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}