{"id":"https://openalex.org/W3038775138","doi":"https://doi.org/10.3233/ao-200233","title":"CODI: A multidimensional theory of mereotopology with closure operations","display_name":"CODI: A multidimensional theory of mereotopology with closure operations","publication_year":2020,"publication_date":"2020-07-03","ids":{"openalex":"https://openalex.org/W3038775138","doi":"https://doi.org/10.3233/ao-200233","mag":"3038775138"},"language":"en","primary_location":{"id":"doi:10.3233/ao-200233","is_oa":false,"landing_page_url":"https://doi.org/10.3233/ao-200233","pdf_url":null,"source":{"id":"https://openalex.org/S31619775","display_name":"Applied Ontology","issn_l":"1570-5838","issn":["1570-5838","1875-8533"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Ontology","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/A5002315545","display_name":"Torsten Hahmann","orcid":"https://orcid.org/0000-0002-5331-5052"},"institutions":[{"id":"https://openalex.org/I7947594","display_name":"University of Maine","ror":"https://ror.org/01adr0w49","country_code":"US","type":"education","lineage":["https://openalex.org/I2802397601","https://openalex.org/I7947594"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Torsten Hahmann","raw_affiliation_strings":["Spatial Informatics, School of Computing and Information Science, University of Maine, Orono, ME 04469, USA. E-mail:\u00a0torsten@spatial.maine.edu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Spatial Informatics, School of Computing and Information Science, University of Maine, Orono, ME 04469, USA. E-mail:\u00a0torsten@spatial.maine.edu","institution_ids":["https://openalex.org/I7947594"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5002315545"],"corresponding_institution_ids":["https://openalex.org/I7947594"],"apc_list":null,"apc_paid":null,"fwci":0.2682,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.62144611,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"15","issue":"3","first_page":"251","last_page":"311"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.9918000102043152,"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":0.9918000102043152,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9894000291824341,"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":0.984000027179718,"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/mereology","display_name":"Mereology","score":0.9081593751907349},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6523008942604065},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.546853244304657},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.5317026376724243},{"id":"https://openalex.org/keywords/geometric-data-analysis","display_name":"Geometric data analysis","score":0.4862312376499176},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4825705587863922},{"id":"https://openalex.org/keywords/polyhedron","display_name":"Polyhedron","score":0.4545716941356659},{"id":"https://openalex.org/keywords/spatial-intelligence","display_name":"Spatial intelligence","score":0.42436283826828003},{"id":"https://openalex.org/keywords/spatial-analysis","display_name":"Spatial analysis","score":0.4109063446521759},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32725077867507935},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.27564486861228943},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.24169504642486572},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.195902019739151},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.1626604199409485},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1170433759689331}],"concepts":[{"id":"https://openalex.org/C152385842","wikidata":"https://www.wikidata.org/wiki/Q1194916","display_name":"Mereology","level":2,"score":0.9081593751907349},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6523008942604065},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.546853244304657},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.5317026376724243},{"id":"https://openalex.org/C136520226","wikidata":"https://www.wikidata.org/wiki/Q302814","display_name":"Geometric data analysis","level":2,"score":0.4862312376499176},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4825705587863922},{"id":"https://openalex.org/C54829058","wikidata":"https://www.wikidata.org/wiki/Q172937","display_name":"Polyhedron","level":2,"score":0.4545716941356659},{"id":"https://openalex.org/C155911833","wikidata":"https://www.wikidata.org/wiki/Q3817354","display_name":"Spatial intelligence","level":2,"score":0.42436283826828003},{"id":"https://openalex.org/C159620131","wikidata":"https://www.wikidata.org/wiki/Q1938983","display_name":"Spatial analysis","level":2,"score":0.4109063446521759},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32725077867507935},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.27564486861228943},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.24169504642486572},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.195902019739151},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.1626604199409485},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1170433759689331},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/ao-200233","is_oa":false,"landing_page_url":"https://doi.org/10.3233/ao-200233","pdf_url":null,"source":{"id":"https://openalex.org/S31619775","display_name":"Applied Ontology","issn_l":"1570-5838","issn":["1570-5838","1875-8533"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Ontology","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":63,"referenced_works":["https://openalex.org/W852874","https://openalex.org/W30700190","https://openalex.org/W70090750","https://openalex.org/W116506501","https://openalex.org/W188981234","https://openalex.org/W606831423","https://openalex.org/W1483417608","https://openalex.org/W1490709150","https://openalex.org/W1526337814","https://openalex.org/W1533244802","https://openalex.org/W1543653180","https://openalex.org/W1562214614","https://openalex.org/W1563428815","https://openalex.org/W1603382969","https://openalex.org/W1644586429","https://openalex.org/W1807555267","https://openalex.org/W1844476468","https://openalex.org/W1871668702","https://openalex.org/W1963829561","https://openalex.org/W1974871840","https://openalex.org/W2001015432","https://openalex.org/W2024632301","https://openalex.org/W2053967911","https://openalex.org/W2066676451","https://openalex.org/W2075123415","https://openalex.org/W2083911811","https://openalex.org/W2092974662","https://openalex.org/W2105134882","https://openalex.org/W2153720118","https://openalex.org/W2226128168","https://openalex.org/W2240909318","https://openalex.org/W2259771146","https://openalex.org/W2485416360","https://openalex.org/W2551756190","https://openalex.org/W2577435553","https://openalex.org/W2760186826","https://openalex.org/W2785432024","https://openalex.org/W2792053886","https://openalex.org/W2893708922","https://openalex.org/W2912402120","https://openalex.org/W2913900359","https://openalex.org/W2978908124","https://openalex.org/W3136285069","https://openalex.org/W3139934447","https://openalex.org/W4237275816","https://openalex.org/W4238516204","https://openalex.org/W4249889216","https://openalex.org/W4256212569","https://openalex.org/W4407809846","https://openalex.org/W6600033781","https://openalex.org/W6638306832","https://openalex.org/W6639430512","https://openalex.org/W6656661440","https://openalex.org/W6670739832","https://openalex.org/W6671486641","https://openalex.org/W6689285282","https://openalex.org/W6731815363","https://openalex.org/W6732361938","https://openalex.org/W6748073800","https://openalex.org/W6758789241","https://openalex.org/W6792505420","https://openalex.org/W6837275519","https://openalex.org/W7081432248"],"related_works":["https://openalex.org/W1491555559","https://openalex.org/W2912584064","https://openalex.org/W2094255012","https://openalex.org/W2394461203","https://openalex.org/W107034217","https://openalex.org/W1492444612","https://openalex.org/W2912068123","https://openalex.org/W1032240194","https://openalex.org/W2067772625","https://openalex.org/W1573847701"],"abstract_inverted_index":{"Geometric":[0],"data":[1,84,104],"models":[2,105,202,208,232],"form":[3],"the":[4,66,142,145,210,231,259],"backbone":[5],"of":[6,21,35,71,92,128,144,157,163,168,172,189,193,224,230,235,258,262],"virtually":[7],"all":[8,187,206,218],"spatial":[9,22,121,133,190,219],"information":[10,23,81],"systems,":[11],"such":[12,131],"as":[13,126,233],"GIS,":[14],"CAD,":[15],"and":[16,57,101,113,175,204,254,265],"CAM.":[17],"Yet":[18],"a":[19,72,86,154,159,222],"lot":[20],"from":[24,141,251],"textual":[25],"sources,":[26],"including":[27],"historical":[28],"documents":[29],"or":[30],"social":[31],"media,":[32],"is":[33,179,197,213],"predominantly":[34],"qualitative,":[36],"especially":[37],"mereotopological,":[38],"rather":[39],"than":[40],"geometric":[41,83,100],"-quantitative":[42],"nature.":[43],"While":[44],"mereotopological":[45,80],"theories":[46],"have":[47],"been":[48],"extensively":[49],"studied":[50],"in":[51,65,148,181],"Logic,":[52],"Computer":[53],"Science,":[54,56,60],"Cognitive":[55],"Geographic":[58],"Information":[59],"most":[61],"are":[62,75,243],"unidimensional":[63,252],"mereotopologies":[64],"sense":[67],"that":[68,132,199],"only":[69],"entities":[70,91,130,147,191,220],"single":[73],"dimension":[74],"permitted":[76],"to":[77,95,98,115,123,186,216,246,255],"co-exist.":[78,116],"Integrating":[79],"with":[82],"requires":[85,119],"multidimensional":[87,164],"mereotopology,":[88],"which":[89,182],"permits":[90],"different":[93],"dimensions":[94],"co-exist,":[96],"similarly":[97],"how":[99],"algebraic":[102],"topological":[103],"permit":[106],"points,":[107],"simple":[108],"lines,":[109],"polylines,":[110],"cells,":[111],"polygons,":[112],"polyhedra":[114],"It":[117,196],"further":[118,244],"complex":[120,136],"objects":[122,137],"be":[124,139],"represented":[125],"sets":[127,234],"atomic":[129,146,201,225],"relations":[134,143],"between":[135],"can":[138],"computed":[140],"their":[149,194],"decomposition.":[150],"This":[151],"paper":[152],"provides":[153],"comprehensive":[155],"study":[156],"CODI,":[158],"first-order":[160],"logic":[161],"ontology":[162],"mereotopology.":[165],"An":[166],"axiomatization":[167],"mereological":[169,249],"closure":[170,241],"operations":[171,184,242],"intersection,":[173],"difference,":[174],"sums":[176],"for":[177,200],"CODI":[178],"proposed":[180],"these":[183],"apply":[185],"pairs":[188],"regardless":[192],"dimension.":[195],"proved":[198],"\u2013":[203,209],"thus":[205],"finite":[207],"extended":[211],"theory":[212],"indeed":[214],"able":[215],"decompose":[217],"into":[221],"partition":[223],"parts.":[226],"A":[227],"full":[228],"representation":[229],"Boolean":[236],"algebras":[237],"verifies":[238],"this.":[239],"The":[240],"shown":[245],"satisfy":[247],"important":[248],"principles":[250],"mereotopology":[253],"preserve":[256],"many":[257],"mathematical":[260],"properties":[261],"set":[263,266],"intersection":[264],"difference.":[267]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-07-30T17:31:21.811387","created_date":"2025-10-10T00:00:00"}