{"id":"https://openalex.org/W2091698138","doi":"https://doi.org/10.1080/0308107021000042462","title":"Searching for the roots of non-contradiction and excluded-middle","display_name":"Searching for the roots of non-contradiction and excluded-middle","publication_year":2002,"publication_date":"2002-09-01","ids":{"openalex":"https://openalex.org/W2091698138","doi":"https://doi.org/10.1080/0308107021000042462","mag":"2091698138"},"language":"en","primary_location":{"id":"doi:10.1080/0308107021000042462","is_oa":false,"landing_page_url":"https://doi.org/10.1080/0308107021000042462","pdf_url":null,"source":{"id":"https://openalex.org/S145553572","display_name":"International Journal of General Systems","issn_l":"0308-1079","issn":["0308-1079","1026-7492","1563-5104"],"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":"International Journal of General Systems","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/A5010221865","display_name":"Enric Trillas","orcid":null},"institutions":[{"id":"https://openalex.org/I88060688","display_name":"Universidad Polit\u00e9cnica de Madrid","ror":"https://ror.org/03n6nwv02","country_code":"ES","type":"education","lineage":["https://openalex.org/I88060688"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"E. Trillas","raw_affiliation_strings":["Department de Inteligencia Artificial , Universidad Polit\u00e9cnica de Madrid , Madrid,  Spain","Dept. de Inteligencia Artificial, Universidad Polit\u00e9cnica de Madrid, Madrid, Spain"],"affiliations":[{"raw_affiliation_string":"Department de Inteligencia Artificial , Universidad Polit\u00e9cnica de Madrid , Madrid,  Spain","institution_ids":["https://openalex.org/I88060688"]},{"raw_affiliation_string":"Dept. de Inteligencia Artificial, Universidad Polit\u00e9cnica de Madrid, Madrid, Spain","institution_ids":["https://openalex.org/I88060688"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113564245","display_name":"C. Alsina","orcid":null},"institutions":[{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"C. Alsina","raw_affiliation_strings":["Secci\u00f3 de Matem\u00e0tiques i Inform\u00e0tica, Department d'Estructures a l'Arquitectura , Universitat Polit\u00e8cnica de Catalunya , Barcelona,  Spain","Secci\u00f3 de Matem\u00e0tiques I Inform\u00e0tica, Department D\u2019Estructures a L\u2019Arquitectura, Universitat Polit\u00e8cnica de Catalunya, Barcelona, Spain"],"affiliations":[{"raw_affiliation_string":"Secci\u00f3 de Matem\u00e0tiques i Inform\u00e0tica, Department d'Estructures a l'Arquitectura , Universitat Polit\u00e8cnica de Catalunya , Barcelona,  Spain","institution_ids":["https://openalex.org/I9617848"]},{"raw_affiliation_string":"Secci\u00f3 de Matem\u00e0tiques I Inform\u00e0tica, Department D\u2019Estructures a L\u2019Arquitectura, Universitat Polit\u00e8cnica de Catalunya, Barcelona, Spain","institution_ids":["https://openalex.org/I9617848"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016634871","display_name":"Ana Pradera","orcid":"https://orcid.org/0000-0002-8364-5087"},"institutions":[{"id":"https://openalex.org/I182083151","display_name":"Universidad Rey Juan Carlos","ror":"https://ror.org/01v5cv687","country_code":"ES","type":"education","lineage":["https://openalex.org/I182083151"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"A. Pradera","raw_affiliation_strings":["Department de Ciencias Experimentales e Ingenier\u00faa , Universidad Rey Juan Carlos , Madrid,  Spain","Department de Ciencias Experimentales e Ingenier\u00faa , Universidad Rey Juan Carlos , Madrid, Spain"],"affiliations":[{"raw_affiliation_string":"Department de Ciencias Experimentales e Ingenier\u00faa , Universidad Rey Juan Carlos , Madrid,  Spain","institution_ids":["https://openalex.org/I182083151"]},{"raw_affiliation_string":"Department de Ciencias Experimentales e Ingenier\u00faa , Universidad Rey Juan Carlos , Madrid, Spain","institution_ids":["https://openalex.org/I182083151"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5010221865"],"corresponding_institution_ids":["https://openalex.org/I88060688"],"apc_list":null,"apc_paid":null,"fwci":1.35636948,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.79266405,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"31","issue":"5","first_page":"499","last_page":"513"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9998000264167786,"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":0.9998000264167786,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9980999827384949,"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":0.9965000152587891,"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/contradiction","display_name":"Contradiction","score":0.9309559464454651},{"id":"https://openalex.org/keywords/falsity","display_name":"Falsity","score":0.907992959022522},{"id":"https://openalex.org/keywords/law-of-excluded-middle","display_name":"Law of excluded middle","score":0.8046371936798096},{"id":"https://openalex.org/keywords/nothing","display_name":"Nothing","score":0.5860000848770142},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5666481256484985},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5562077164649963},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.5210413336753845},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4632170796394348},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.41499632596969604},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38223332166671753},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.37120363116264343},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3592822551727295},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.3309539556503296},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.327501505613327},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.281948447227478},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.24004334211349487},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.22005605697631836},{"id":"https://openalex.org/keywords/political-science","display_name":"Political science","score":0.08222681283950806}],"concepts":[{"id":"https://openalex.org/C2776728590","wikidata":"https://www.wikidata.org/wiki/Q363948","display_name":"Contradiction","level":2,"score":0.9309559464454651},{"id":"https://openalex.org/C2777685122","wikidata":"https://www.wikidata.org/wiki/Q170028","display_name":"Falsity","level":2,"score":0.907992959022522},{"id":"https://openalex.org/C137155000","wikidata":"https://www.wikidata.org/wiki/Q468422","display_name":"Law of excluded middle","level":2,"score":0.8046371936798096},{"id":"https://openalex.org/C136815107","wikidata":"https://www.wikidata.org/wiki/Q154242","display_name":"Nothing","level":2,"score":0.5860000848770142},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5666481256484985},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5562077164649963},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5210413336753845},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4632170796394348},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.41499632596969604},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38223332166671753},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.37120363116264343},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3592822551727295},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.3309539556503296},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.327501505613327},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.281948447227478},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.24004334211349487},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.22005605697631836},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.08222681283950806},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/0308107021000042462","is_oa":false,"landing_page_url":"https://doi.org/10.1080/0308107021000042462","pdf_url":null,"source":{"id":"https://openalex.org/S145553572","display_name":"International Journal of General Systems","issn_l":"0308-1079","issn":["0308-1079","1026-7492","1563-5104"],"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":"International Journal of General Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.75,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1485625483","https://openalex.org/W1544789403","https://openalex.org/W1963923925","https://openalex.org/W1989959848","https://openalex.org/W2018670695","https://openalex.org/W2031750296","https://openalex.org/W2039611746","https://openalex.org/W2054416947","https://openalex.org/W2154820307","https://openalex.org/W2164429865","https://openalex.org/W2182044576","https://openalex.org/W2211815936","https://openalex.org/W2320516263","https://openalex.org/W2616337127","https://openalex.org/W2808650095","https://openalex.org/W4234672050"],"related_works":["https://openalex.org/W262916403","https://openalex.org/W2382448393","https://openalex.org/W4245674526","https://openalex.org/W2740779761","https://openalex.org/W2379388383","https://openalex.org/W2091698138","https://openalex.org/W99640185","https://openalex.org/W2150425213","https://openalex.org/W2253128004","https://openalex.org/W2103953657"],"abstract_inverted_index":{"This":[0],"paper":[1],"tries":[2],"to":[3,54,72,80,84,106],"obtain":[4],"frameworks":[5],"in":[6,90],"which":[7],"one":[8],"can":[9],"prove":[10],"as":[11,39,41,86],"theorems,":[12],"and":[13,22,35,70,82],"with":[14,56],"few":[15],"assumptions,":[16],"the":[17,42,60,76],"laws":[18,77],"of":[19,29,44,63],"non-contradiction":[20],"(NC)":[21],"excluded-middle":[23],"(EM),":[24],"for":[25,59],"a":[26,57,68],"large":[27],"class":[28],"very":[30],"general":[31],"systems":[32],"including":[33],"orthocomplemented":[34],"De":[36],"Morgan":[37],"lattices,":[38],"well":[40],"theories":[43],"L":[45],"-fuzzy":[46],"sets.":[47],"Its":[48],"goal":[49],"is":[50,88,94,104],"nothing":[51],"else":[52],"than":[53],"begin":[55],"search":[58],"algebraic":[61],"roots":[62],"these":[64],"laws.":[65],"For":[66],"such":[67],"goal,":[69],"similarly":[71],"ancient":[73],"Aristotelian":[74],"logic,":[75],"are":[78,99],"referred":[79],"self-contradiction":[81],"not":[83],"falsity":[85],"it":[87,103],"done":[89],"modern":[91],"logics.":[92],"It":[93],"additionally":[95],"shown":[96],"that":[97,110,114],"there":[98],"some":[100],"structures":[101],"where":[102],"possible":[105],"find":[107],"special":[108],"operations":[109,113],"separate":[111],"those":[112,118],"verify":[115],"NC":[116],"from":[117],"verifying":[119],"EM.":[120]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}