{"id":"https://openalex.org/W2026457733","doi":"https://doi.org/10.1215/00294527-2009-012","title":"\u2208 I : An Intuitionistic Logic without Fregean Axiom and with Predicates for Truth and Falsity","display_name":"\u2208 I : An Intuitionistic Logic without Fregean Axiom and with Predicates for Truth and Falsity","publication_year":2009,"publication_date":"2009-07-01","ids":{"openalex":"https://openalex.org/W2026457733","doi":"https://doi.org/10.1215/00294527-2009-012","mag":"2026457733"},"language":"en","primary_location":{"id":"doi:10.1215/00294527-2009-012","is_oa":true,"landing_page_url":"https://doi.org/10.1215/00294527-2009-012","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-50/issue-3/-I---An-Intuitionistic-Logic-without-Fregean-Axiom/10.1215/00294527-2009-012.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-50/issue-3/-I---An-Intuitionistic-Logic-without-Fregean-Axiom/10.1215/00294527-2009-012.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015019892","display_name":"Steffen Lewitzka","orcid":"https://orcid.org/0000-0003-0685-9134"},"institutions":[{"id":"https://openalex.org/I169045520","display_name":"Universidade Federal da Para\u00edba","ror":"https://ror.org/00p9vpz11","country_code":"BR","type":"education","lineage":["https://openalex.org/I169045520"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Steffen Lewitzka","raw_affiliation_strings":["Universidade Federal da Para\u00edba-UFPB Departamento de Inform\u00e1tica Centro de Ci\u00eancias Exatas e da Natureza CEP 58.035-000 Jo\u00e3o Pessoa PB BRAZIL"],"affiliations":[{"raw_affiliation_string":"Universidade Federal da Para\u00edba-UFPB Departamento de Inform\u00e1tica Centro de Ci\u00eancias Exatas e da Natureza CEP 58.035-000 Jo\u00e3o Pessoa PB BRAZIL","institution_ids":["https://openalex.org/I169045520"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5015019892"],"corresponding_institution_ids":["https://openalex.org/I169045520"],"apc_list":null,"apc_paid":null,"fwci":2.6171,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.90432942,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"50","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9994999766349792,"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":0.9987999796867371,"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/T10215","display_name":"Semantic Web and Ontologies","score":0.9961000084877014,"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/falsity","display_name":"Falsity","score":0.5301284193992615},{"id":"https://openalex.org/keywords/truth-value","display_name":"Truth value","score":0.48546651005744934},{"id":"https://openalex.org/keywords/intuitionistic-logic","display_name":"Intuitionistic logic","score":0.48293110728263855},{"id":"https://openalex.org/keywords/predicate","display_name":"Predicate (mathematical logic)","score":0.4728042483329773},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42622435092926025},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3907359838485718},{"id":"https://openalex.org/keywords/propositional-calculus","display_name":"Propositional calculus","score":0.3720719516277313},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.287345826625824},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.27950865030288696},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.21779906749725342},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.12173396348953247}],"concepts":[{"id":"https://openalex.org/C2777685122","wikidata":"https://www.wikidata.org/wiki/Q170028","display_name":"Falsity","level":2,"score":0.5301284193992615},{"id":"https://openalex.org/C46274116","wikidata":"https://www.wikidata.org/wiki/Q185521","display_name":"Truth value","level":2,"score":0.48546651005744934},{"id":"https://openalex.org/C178421362","wikidata":"https://www.wikidata.org/wiki/Q176786","display_name":"Intuitionistic logic","level":3,"score":0.48293110728263855},{"id":"https://openalex.org/C140146324","wikidata":"https://www.wikidata.org/wiki/Q1144319","display_name":"Predicate (mathematical logic)","level":2,"score":0.4728042483329773},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42622435092926025},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3907359838485718},{"id":"https://openalex.org/C69562738","wikidata":"https://www.wikidata.org/wiki/Q200694","display_name":"Propositional calculus","level":2,"score":0.3720719516277313},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.287345826625824},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.27950865030288696},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.21779906749725342},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.12173396348953247}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1215/00294527-2009-012","is_oa":true,"landing_page_url":"https://doi.org/10.1215/00294527-2009-012","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-50/issue-3/-I---An-Intuitionistic-Logic-without-Fregean-Axiom/10.1215/00294527-2009-012.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.ndjfl/1257862039","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.ndjfl/1257862039","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1215/00294527-2009-012","is_oa":true,"landing_page_url":"https://doi.org/10.1215/00294527-2009-012","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-50/issue-3/-I---An-Intuitionistic-Logic-without-Fregean-Axiom/10.1215/00294527-2009-012.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.47999998927116394,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2026457733.pdf","grobid_xml":"https://content.openalex.org/works/W2026457733.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W46517763","https://openalex.org/W124229871","https://openalex.org/W197729581","https://openalex.org/W329876089","https://openalex.org/W1548945680","https://openalex.org/W1760954332","https://openalex.org/W1973517051","https://openalex.org/W2004833088","https://openalex.org/W2006426192","https://openalex.org/W2039426105","https://openalex.org/W2056546032","https://openalex.org/W2077094328","https://openalex.org/W2092370259","https://openalex.org/W2160745555","https://openalex.org/W2313916554","https://openalex.org/W2402064102","https://openalex.org/W2403653109","https://openalex.org/W3183889129","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W150180408","https://openalex.org/W4388372553","https://openalex.org/W1991636605","https://openalex.org/W1986625420","https://openalex.org/W2383907964","https://openalex.org/W2351034882","https://openalex.org/W2363368467","https://openalex.org/W2384278060","https://openalex.org/W2387802791","https://openalex.org/W2516402362"],"abstract_inverted_index":{"We":[0,139,167],"present":[1,63,172],"\u2208":[2,21,33,52,151],"I":[3,22,152],"-Logic":[4],"(Epsilon-I-Logic),":[5],"a":[6,11,15,41,55,97,111,120,129,173],"non-Fregean":[7],"intuitionistic":[8,19,27,68,107,146],"logic":[9,32],"with":[10,45],"truth":[12,44],"predicate":[13,17],"and":[14,26,70,95,122,171],"falsity":[16],"as":[18,40],"negation.":[20],"is":[23,160],"an":[24,67,145],"extension":[25,127],"generalization":[28],"of":[29,43,51,100,117,119,126,128,157,163,178],"the":[30,62,82,86,106,115,123,136,141,158,161,176],"classical":[31,137],"T":[34,53],"(without":[35],"quantifiers)":[36],"designed":[37],"by":[38,85],"Str\u00e4ter":[39],"theory":[42],"propositional":[46],"self-reference.":[47],"The":[48],"intensional":[49,101,169],"semantics":[50,69],"offers":[54],"new":[56,87],"solution":[57],"to":[58,110,144],"semantic":[59,73],"paradoxes.":[60],"In":[61],"paper":[64,159],"we":[65,80],"introduce":[66],"study":[71],"some":[72],"notions":[74],"in":[75,105,135,150],"this":[76],"broader":[77],"context.":[78],"Also":[79],"enrich":[81],"quantifier-free":[83],"language":[84],"connective":[88],"<":[89],"that":[90],"expresses":[91],"reference":[92],"between":[93,114],"statements":[94],"yields":[96],"finer":[98],"characterization":[99],"models.":[102],"Our":[103],"results":[104],"setting":[108],"lead":[109],"clear":[112],"distinction":[113],"notion":[116,125],"denotation":[118],"sentence":[121,130],"here-proposed":[124],"(both":[131],"concepts":[132],"are":[133],"equivalent":[134],"context).":[138],"generalize":[140],"Fregean":[142],"Axiom":[143],"version":[147],"not":[148],"valid":[149],".":[153],"A":[154],"main":[155],"result":[156],"development":[162],"several":[164],"model":[165],"constructions.":[166],"construct":[168],"models":[170,180],"method":[174],"for":[175],"construction":[177],"standard":[179],"which":[181],"contain":[182],"specific":[183],"(self-)referential":[184],"propositions.":[185]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}