{"id":"https://openalex.org/W2042433712","doi":"https://doi.org/10.1305/ndjfl/1040248454","title":"Levels of Truth","display_name":"Levels of Truth","publication_year":1995,"publication_date":"1995-04-01","ids":{"openalex":"https://openalex.org/W2042433712","doi":"https://doi.org/10.1305/ndjfl/1040248454","mag":"2042433712"},"language":"fr","primary_location":{"id":"doi:10.1305/ndjfl/1040248454","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1040248454","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-36/issue-2/Levels-of-Truth/10.1305/ndjfl/1040248454.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-36/issue-2/Levels-of-Truth/10.1305/ndjfl/1040248454.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5009435902","display_name":"Andrea Cantini","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Andrea Cantini","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5009435902"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.16896032,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"36","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9972000122070312,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9972000122070312,"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":0.9958999752998352,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9930999875068665,"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/predicative-expression","display_name":"Predicative expression","score":0.8877843618392944},{"id":"https://openalex.org/keywords/predicate","display_name":"Predicate (mathematical logic)","score":0.5500676035881042},{"id":"https://openalex.org/keywords/partial-function","display_name":"Partial function","score":0.5287700891494751},{"id":"https://openalex.org/keywords/predicate-abstraction","display_name":"Predicate abstraction","score":0.4828091859817505},{"id":"https://openalex.org/keywords/semantic-theory-of-truth","display_name":"Semantic theory of truth","score":0.44457656145095825},{"id":"https://openalex.org/keywords/combinatory-logic","display_name":"Combinatory logic","score":0.439073383808136},{"id":"https://openalex.org/keywords/type-theory","display_name":"Type theory","score":0.4389571249485016},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4346919059753418},{"id":"https://openalex.org/keywords/abstraction","display_name":"Abstraction","score":0.4344256818294525},{"id":"https://openalex.org/keywords/model-theory","display_name":"Model theory","score":0.4263145923614502},{"id":"https://openalex.org/keywords/semantics","display_name":"Semantics (computer science)","score":0.42362987995147705},{"id":"https://openalex.org/keywords/coherence-theory-of-truth","display_name":"Coherence theory of truth","score":0.4152927100658417},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.413627028465271},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.36182111501693726},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3379537761211395},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.32168659567832947},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.2948954999446869},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.28613442182540894},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.28025054931640625},{"id":"https://openalex.org/keywords/pragmatic-theory-of-truth","display_name":"Pragmatic theory of truth","score":0.2799847722053528},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.2687488794326782},{"id":"https://openalex.org/keywords/model-checking","display_name":"Model checking","score":0.1213138997554779}],"concepts":[{"id":"https://openalex.org/C129131279","wikidata":"https://www.wikidata.org/wiki/Q1931259","display_name":"Predicative expression","level":2,"score":0.8877843618392944},{"id":"https://openalex.org/C140146324","wikidata":"https://www.wikidata.org/wiki/Q1144319","display_name":"Predicate (mathematical logic)","level":2,"score":0.5500676035881042},{"id":"https://openalex.org/C182359184","wikidata":"https://www.wikidata.org/wiki/Q1756942","display_name":"Partial function","level":2,"score":0.5287700891494751},{"id":"https://openalex.org/C2779907942","wikidata":"https://www.wikidata.org/wiki/Q7239630","display_name":"Predicate abstraction","level":3,"score":0.4828091859817505},{"id":"https://openalex.org/C39095165","wikidata":"https://www.wikidata.org/wiki/Q7449101","display_name":"Semantic theory of truth","level":2,"score":0.44457656145095825},{"id":"https://openalex.org/C79678938","wikidata":"https://www.wikidata.org/wiki/Q1481571","display_name":"Combinatory logic","level":2,"score":0.439073383808136},{"id":"https://openalex.org/C93682546","wikidata":"https://www.wikidata.org/wiki/Q1056428","display_name":"Type theory","level":3,"score":0.4389571249485016},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4346919059753418},{"id":"https://openalex.org/C124304363","wikidata":"https://www.wikidata.org/wiki/Q673661","display_name":"Abstraction","level":2,"score":0.4344256818294525},{"id":"https://openalex.org/C47030870","wikidata":"https://www.wikidata.org/wiki/Q467606","display_name":"Model theory","level":2,"score":0.4263145923614502},{"id":"https://openalex.org/C184337299","wikidata":"https://www.wikidata.org/wiki/Q1437428","display_name":"Semantics (computer science)","level":2,"score":0.42362987995147705},{"id":"https://openalex.org/C107553210","wikidata":"https://www.wikidata.org/wiki/Q4179467","display_name":"Coherence theory of truth","level":3,"score":0.4152927100658417},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.413627028465271},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.36182111501693726},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3379537761211395},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.32168659567832947},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.2948954999446869},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.28613442182540894},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.28025054931640625},{"id":"https://openalex.org/C197199266","wikidata":"https://www.wikidata.org/wiki/Q7237641","display_name":"Pragmatic theory of truth","level":2,"score":0.2799847722053528},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.2687488794326782},{"id":"https://openalex.org/C110251889","wikidata":"https://www.wikidata.org/wiki/Q1569697","display_name":"Model checking","level":2,"score":0.1213138997554779},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1305/ndjfl/1040248454","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1040248454","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-36/issue-2/Levels-of-Truth/10.1305/ndjfl/1040248454.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/1040248454","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.ndjfl/1040248454","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:10.1305/ndjfl/1040248454","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1040248454","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-36/issue-2/Levels-of-Truth/10.1305/ndjfl/1040248454.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":[{"display_name":"Quality Education","score":0.5799999833106995,"id":"https://metadata.un.org/sdg/4"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320310992","display_name":"University of Bern","ror":"https://ror.org/02k7v4d05"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2042433712.pdf","grobid_xml":"https://content.openalex.org/works/W2042433712.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W40029885","https://openalex.org/W45464644","https://openalex.org/W46517763","https://openalex.org/W78146983","https://openalex.org/W83139932","https://openalex.org/W91708239","https://openalex.org/W191705811","https://openalex.org/W1491173026","https://openalex.org/W1495279852","https://openalex.org/W1587614821","https://openalex.org/W1980836075","https://openalex.org/W1989033022","https://openalex.org/W2006111919","https://openalex.org/W2010145817","https://openalex.org/W2025127850","https://openalex.org/W2026625753","https://openalex.org/W2050939025","https://openalex.org/W2057420885","https://openalex.org/W2074338252","https://openalex.org/W2114374802","https://openalex.org/W2154273644","https://openalex.org/W2193662464","https://openalex.org/W2217500413","https://openalex.org/W2272797014","https://openalex.org/W2614091510","https://openalex.org/W4236867936","https://openalex.org/W4247606924","https://openalex.org/W4293117209","https://openalex.org/W6607793215","https://openalex.org/W6647461974","https://openalex.org/W6737909288","https://openalex.org/W6996798720"],"related_works":["https://openalex.org/W652392562","https://openalex.org/W4236954471","https://openalex.org/W114558113","https://openalex.org/W4386050346","https://openalex.org/W2481351689","https://openalex.org/W2364674872","https://openalex.org/W4200315634","https://openalex.org/W2387718228","https://openalex.org/W2366294845","https://openalex.org/W2143745068"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2,84],"concerned":[3],"with":[4,33,64],"the":[5,11,25],"interaction":[6],"between":[7],"formal":[8,18],"semantics":[9],"and":[10,38],"foundations":[12],"of":[13,20,30,41,56,78],"mathematics.":[14],"We":[15],"introduce":[16],"a":[17,34,39,46,54,73],"theory":[19,29,55],"truth,":[21],"TLR,":[22],"which":[23,60],"extends":[24],"classical":[26],"first":[27],"order":[28,80],"pure":[31],"combinators":[32],"primitive":[35],"truth":[36,42],"predicate":[37],"family":[40],"approximations,":[43],"indexed":[44],"by":[45],"directed":[47],"partial":[48,57],"ordering.":[49],"TLR":[50,67,83],"naturally":[51],"works":[52],"as":[53],"classifications,":[58],"in":[59],"type-free":[61],"comprehension":[62],"coexists":[63],"functional":[65],"abstraction.":[66],"provides":[68],"an":[69],"inner":[70],"model":[71],"for":[72],"well":[74],"known":[75],"subsystem":[76],"$\\mbox{ATR}_0$":[77],"second":[79],"arithmetic;":[81],"indeed,":[82],"proof-theoretically":[85],"equivalent":[86],"to":[87],"Predicative":[88],"Analysis.":[89]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}