{"id":"https://openalex.org/W2069430084","doi":"https://doi.org/10.1305/ndjfl/1093882937","title":"Substitutions for predicate variables and functional variables.","display_name":"Substitutions for predicate variables and functional variables.","publication_year":1980,"publication_date":"1980-01-01","ids":{"openalex":"https://openalex.org/W2069430084","doi":"https://doi.org/10.1305/ndjfl/1093882937","mag":"2069430084"},"language":"en","primary_location":{"id":"doi:10.1305/ndjfl/1093882937","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093882937","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-21/issue-1/Substitutions-for-predicate-variables-and-functional-variables/10.1305/ndjfl/1093882937.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-21/issue-1/Substitutions-for-predicate-variables-and-functional-variables/10.1305/ndjfl/1093882937.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041294923","display_name":"Hubert H. Schneider","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Hubert H. Schneider","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5041294923"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.10414475,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"21","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10215","display_name":"Semantic Web and Ontologies","score":0.6211000084877014,"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/T10215","display_name":"Semantic Web and Ontologies","score":0.6211000084877014,"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/T10317","display_name":"Advanced Database Systems and Queries","score":0.590499997138977,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/predicate","display_name":"Predicate (mathematical logic)","score":0.6772845983505249},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4585556387901306},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4063534736633301},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.3166075646877289}],"concepts":[{"id":"https://openalex.org/C140146324","wikidata":"https://www.wikidata.org/wiki/Q1144319","display_name":"Predicate (mathematical logic)","level":2,"score":0.6772845983505249},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4585556387901306},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4063534736633301},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.3166075646877289}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1305/ndjfl/1093882937","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093882937","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-21/issue-1/Substitutions-for-predicate-variables-and-functional-variables/10.1305/ndjfl/1093882937.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/1093882937","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.ndjfl/1093882937","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/1093882937","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093882937","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-21/issue-1/Substitutions-for-predicate-variables-and-functional-variables/10.1305/ndjfl/1093882937.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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2069430084.pdf","grobid_xml":"https://content.openalex.org/works/W2069430084.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W1486199300","https://openalex.org/W2041833446"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644"],"abstract_inverted_index":{"The":[0,230,234],"customary":[1],"descriptions":[2],"regarding":[3],"substitution":[4,29,44,133,144,157,193,217,227,250],"for":[5,68,134,145,158,164,194,213,261],"predicate":[6,135,159,195],"variables":[7,147,160,166,196],"are":[8],"quite":[9],"involved":[10],"and":[11,35,100,179],"sometimes":[12],"more":[13],"restrictive":[14,120],"than":[15],"would":[16],"be":[17,113,170,219],"necessary.A":[18],"precise":[19],"statement":[20],"of":[21,28,56,77,85,143,156,189,192,210,216,226,236,239,246,249,258],"the":[22,57,61,65,75,83,88,92,103,126,130,176,182,199,202,255,259],"conditions":[23],"under":[24],"which":[25,167,180],"this":[26,150],"type":[27,225],"is":[30,32,148,197],"permissible":[31],"very":[33],"complex":[34,186],"often":[36],"has":[37],"been":[38],"inadequate":[39],"in":[40,102,115,129,264],"rendering":[41],"a":[42,47],"validity-preserving":[43],"rule":[45],"(for":[46],"detailed":[48],"account":[49],"with":[50],"references":[51],"see":[52],"Church":[53,206],"[1],":[54,207],"pp.289-290).Some":[55],"difficulties":[58,137],"arise":[59],"from":[60,74],"restrictions":[62,72,107],"placed":[63,108],"on":[64,109],"formation":[66],"rules":[67,122],"(well-formed)":[69],"formulas;":[70],"these":[71],"range":[73],"inadmissibility":[76],"vacuous":[78],"quantifiers":[79,81,86],"or":[80],"within":[82],"scope":[84,188],"using":[87],"same":[89,104,183,200],"variables,":[90],"to":[91,112,169],"requirement":[93],"that":[94,223],"no":[95],"variable":[96],"may":[97],"occur":[98,138],"free":[99],"bound":[101],"formula.Although":[105],"such":[106],"formulas":[110],"appear":[111],"impractical":[114],"many":[116],"respects,":[117],"even":[118],"less":[119],"formulation":[121,142],"do":[123],"not":[124],"eliminate":[125],"complications":[127],"inherent":[128],"process":[131],"involving":[132],"variables.Additional":[136],"when":[139],"an":[140],"adequate":[141],"functional":[146,165],"considered.In":[149],"paper*":[151],"we":[152],"present":[153],"recursive":[154],"definitions":[155],"as":[161,163,173,175,201],"well":[162],"seem":[168],"at":[171,181,254],"least":[172],"general":[174],"usual":[177],"formulations":[178,212],"time":[184],"avoid":[185],"descriptions.The":[187],"our":[190,211,240],"definition":[191],"essentially":[198],"description":[203,245],"given":[204],"by":[205,221],"pp.192-193.The":[208],"adequacy":[209],"both":[214,247],"types":[215,248],"will":[218],"established":[220],"showing":[222],"each":[224],"preserves":[228],"validity.1":[229],"formal":[231,241],"language":[232,242],"1.1":[233],"list":[235],"primitive":[237],"symbols":[238],"includes":[243],"*A":[244],"was":[251],"first":[252],"presented":[253],"1974":[256],"meeting":[257],"Association":[260],"Symbolic":[262],"Logic":[263],"New":[265],"York":[266],"[3].":[267]},"counts_by_year":[{"year":2019,"cited_by_count":1}],"updated_date":"2026-08-04T08:18:43.703281","created_date":"2025-10-10T00:00:00"}