{"id":"https://openalex.org/W2088329476","doi":"https://doi.org/10.1305/ndjfl/1093883043","title":"On substitution for variable one-place functors.","display_name":"On substitution for variable one-place functors.","publication_year":1980,"publication_date":"1980-04-01","ids":{"openalex":"https://openalex.org/W2088329476","doi":"https://doi.org/10.1305/ndjfl/1093883043","mag":"2088329476"},"language":"en","primary_location":{"id":"doi:10.1305/ndjfl/1093883043","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093883043","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-21/issue-2/On-substitution-for-variable-one-place-functors/10.1305/ndjfl/1093883043.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-2/On-substitution-for-variable-one-place-functors/10.1305/ndjfl/1093883043.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018942953","display_name":"Stanley J. Krolikoski","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Stanley J. Krolikoski","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5018942953"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.28518791,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"21","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.9886999726295471,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.9886999726295471,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.9686999917030334,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9570000171661377,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/substitution","display_name":"Substitution (logic)","score":0.8192526698112488},{"id":"https://openalex.org/keywords/functor","display_name":"Functor","score":0.6374256014823914},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.574590802192688},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4885629117488861},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2667064666748047},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2654988765716553},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.1476580798625946},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07008969783782959}],"concepts":[{"id":"https://openalex.org/C2778220771","wikidata":"https://www.wikidata.org/wiki/Q1522579","display_name":"Substitution (logic)","level":2,"score":0.8192526698112488},{"id":"https://openalex.org/C156772000","wikidata":"https://www.wikidata.org/wiki/Q864475","display_name":"Functor","level":2,"score":0.6374256014823914},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.574590802192688},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4885629117488861},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2667064666748047},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2654988765716553},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.1476580798625946},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07008969783782959}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1305/ndjfl/1093883043","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093883043","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-21/issue-2/On-substitution-for-variable-one-place-functors/10.1305/ndjfl/1093883043.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/1093883043","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.ndjfl/1093883043","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/1093883043","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093883043","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-21/issue-2/On-substitution-for-variable-one-place-functors/10.1305/ndjfl/1093883043.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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2088329476.pdf","grobid_xml":"https://content.openalex.org/works/W2088329476.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2379444625","https://openalex.org/W2393147081","https://openalex.org/W2575869988","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4308647020","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2370088286","https://openalex.org/W2061531152"],"abstract_inverted_index":{"In":[0],"this":[1,66],"paper*":[2],"I":[3],"develop":[4],"rules":[5,28,43],"of":[6,26,41,47,76,79,109,130,135,184],"substitution":[7],"for":[8,38,179],"variable":[9],"one-place":[10,186],"functors":[11,187],"(\u03b4)":[12],"as":[13,196],"they":[14],"appear":[15],"in":[16,62,121,168,189],"Lukasiewicz's":[17,176],"i-modal":[18],"system":[19,67],"[2].I":[20],"also":[21,194],"prove":[22],"that":[23,32,65,82,88,162,210],"the":[24,33,39,45,74,77,106,128,147,211],"first":[25],"these":[27,42],"preserves":[29,35],"validity":[30],"and":[31,44,102,203],"second":[34],"invalidity.The":[36],"need":[37],"formulation":[40],"proof":[46,64],"their":[48],"validity-or":[49],"invalidity-preserving":[50],"characteristic":[51,70],"became":[52],"apparent":[53],"to":[54,86,126,137,152,182,220,224],"me":[55],"upon":[56],"questioning":[57],"whether":[58],"L":[59],"was":[60],"sound.Smiley,":[61],"his":[63],"has":[68],"a":[69,133],"matrix,":[71],"slides":[72],"over":[73],"problem":[75,108],"soundness":[78,129],"\u00a3,":[80],"noting":[81],"it":[83,159,172,206],"is":[84,91,160,165,173,193,207],"easy":[85,125],"show":[87],"every":[89],"theorem":[90],"verified":[92,174],"by":[93,175],"(never":[94],"takes":[95],"an":[96,156],"undesignated":[97],"value":[98],"in)":[99],"M":[100],"[5]":[101],"instead":[103],"concentrates":[104],"on":[105],"difficult":[107],"proving":[110],"h":[111,201],"complete.It":[112],"turns":[113],"out,":[114],"however,":[115],"that,":[116],"like":[117,219],"so":[118,204],"many":[119],"things":[120],"logic":[122],"which":[123],"seem":[124],"prove,":[127],"\u00a3":[131],"requires":[132],"bit":[134],"work":[136],"prove.The":[138],"difficulty":[139],"may":[140],"be":[141],"briefly":[142],"seen":[143],"if":[144,163,171],"we":[145,214],"consider":[146],"inference":[148],"from":[149],"(1)":[150,164],"V-CEpqC\u03b4pbq":[151],"(":[153],"2)":[154],"hCEpqCCppCqp.On":[155],"intuitive":[157],"level":[158],"clear":[161,209],"valid":[166],"1":[167],"-\u00a3,":[169],"i.e.,":[170],"5W9":[177],"matrix":[178],"all":[180],"assignments":[181],"\u03b4":[183],"constant":[185],"definable":[188],"L,":[190],"then":[191],"(2)":[192],"valid,":[195],"are(3)":[197],"H":[198],"CEpqCAKprEpsAKprEqs":[199],"(4)":[200],"CEpqCKApNpKApNq,":[202],"on.Hence,":[205],"intuitively":[208],"rule,":[212],"(which":[213],"have":[215],"not":[216],"*I":[217],"would":[218],"express":[221],"my":[222],"appreciation":[223],"Dr.":[225]},"counts_by_year":[],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-10T00:00:00"}