{"id":"https://openalex.org/W1994385438","doi":"https://doi.org/10.1305/ndjfl/1094155276","title":"A Simple Embedding of T into Double S5","display_name":"A Simple Embedding of T into Double S5","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W1994385438","doi":"https://doi.org/10.1305/ndjfl/1094155276","mag":"1994385438"},"language":"en","primary_location":{"id":"doi:10.1305/ndjfl/1094155276","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1094155276","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-45/issue-1/A-Simple-Embedding-of-T-into-Double-S5/10.1305/ndjfl/1094155276.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-45/issue-1/A-Simple-Embedding-of-T-into-Double-S5/10.1305/ndjfl/1094155276.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003195897","display_name":"Steven T. Kuhn","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Steven Kuhn","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5003195897"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.09032637,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"45","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.9940999746322632,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.9940999746322632,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9865999817848206,"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9821000099182129,"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/decidability","display_name":"Decidability","score":0.8425630331039429},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.688052237033844},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.5810224413871765},{"id":"https://openalex.org/keywords/propositional-variable","display_name":"Propositional variable","score":0.5766022801399231},{"id":"https://openalex.org/keywords/translation","display_name":"Translation (biology)","score":0.5275330543518066},{"id":"https://openalex.org/keywords/propositional-calculus","display_name":"Propositional calculus","score":0.5081062316894531},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4767802059650421},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4480654001235962},{"id":"https://openalex.org/keywords/atomic-formula","display_name":"Atomic formula","score":0.4442169964313507},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4417750835418701},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.40198445320129395},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3828257620334625},{"id":"https://openalex.org/keywords/intermediate-logic","display_name":"Intermediate logic","score":0.3814981281757355},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36565351486206055},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.22619184851646423},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.1115202009677887},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11019095778465271},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.06542322039604187}],"concepts":[{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.8425630331039429},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.688052237033844},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.5810224413871765},{"id":"https://openalex.org/C14523651","wikidata":"https://www.wikidata.org/wiki/Q3492863","display_name":"Propositional variable","level":4,"score":0.5766022801399231},{"id":"https://openalex.org/C149364088","wikidata":"https://www.wikidata.org/wiki/Q185917","display_name":"Translation (biology)","level":4,"score":0.5275330543518066},{"id":"https://openalex.org/C69562738","wikidata":"https://www.wikidata.org/wiki/Q200694","display_name":"Propositional calculus","level":2,"score":0.5081062316894531},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4767802059650421},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4480654001235962},{"id":"https://openalex.org/C203264685","wikidata":"https://www.wikidata.org/wiki/Q2328174","display_name":"Atomic formula","level":2,"score":0.4442169964313507},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4417750835418701},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40198445320129395},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3828257620334625},{"id":"https://openalex.org/C33203268","wikidata":"https://www.wikidata.org/wiki/Q5361594","display_name":"Intermediate logic","level":3,"score":0.3814981281757355},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36565351486206055},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.22619184851646423},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.1115202009677887},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11019095778465271},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.06542322039604187},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C105580179","wikidata":"https://www.wikidata.org/wiki/Q188928","display_name":"Messenger RNA","level":3,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1305/ndjfl/1094155276","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1094155276","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-45/issue-1/A-Simple-Embedding-of-T-into-Double-S5/10.1305/ndjfl/1094155276.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/1094155276","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.ndjfl/1094155276","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.596.7805","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.596.7805","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www9.georgetown.edu/faculty/kuhns/supp_files/embedding.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1305/ndjfl/1094155276","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1094155276","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-45/issue-1/A-Simple-Embedding-of-T-into-Double-S5/10.1305/ndjfl/1094155276.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":0.4399999976158142,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1994385438.pdf","grobid_xml":"https://content.openalex.org/works/W1994385438.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W2074944668","https://openalex.org/W2124207901"],"related_works":["https://openalex.org/W2081976468","https://openalex.org/W2129318326","https://openalex.org/W2045432969","https://openalex.org/W3105926622","https://openalex.org/W2155056973","https://openalex.org/W2014322692","https://openalex.org/W2732055457","https://openalex.org/W1994385438","https://openalex.org/W59622013","https://openalex.org/W2140541040"],"abstract_inverted_index":{"The":[0],"system":[1,39,75],"obtained":[2,17],"by":[3,18],"adding":[4],"full":[5,30,45],"propositional":[6,46],"quantification":[7,47],"to":[8,12,25,63],"S5":[9,42,79],"is":[10,23,48],"known":[11,24],"be":[13,26],"decidable,":[14],"while":[15],"that":[16,37,58],"doing":[19],"so":[20],"for":[21],"T":[22,74],"recursively":[27,50],"intertranslatable":[28,51],"with":[29,40,52],"second-order":[31,53],"logic.":[32,54],"Recently":[33],"it":[34],"was":[35],"shown":[36],"the":[38,59,73,77,87],"two":[41],"operators":[43],"and":[44,68,76],"also":[49],"This":[55],"note":[56],"establishes":[57],"map":[60],"assigning":[61],"[1][2]p":[62],"\\squarep":[64],"provides":[65],"a":[66],"validity":[67],"satisfaction":[69],"preserving":[70],"translation":[71],"between":[72],"double":[78],"system,":[80],"thus":[81],"providing":[82],"an":[83],"easier":[84],"proof":[85],"of":[86],"recent":[88],"result.":[89]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
