{"id":"https://openalex.org/W2112784644","doi":"https://doi.org/10.2307/2273355","title":"A cut-free Gentzen-type system for the modal logic S5","display_name":"A cut-free Gentzen-type system for the modal logic S5","publication_year":1980,"publication_date":"1980-03-01","ids":{"openalex":"https://openalex.org/W2112784644","doi":"https://doi.org/10.2307/2273355","mag":"2112784644"},"language":"en","primary_location":{"id":"doi:10.2307/2273355","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2273355","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101569675","display_name":"Masahiko Sato","orcid":"https://orcid.org/0000-0002-2475-3942"},"institutions":[{"id":"https://openalex.org/I3125079907","display_name":"Japan Graduate School of Education University","ror":"https://ror.org/03a6vay74","country_code":"JP","type":"education","lineage":["https://openalex.org/I3125079907"]},{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Masahiko Sato","raw_affiliation_strings":["University of Tokyo, College Of General Education, Tokyo 153, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Tokyo, College Of General Education, Tokyo 153, Japan","institution_ids":["https://openalex.org/I3125079907","https://openalex.org/I74801974"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101569675"],"corresponding_institution_ids":["https://openalex.org/I3125079907","https://openalex.org/I74801974"],"apc_list":null,"apc_paid":null,"fwci":4.3622,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.94556197,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"45","issue":"1","first_page":"67","last_page":"84"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9965000152587891,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9965000152587891,"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":0.9922999739646912,"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":0.9890000224113464,"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/sequent","display_name":"Sequent","score":0.8916923999786377},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.696792483329773},{"id":"https://openalex.org/keywords/sequent-calculus","display_name":"Sequent calculus","score":0.5721796154975891},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5555028319358826},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.4978935718536377},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.44100379943847656},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.43836861848831177},{"id":"https://openalex.org/keywords/natural-deduction","display_name":"Natural deduction","score":0.4178028404712677},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.4127139151096344},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.378295361995697},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17101752758026123},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.12777191400527954},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.0676291286945343}],"concepts":[{"id":"https://openalex.org/C89421646","wikidata":"https://www.wikidata.org/wiki/Q843632","display_name":"Sequent","level":2,"score":0.8916923999786377},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.696792483329773},{"id":"https://openalex.org/C65880906","wikidata":"https://www.wikidata.org/wiki/Q1771121","display_name":"Sequent calculus","level":3,"score":0.5721796154975891},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5555028319358826},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.4978935718536377},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.44100379943847656},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43836861848831177},{"id":"https://openalex.org/C62073222","wikidata":"https://www.wikidata.org/wiki/Q1572108","display_name":"Natural deduction","level":2,"score":0.4178028404712677},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.4127139151096344},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.378295361995697},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17101752758026123},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.12777191400527954},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0676291286945343},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2307/2273355","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2273355","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1183740511","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183740511","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":null,"sustainable_development_goals":[{"score":0.800000011920929,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1939483552","https://openalex.org/W1946912229","https://openalex.org/W1974866079","https://openalex.org/W1987663025","https://openalex.org/W2034576617","https://openalex.org/W2039977878","https://openalex.org/W2488459213","https://openalex.org/W4238292764","https://openalex.org/W6722955555"],"related_works":["https://openalex.org/W2280276996","https://openalex.org/W1488351281","https://openalex.org/W2096191306","https://openalex.org/W4253113110","https://openalex.org/W2891688494","https://openalex.org/W2023557900","https://openalex.org/W2584381231","https://openalex.org/W4251049234","https://openalex.org/W1562648369","https://openalex.org/W182117412"],"abstract_inverted_index":{"The":[0,25,68,180],"modal":[1],"logic":[2],"S5":[3,70,159,173],"has":[4],"been":[5],"formulated":[6],"in":[7,37,59,114,129,136,145,165,192],"Gentzen-style":[8],"by":[9,27,64],"several":[10],"authors":[11],"such":[12],"as":[13,177,199,201],"Ohnishi":[14,28],"and":[15,22,29,77,160],"Matsumoto":[16,30],"[4],":[17],"Kanger":[18],"[2],":[19],"Mints":[20,73],"[3]":[21],"Sato":[23],"[5].":[24],"system":[26,43,55,69,113,128,138,157],"is":[31,51,62,74,81,104,123],"natural,":[32],"but":[33],"the":[34,85,99,107,118,130,146,150,162,185,193,197,207,210],"cut-elimination":[35,45,79,86,119,163],"theorem":[36,80,87,164],"it":[38,50,122],"fails":[39],"to":[40,183],"hold.":[41],"Kanger's":[42],"enjoys":[44,117],"theorem,":[46],"but,":[47],"strictly":[48],"speaking,":[49],"not":[52,97,125],"a":[53,60,65,126,141,155,166,178],"Gentzen-type":[54,127,156],"since":[56,133],"each":[57,134],"formula":[58],"sequent":[61,135],"indexed":[63],"natural":[66],"number.":[67],"+":[71],"of":[72,88,93,110,140,143,196,209],"also":[75,116,124],"cut-free,":[76],"its":[78],"proved":[82],"constructively":[83],"via":[84],"Gentzen's":[89],"LK.":[90],"However,":[91,121],"one":[92],"his":[94,203],"rules":[95],"does":[96],"have":[98],"so-called":[100],"subformula":[101],"property,":[102],"which":[103,205],"desirable":[105],"from":[106],"proof-theoretic":[108],"point":[109],"view.":[111],"Our":[112],"[5]":[115],"theorem.":[120],"strict":[131],"sense,":[132],"this":[137],"consists":[139],"pair":[142],"sequents":[144],"usual":[147],"sense.":[148],"In":[149],"present":[151],"paper,":[152],"we":[153],"give":[154],"for":[158,172,187,202],"prove":[161],"constructive":[167],"way.":[168],"A":[169],"decision":[170],"procedure":[171],"can":[174],"be":[175],"obtained":[176],"by-product.":[179],"author":[181],"wishes":[182],"thank":[184],"referee":[186],"pointing":[188],"out":[189],"some":[190],"errors":[191],"first":[194],"version":[195],"paper":[198],"well":[200],"suggestions":[204],"improved":[206],"readability":[208],"paper.":[211]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}