{"id":"https://openalex.org/W2151083705","doi":"https://doi.org/10.1305/ndjfl/1093891400","title":"Logical consequence in modal logic. II. Some semantic systems for ${\\rm S}4$.","display_name":"Logical consequence in modal logic. II. Some semantic systems for ${\\rm S}4$.","publication_year":1974,"publication_date":"1974-07-01","ids":{"openalex":"https://openalex.org/W2151083705","doi":"https://doi.org/10.1305/ndjfl/1093891400","mag":"2151083705"},"language":"en","primary_location":{"id":"doi:10.1305/ndjfl/1093891400","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093891400","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-15/issue-3/Logical-consequence-in-modal-logic-II-Some-semantic-systems-for/10.1305/ndjfl/1093891400.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-15/issue-3/Logical-consequence-in-modal-logic-II-Some-semantic-systems-for/10.1305/ndjfl/1093891400.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091446213","display_name":"John Corcoran","orcid":null},"institutions":[{"id":"https://openalex.org/I102373834","display_name":"Bryn Mawr College","ror":"https://ror.org/05sjwtp51","country_code":"US","type":"education","lineage":["https://openalex.org/I102373834"]},{"id":"https://openalex.org/I63190737","display_name":"University at Buffalo, State University of New York","ror":"https://ror.org/01y64my43","country_code":"US","type":"education","lineage":["https://openalex.org/I63190737"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"John Corcoran","raw_affiliation_strings":["Bryn Mawr College Bryn Mawr, Pennsylvania","State University of New York at Buffalo Buffalo, New York"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bryn Mawr College Bryn Mawr, Pennsylvania","institution_ids":["https://openalex.org/I102373834"]},{"raw_affiliation_string":"State University of New York at Buffalo Buffalo, New York","institution_ids":["https://openalex.org/I63190737"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083923777","display_name":"George Weaver","orcid":null},"institutions":[{"id":"https://openalex.org/I102373834","display_name":"Bryn Mawr College","ror":"https://ror.org/05sjwtp51","country_code":"US","type":"education","lineage":["https://openalex.org/I102373834"]},{"id":"https://openalex.org/I63190737","display_name":"University at Buffalo, State University of New York","ror":"https://ror.org/01y64my43","country_code":"US","type":"education","lineage":["https://openalex.org/I63190737"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"George Weaver","raw_affiliation_strings":["Bryn Mawr College Bryn Mawr, Pennsylvania","State University of New York at Buffalo Buffalo, New York"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bryn Mawr College Bryn Mawr, Pennsylvania","institution_ids":["https://openalex.org/I102373834"]},{"raw_affiliation_string":"State University of New York at Buffalo Buffalo, New York","institution_ids":["https://openalex.org/I63190737"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.1460276,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"15","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9941999912261963,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9941999912261963,"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":0.9901999831199646,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9740999937057495,"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/modal-logic","display_name":"Modal logic","score":0.6368733048439026},{"id":"https://openalex.org/keywords/normal-modal-logic","display_name":"Normal modal logic","score":0.6205960512161255},{"id":"https://openalex.org/keywords/modal","display_name":"Modal","score":0.5181114077568054},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4698105454444885},{"id":"https://openalex.org/keywords/non-classical-logic","display_name":"Non-classical logic","score":0.4120795428752899},{"id":"https://openalex.org/keywords/multimodal-logic","display_name":"Multimodal logic","score":0.3979370594024658},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.3767409026622772},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.35869020223617554},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.2999662160873413},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.2965332865715027},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.24157115817070007},{"id":"https://openalex.org/keywords/logical-consequence","display_name":"Logical consequence","score":0.2350555956363678},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.09792846441268921},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.0862082839012146}],"concepts":[{"id":"https://openalex.org/C27508121","wikidata":"https://www.wikidata.org/wiki/Q210841","display_name":"Modal logic","level":3,"score":0.6368733048439026},{"id":"https://openalex.org/C114092440","wikidata":"https://www.wikidata.org/wiki/Q840226","display_name":"Normal modal logic","level":4,"score":0.6205960512161255},{"id":"https://openalex.org/C71139939","wikidata":"https://www.wikidata.org/wiki/Q910194","display_name":"Modal","level":2,"score":0.5181114077568054},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4698105454444885},{"id":"https://openalex.org/C74992188","wikidata":"https://www.wikidata.org/wiki/Q239179","display_name":"Non-classical logic","level":3,"score":0.4120795428752899},{"id":"https://openalex.org/C203659156","wikidata":"https://www.wikidata.org/wiki/Q6934805","display_name":"Multimodal logic","level":3,"score":0.3979370594024658},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.3767409026622772},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.35869020223617554},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.2999662160873413},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.2965332865715027},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.24157115817070007},{"id":"https://openalex.org/C134752490","wikidata":"https://www.wikidata.org/wiki/Q374182","display_name":"Logical consequence","level":2,"score":0.2350555956363678},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.09792846441268921},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0862082839012146},{"id":"https://openalex.org/C188027245","wikidata":"https://www.wikidata.org/wiki/Q750446","display_name":"Polymer chemistry","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1305/ndjfl/1093891400","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093891400","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-15/issue-3/Logical-consequence-in-modal-logic-II-Some-semantic-systems-for/10.1305/ndjfl/1093891400.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/1093891400","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.ndjfl/1093891400","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/1093891400","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093891400","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-15/issue-3/Logical-consequence-in-modal-logic-II-Some-semantic-systems-for/10.1305/ndjfl/1093891400.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/W2151083705.pdf","grobid_xml":"https://content.openalex.org/works/W2151083705.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W69348146","https://openalex.org/W1488538795","https://openalex.org/W1528534845","https://openalex.org/W1992670332","https://openalex.org/W2039416535","https://openalex.org/W2155581733","https://openalex.org/W2158016185","https://openalex.org/W6602785198","https://openalex.org/W6602844375","https://openalex.org/W6648386711","https://openalex.org/W6682590233","https://openalex.org/W6683565925"],"related_works":["https://openalex.org/W2101793126","https://openalex.org/W119381390","https://openalex.org/W2028144918","https://openalex.org/W142011187","https://openalex.org/W1530784265","https://openalex.org/W2175984923","https://openalex.org/W2534562289","https://openalex.org/W4318188140","https://openalex.org/W2795425183","https://openalex.org/W4200472121"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2],"a":[3,51,57,104],"continuation":[4],"of":[5,112,120,123],"the":[6,32,101,121,129],"investigations":[7,63],"reported":[8],"in":[9,42,103,137],"Corcoran":[10,80],"and":[11,18,128],"Weaver":[12],"[1]":[13],"where":[14],"two":[15,109],"logics":[16],"j":[17],"-CDD,":[19],"having":[20],"natural":[21,53],"deduction":[22,54],"systems":[23,78,94],"based":[24,70],"on":[25],"Lewis's":[26],"S5,":[27],"are":[28,64,84,125],"shown":[29],"to":[30,46,86],"have":[31],"usually":[33],"desired":[34],"properties":[35],"(strong":[36],"soundness,":[37],"strong":[38],"completeness,":[39],"compactness).":[40],"As":[41],"[1],":[43],"we":[44],"desire":[45],"treat":[47],"modal":[48],"logic":[49],"as":[50,76,92],"\"clean\"":[52],"system":[55],"with":[56],"conceptually":[58],"meaningful":[59],"semantics.":[60],"Here,":[61],"our":[62],"carried":[65],"out":[66],"for":[67],"several":[68],"S4":[69],"logics.":[71],"These":[72],"logics,":[73],"when":[74,90],"regarded":[75,91],"logistic":[77],"(cf.":[79],"[2],":[81],"p.":[82,96],"154),":[83],"seen":[85],"be":[87,117,135],"equivalent;":[88],"but,":[89],"consequence":[93],"(ibid.,":[95],"157),":[97],"one":[98],"diverges":[99],"from":[100],"others":[102],"fashion":[105],"which":[106],"suggests":[107],"that":[108],"standard":[110],"measures":[111],"semantic":[113],"complexity":[114],"may":[115],"not":[116,134],"linked.":[118],"Some":[119],"results":[122],"[l]":[124],"presupposed":[126],"here":[127],"more":[130],"obvious":[131],"definitions":[132],"will":[133],"repeated":[136],"detail.":[138]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2016-06-24T00:00:00"}
