{"id":"https://openalex.org/W2022430114","doi":"https://doi.org/10.1305/ndjfl/1093883565","title":"Generalized ${\\rm S}2$-like systems of propositional modal logic.","display_name":"Generalized ${\\rm S}2$-like systems of propositional modal logic.","publication_year":1982,"publication_date":"1982-01-01","ids":{"openalex":"https://openalex.org/W2022430114","doi":"https://doi.org/10.1305/ndjfl/1093883565","mag":"2022430114"},"language":"en","primary_location":{"id":"doi:10.1305/ndjfl/1093883565","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093883565","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-23/issue-1/Generalized-rm-S2-like-systems-of-propositional-modal-logic/10.1305/ndjfl/1093883565.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-23/issue-1/Generalized-rm-S2-like-systems-of-propositional-modal-logic/10.1305/ndjfl/1093883565.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101709770","display_name":"Mark A. Brown","orcid":"https://orcid.org/0000-0003-4491-5600"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Mark A. Brown","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5101709770"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.12836208,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"23","issue":"1","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":0.9914000034332275,"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":0.9914000034332275,"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/T10215","display_name":"Semantic Web and Ontologies","score":0.972599983215332,"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/T10456","display_name":"Multi-Agent Systems and Negotiation","score":0.9452999830245972,"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":0.7273629307746887},{"id":"https://openalex.org/keywords/propositional-variable","display_name":"Propositional variable","score":0.6093704700469971},{"id":"https://openalex.org/keywords/normal-modal-logic","display_name":"Normal modal logic","score":0.5441246628761292},{"id":"https://openalex.org/keywords/modal-\u03bc-calculus","display_name":"Modal \u03bc-calculus","score":0.5377495288848877},{"id":"https://openalex.org/keywords/modal","display_name":"Modal","score":0.5284885168075562},{"id":"https://openalex.org/keywords/propositional-calculus","display_name":"Propositional calculus","score":0.5164501667022705},{"id":"https://openalex.org/keywords/zeroth-order-logic","display_name":"Zeroth-order logic","score":0.49442505836486816},{"id":"https://openalex.org/keywords/dynamic-logic","display_name":"Dynamic logic (digital electronics)","score":0.4827820360660553},{"id":"https://openalex.org/keywords/intermediate-logic","display_name":"Intermediate logic","score":0.4787953794002533},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.44368988275527954},{"id":"https://openalex.org/keywords/intuitionistic-logic","display_name":"Intuitionistic logic","score":0.4360713064670563},{"id":"https://openalex.org/keywords/autoepistemic-logic","display_name":"Autoepistemic logic","score":0.4342030882835388},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.4234990179538727},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37785831093788147},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3695448040962219},{"id":"https://openalex.org/keywords/multimodal-logic","display_name":"Multimodal logic","score":0.25149452686309814},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.21812665462493896},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13198387622833252},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.08076956868171692},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.04965907335281372}],"concepts":[{"id":"https://openalex.org/C27508121","wikidata":"https://www.wikidata.org/wiki/Q210841","display_name":"Modal logic","level":3,"score":0.7273629307746887},{"id":"https://openalex.org/C14523651","wikidata":"https://www.wikidata.org/wiki/Q3492863","display_name":"Propositional variable","level":4,"score":0.6093704700469971},{"id":"https://openalex.org/C114092440","wikidata":"https://www.wikidata.org/wiki/Q840226","display_name":"Normal modal logic","level":4,"score":0.5441246628761292},{"id":"https://openalex.org/C173125200","wikidata":"https://www.wikidata.org/wiki/Q5275729","display_name":"Modal \u03bc-calculus","level":5,"score":0.5377495288848877},{"id":"https://openalex.org/C71139939","wikidata":"https://www.wikidata.org/wiki/Q910194","display_name":"Modal","level":2,"score":0.5284885168075562},{"id":"https://openalex.org/C69562738","wikidata":"https://www.wikidata.org/wiki/Q200694","display_name":"Propositional calculus","level":2,"score":0.5164501667022705},{"id":"https://openalex.org/C110039528","wikidata":"https://www.wikidata.org/wiki/Q8069651","display_name":"Zeroth-order logic","level":4,"score":0.49442505836486816},{"id":"https://openalex.org/C2777796570","wikidata":"https://www.wikidata.org/wiki/Q2351326","display_name":"Dynamic logic (digital electronics)","level":4,"score":0.4827820360660553},{"id":"https://openalex.org/C33203268","wikidata":"https://www.wikidata.org/wiki/Q5361594","display_name":"Intermediate logic","level":3,"score":0.4787953794002533},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44368988275527954},{"id":"https://openalex.org/C178421362","wikidata":"https://www.wikidata.org/wiki/Q176786","display_name":"Intuitionistic logic","level":3,"score":0.4360713064670563},{"id":"https://openalex.org/C3845977","wikidata":"https://www.wikidata.org/wiki/Q4826262","display_name":"Autoepistemic logic","level":4,"score":0.4342030882835388},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.4234990179538727},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37785831093788147},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3695448040962219},{"id":"https://openalex.org/C203659156","wikidata":"https://www.wikidata.org/wiki/Q6934805","display_name":"Multimodal logic","level":3,"score":0.25149452686309814},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.21812665462493896},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13198387622833252},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.08076956868171692},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.04965907335281372},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.0},{"id":"https://openalex.org/C172385210","wikidata":"https://www.wikidata.org/wiki/Q5339","display_name":"Transistor","level":3,"score":0.0},{"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/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/1093883565","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093883565","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-23/issue-1/Generalized-rm-S2-like-systems-of-propositional-modal-logic/10.1305/ndjfl/1093883565.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/1093883565","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.ndjfl/1093883565","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/1093883565","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1093883565","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-23/issue-1/Generalized-rm-S2-like-systems-of-propositional-modal-logic/10.1305/ndjfl/1093883565.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":[{"display_name":"Reduced inequalities","score":0.5099999904632568,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2022430114.pdf","grobid_xml":"https://content.openalex.org/works/W2022430114.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W1596067335","https://openalex.org/W2082884384","https://openalex.org/W2163751633","https://openalex.org/W3126734519","https://openalex.org/W3129277215","https://openalex.org/W6671226180"],"related_works":["https://openalex.org/W3100510665","https://openalex.org/W2020323165","https://openalex.org/W1573206013","https://openalex.org/W2154555144","https://openalex.org/W2055558461","https://openalex.org/W2952893544","https://openalex.org/W2081976468","https://openalex.org/W2078736672","https://openalex.org/W2163197731","https://openalex.org/W1984651728"],"abstract_inverted_index":{"In":[0],"the":[1,6,33,36,47,88,92,129],"usual":[2,37,89],"semantics":[3,118],"for":[4,40,134,152],"S2,":[5],"models":[7,151,165],"are":[8,22,26,44,84,96,109],"permitted":[9],"to":[10,127],"contain":[11],"\"abnormal\"":[12],"worlds,":[13],"i.e.,":[14],"possible":[15],"worlds":[16,25,35,83,108,139,143],"meeting":[17],"two":[18,93],"conditions:":[19],"(1)":[20],"they":[21,147],"terminal":[23],"(no":[24],"accessible":[27],"from":[28],"them),":[29],"and":[30,42,53,73,99,154],"(2)":[31],"at":[32,70,86,116],"abnormal":[34,82,107,142],"truth":[38],"conditions":[39,48,130],"Dp":[41],"Op":[43,50,54,74],"replaced":[45],"by":[46,137],"that":[49,71,81,100,105,120,146],"be":[51,55,67,123,148,159],"false":[52],"true.":[56],"1":[57],"If":[58],"a":[59,132],"normal":[60],"world":[61,72],"were":[62],"terminal,":[63],"then":[64],"Up":[65],"would":[66],"vacuously":[68],"true":[69],"trivially":[75],"false.":[76],"Hence":[77],"we":[78],"might":[79,122,158],"consider":[80],"ones":[85],"which":[87],"meanings":[90],"of":[91,114,124,164,166],"modal":[94,135],"operators":[95],"simply":[97],"interchanged,":[98],"in":[101],"S2":[102,117,153],"it":[103,121],"happens":[104],"such":[106],"always":[110],"terminal.":[111,149],"This":[112],"way":[113],"looking":[115],"suggests":[119],"some":[125],"interest":[126],"weaken":[128],"on":[131],"model":[133],"logic":[136],"permitting":[138],"like":[140],"S2's":[141],"without":[144],"demanding":[145],"Then":[150],"its":[155],"various":[156],"extensions":[157],"seen":[160],"as":[161],"special":[162],"cases":[163],"this":[167],"very":[168],"general":[169],"sort.":[170]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}