{"id":"https://openalex.org/W2150034744","doi":"https://doi.org/10.2307/2271619","title":"Ten modal models","display_name":"Ten modal models","publication_year":1964,"publication_date":"1964-09-01","ids":{"openalex":"https://openalex.org/W2150034744","doi":"https://doi.org/10.2307/2271619","mag":"2150034744"},"language":"en","primary_location":{"id":"doi:10.2307/2271619","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2271619","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/A5109366683","display_name":"Ivo Thomas","orcid":null},"institutions":[{"id":"https://openalex.org/I107639228","display_name":"University of Notre Dame","ror":"https://ror.org/00mkhxb43","country_code":"US","type":"education","lineage":["https://openalex.org/I107639228"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ivo Thomas","raw_affiliation_strings":["University of Notre Dame, Indiana"],"affiliations":[{"raw_affiliation_string":"University of Notre Dame, Indiana","institution_ids":["https://openalex.org/I107639228"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5109366683"],"corresponding_institution_ids":["https://openalex.org/I107639228"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.12649402,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"29","issue":"3","first_page":"125","last_page":"128"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9296000003814697,"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":0.9296000003814697,"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","display_name":"Modal","score":0.7424381375312805},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.682949423789978},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6035517454147339},{"id":"https://openalex.org/keywords/predicate","display_name":"Predicate (mathematical logic)","score":0.603026270866394},{"id":"https://openalex.org/keywords/simplicity","display_name":"Simplicity","score":0.5483641028404236},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.46433863043785095},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.45228075981140137},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.4396651089191437},{"id":"https://openalex.org/keywords/repetition","display_name":"Repetition (rhetorical device)","score":0.43730950355529785},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3400028944015503},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3382068872451782},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3365810215473175},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.27038970589637756},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.20980370044708252},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08746924996376038},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07623448967933655},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.06365150213241577},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.058703869581222534},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.056341201066970825},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.04807046055793762}],"concepts":[{"id":"https://openalex.org/C71139939","wikidata":"https://www.wikidata.org/wiki/Q910194","display_name":"Modal","level":2,"score":0.7424381375312805},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.682949423789978},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6035517454147339},{"id":"https://openalex.org/C140146324","wikidata":"https://www.wikidata.org/wiki/Q1144319","display_name":"Predicate (mathematical logic)","level":2,"score":0.603026270866394},{"id":"https://openalex.org/C2776372474","wikidata":"https://www.wikidata.org/wiki/Q508291","display_name":"Simplicity","level":2,"score":0.5483641028404236},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.46433863043785095},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.45228075981140137},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.4396651089191437},{"id":"https://openalex.org/C2776141515","wikidata":"https://www.wikidata.org/wiki/Q1274479","display_name":"Repetition (rhetorical device)","level":2,"score":0.43730950355529785},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3400028944015503},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3382068872451782},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3365810215473175},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27038970589637756},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.20980370044708252},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08746924996376038},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07623448967933655},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.06365150213241577},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.058703869581222534},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.056341201066970825},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.04807046055793762},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","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/C188027245","wikidata":"https://www.wikidata.org/wiki/Q750446","display_name":"Polymer chemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2307/2271619","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2271619","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1991325954","https://openalex.org/W2017765338","https://openalex.org/W2022192687","https://openalex.org/W2057515027","https://openalex.org/W2070290404","https://openalex.org/W2084810265","https://openalex.org/W2087555111","https://openalex.org/W4388216430"],"related_works":["https://openalex.org/W2368019753","https://openalex.org/W2333930193","https://openalex.org/W2737356002","https://openalex.org/W2246241526","https://openalex.org/W4301122218","https://openalex.org/W2374150061","https://openalex.org/W2081340182","https://openalex.org/W2369703001","https://openalex.org/W2372323577","https://openalex.org/W2321432690"],"abstract_inverted_index":{"We":[0],"consider":[1],"the":[2,13,70,107,111,116],"results":[3,71,112],"of":[4,44,53,69,106],"adding":[5],"to":[6,50],"a":[7,62],"basic":[8],"modal":[9],"system":[10],"T":[11],"0":[12,91],"axioms":[14],"G1.":[15],"CLpp;":[16],"P":[17],"n":[18,21,27,30,34],".":[19,28,67],"CL":[20],"pL":[22],"n+1":[23],"p":[24],";":[25],"B":[26],"CpL":[29],"Mp":[31],",":[32,38],"where":[33],"\u2267":[35],"1":[36,37],"in":[39,56,75,80,92,96,104],"all":[40],"combinations.":[41],"The":[42],"method":[43],"Meredith's":[45],"[7]":[46],"will":[47],"be":[48,102],"extended":[49],"get":[51],"models":[52],"these":[54],"systems":[55,78],"lower":[57],"predicate":[58],"calculus":[59],"(LPC)":[60],"with":[61,109],"constant":[63],"binary":[64],"relation,":[65],"U":[66],"Most":[68],"were":[72,85],"already":[73],"obtained":[74,114],"[1]\u2013[6],":[76],"though":[77],"as":[79],"(i)":[81],"and":[82],"(ii)":[83,93],"below":[84],"not":[86],"investigated,":[87],"except":[88],"that":[89],"S4":[90],"was":[94],"mentioned":[95],"[1].":[97],"However":[98],"some":[99],"repetition":[100],"may":[101],"excused":[103],"view":[105],"simplicity":[108],"which":[110],"are":[113],"by":[115],"present":[117],"method.":[118]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}