{"id":"https://openalex.org/W2051167594","doi":"https://doi.org/10.2307/2275262","title":"A quantitative analysis of modal logic","display_name":"A quantitative analysis of modal logic","publication_year":1994,"publication_date":"1994-03-01","ids":{"openalex":"https://openalex.org/W2051167594","doi":"https://doi.org/10.2307/2275262","mag":"2051167594"},"language":"en","primary_location":{"id":"doi:10.2307/2275262","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2275262","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/A5027117465","display_name":"Ronald Fagin","orcid":"https://orcid.org/0000-0002-7374-0347"},"institutions":[{"id":"https://openalex.org/I4210085935","display_name":"IBM Research - Almaden","ror":"https://ror.org/005w8dd04","country_code":"US","type":"facility","lineage":["https://openalex.org/I1341412227","https://openalex.org/I4210085935","https://openalex.org/I4210114115"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ronald Fagin","raw_affiliation_strings":["IBM Almaden Research Center, San Jose, California 95120-6099,, E-mail:"],"affiliations":[{"raw_affiliation_string":"IBM Almaden Research Center, San Jose, California 95120-6099,, E-mail:","institution_ids":["https://openalex.org/I4210085935"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5027117465"],"corresponding_institution_ids":["https://openalex.org/I4210085935"],"apc_list":null,"apc_paid":null,"fwci":1.1297,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.82436007,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"59","issue":"1","first_page":"209","last_page":"252"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9966999888420105,"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/T10456","display_name":"Multi-Agent Systems and Negotiation","score":0.9934999942779541,"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/countable-set","display_name":"Countable set","score":0.8986622095108032},{"id":"https://openalex.org/keywords/modal-logic","display_name":"Modal logic","score":0.6367164850234985},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6078550219535828},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5827303528785706},{"id":"https://openalex.org/keywords/modal","display_name":"Modal","score":0.5344134569168091},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3792843222618103},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.32948800921440125}],"concepts":[{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.8986622095108032},{"id":"https://openalex.org/C27508121","wikidata":"https://www.wikidata.org/wiki/Q210841","display_name":"Modal logic","level":3,"score":0.6367164850234985},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6078550219535828},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5827303528785706},{"id":"https://openalex.org/C71139939","wikidata":"https://www.wikidata.org/wiki/Q910194","display_name":"Modal","level":2,"score":0.5344134569168091},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3792843222618103},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32948800921440125},{"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2307/2275262","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2275262","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/1183744446","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183744446","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:10.1.1.65.9186","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.65.9186","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.almaden.ibm.com/cs/people/fagin/jsl94.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W35276785","https://openalex.org/W179751113","https://openalex.org/W251225716","https://openalex.org/W584597337","https://openalex.org/W1527588453","https://openalex.org/W1547562281","https://openalex.org/W1565331687","https://openalex.org/W1572577884","https://openalex.org/W1574129634","https://openalex.org/W1591825827","https://openalex.org/W1600348701","https://openalex.org/W1995355963","https://openalex.org/W2016917647","https://openalex.org/W2022205872","https://openalex.org/W2036639698","https://openalex.org/W2049069994","https://openalex.org/W2075277371","https://openalex.org/W2076073997","https://openalex.org/W2086035610","https://openalex.org/W2093270475","https://openalex.org/W2105505307","https://openalex.org/W2117832390","https://openalex.org/W2127554421","https://openalex.org/W2136935557","https://openalex.org/W2146819619","https://openalex.org/W2476754787","https://openalex.org/W2530006810","https://openalex.org/W2912686676","https://openalex.org/W2913222977","https://openalex.org/W3140030144","https://openalex.org/W4231393247","https://openalex.org/W6654618685"],"related_works":["https://openalex.org/W2028144918","https://openalex.org/W3016746667","https://openalex.org/W1587059467","https://openalex.org/W119381390","https://openalex.org/W4287814874","https://openalex.org/W2962420748","https://openalex.org/W2541640833","https://openalex.org/W4206367340","https://openalex.org/W2086359902","https://openalex.org/W1587340481"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"do":[2],"a":[3,85,94,112,115,169,192],"quantitative":[4],"analysis":[5],"of":[6,28,62,69,97,106,114,126,138,142,154,161,164,176,184,187],"modal":[7],"logic.":[8],"For":[9],"example,":[10,57],"for":[11,25,74],"each":[12,26],"Kripke":[13,117],"structure":[14],"M":[15,29],",":[16,30],"we":[17,58],"study":[18],"the":[19,31,38,60,67,81,104,107,124,127,162,165,182,185,188],"least":[20],"ordinal":[21],"\u03bc":[22,36],"such":[23],"that":[24,65,80,103,123,150,174],"state":[27,113],"beliefs":[32,40,51,83,105,125,190],"up":[33],"to":[34,48,52,78,158],"level":[35],"characterize":[37],"agents'":[39,82,189],"(that":[41],"is,":[42],"there":[43],"is":[44],"only":[45],"one":[46],"way":[47],"extend":[49],"these":[50,177],"higher":[53],"levels).":[54],"As":[55],"another":[56,91],"show":[59],"equivalence":[61],"three":[63],"conditions,":[64],"on":[66],"face":[68],"it":[70,76,90],"look":[71],"quite":[72],"different,":[73],"what":[75],"means":[77],"say":[79],"have":[84,93],"countable":[86,116,140],"description,":[87],"or":[88],"putting":[89],"way,":[92],"\u201ccountable":[95,193],"amount":[96],"information\u201d.":[98],"The":[99,119,146,172],"first":[100],"condition":[101,121,148],"says":[102,122,149],"agents":[108,128,166],"are":[109,144,156,179],"those":[110],"at":[111],"structure.":[118],"second":[120],"can":[129],"be":[130],"described":[131],"in":[132],"an":[133],"infinitary":[134],"language,":[135],"where":[136],"conjunctions":[137],"arbitrary":[139],"sets":[141],"formulas":[143],"allowed.":[145],"third":[147],"countably":[151],"many":[152],"levels":[153],"belief":[155],"sufficient":[157],"capture":[159],"all":[160,175],"uncertainty":[163],"(along":[167],"with":[168],"technical":[170],"condition).":[171],"fact":[173],"conditions":[178],"equivalent":[180],"shows":[181],"robustness":[183],"concept":[186],"having":[191],"description\u201d.":[194]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
