{"id":"https://openalex.org/W1588790262","doi":"https://doi.org/10.1016/s1570-2464(07)80012-7","title":"9 First-order modal logic","display_name":"9 First-order modal logic","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W1588790262","doi":"https://doi.org/10.1016/s1570-2464(07)80012-7","mag":"1588790262"},"language":"en","primary_location":{"id":"doi:10.1016/s1570-2464(07)80012-7","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s1570-2464(07)80012-7","pdf_url":null,"source":{"id":"https://openalex.org/S71695317","display_name":"Studies in logic and practical reasoning","issn_l":"1570-2464","issn":["1570-2464","2212-1137"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Studies in Logic and Practical Reasoning","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.7249,"has_fulltext":false,"cited_by_count":91,"citation_normalized_percentile":{"value":0.97221784,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"549","last_page":"620"},"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/T10126","display_name":"Logic, programming, and type systems","score":0.9977999925613403,"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":0.9972000122070312,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/normal-modal-logic","display_name":"Normal modal logic","score":0.6813365817070007},{"id":"https://openalex.org/keywords/modal-logic","display_name":"Modal logic","score":0.6797704100608826},{"id":"https://openalex.org/keywords/accessibility-relation","display_name":"Accessibility relation","score":0.6340650320053101},{"id":"https://openalex.org/keywords/s5","display_name":"S5","score":0.6028532385826111},{"id":"https://openalex.org/keywords/t-norm-fuzzy-logics","display_name":"T-norm fuzzy logics","score":0.5997445583343506},{"id":"https://openalex.org/keywords/kripke-semantics","display_name":"Kripke semantics","score":0.584086537361145},{"id":"https://openalex.org/keywords/multimodal-logic","display_name":"Multimodal logic","score":0.5605865120887756},{"id":"https://openalex.org/keywords/intermediate-logic","display_name":"Intermediate logic","score":0.5576531291007996},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.49944424629211426},{"id":"https://openalex.org/keywords/modal","display_name":"Modal","score":0.49448537826538086},{"id":"https://openalex.org/keywords/dynamic-logic","display_name":"Dynamic logic (digital electronics)","score":0.48755258321762085},{"id":"https://openalex.org/keywords/first-order-logic","display_name":"First-order logic","score":0.48174571990966797},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.4808529019355774},{"id":"https://openalex.org/keywords/classical-logic","display_name":"Classical logic","score":0.45477670431137085},{"id":"https://openalex.org/keywords/higher-order-logic","display_name":"Higher-order logic","score":0.4481396973133087},{"id":"https://openalex.org/keywords/modal-operator","display_name":"Modal operator","score":0.4421161413192749},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4365920126438141},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4355411231517792},{"id":"https://openalex.org/keywords/decidability","display_name":"Decidability","score":0.4309268891811371},{"id":"https://openalex.org/keywords/predicate-logic","display_name":"Predicate logic","score":0.420663058757782},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3639175295829773},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3454774022102356},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3194654881954193},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1699334979057312},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.08599263429641724}],"concepts":[{"id":"https://openalex.org/C114092440","wikidata":"https://www.wikidata.org/wiki/Q840226","display_name":"Normal modal logic","level":4,"score":0.6813365817070007},{"id":"https://openalex.org/C27508121","wikidata":"https://www.wikidata.org/wiki/Q210841","display_name":"Modal logic","level":3,"score":0.6797704100608826},{"id":"https://openalex.org/C11191006","wikidata":"https://www.wikidata.org/wiki/Q2663311","display_name":"Accessibility relation","level":4,"score":0.6340650320053101},{"id":"https://openalex.org/C192609573","wikidata":"https://www.wikidata.org/wiki/Q7388341","display_name":"S5","level":5,"score":0.6028532385826111},{"id":"https://openalex.org/C86602344","wikidata":"https://www.wikidata.org/wiki/Q7667918","display_name":"T-norm fuzzy logics","level":5,"score":0.5997445583343506},{"id":"https://openalex.org/C160131679","wikidata":"https://www.wikidata.org/wiki/Q2462350","display_name":"Kripke semantics","level":4,"score":0.584086537361145},{"id":"https://openalex.org/C203659156","wikidata":"https://www.wikidata.org/wiki/Q6934805","display_name":"Multimodal logic","level":3,"score":0.5605865120887756},{"id":"https://openalex.org/C33203268","wikidata":"https://www.wikidata.org/wiki/Q5361594","display_name":"Intermediate logic","level":3,"score":0.5576531291007996},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.49944424629211426},{"id":"https://openalex.org/C71139939","wikidata":"https://www.wikidata.org/wiki/Q910194","display_name":"Modal","level":2,"score":0.49448537826538086},{"id":"https://openalex.org/C2777796570","wikidata":"https://www.wikidata.org/wiki/Q2351326","display_name":"Dynamic logic (digital electronics)","level":4,"score":0.48755258321762085},{"id":"https://openalex.org/C100481476","wikidata":"https://www.wikidata.org/wiki/Q4055684","display_name":"First-order logic","level":2,"score":0.48174571990966797},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.4808529019355774},{"id":"https://openalex.org/C32241873","wikidata":"https://www.wikidata.org/wiki/Q236975","display_name":"Classical logic","level":2,"score":0.45477670431137085},{"id":"https://openalex.org/C169896238","wikidata":"https://www.wikidata.org/wiki/Q1644136","display_name":"Higher-order logic","level":3,"score":0.4481396973133087},{"id":"https://openalex.org/C78344899","wikidata":"https://www.wikidata.org/wiki/Q638442","display_name":"Modal operator","level":4,"score":0.4421161413192749},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4365920126438141},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4355411231517792},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.4309268891811371},{"id":"https://openalex.org/C19689857","wikidata":"https://www.wikidata.org/wiki/Q4055684","display_name":"Predicate logic","level":3,"score":0.420663058757782},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3639175295829773},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3454774022102356},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3194654881954193},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1699334979057312},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.08599263429641724},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C5263885","wikidata":"https://www.wikidata.org/wiki/Q1967302","display_name":"Membership function","level":4,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"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/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s1570-2464(07)80012-7","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s1570-2464(07)80012-7","pdf_url":null,"source":{"id":"https://openalex.org/S71695317","display_name":"Studies in logic and practical reasoning","issn_l":"1570-2464","issn":["1570-2464","2212-1137"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Studies in Logic and Practical Reasoning","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":142,"referenced_works":["https://openalex.org/W23277219","https://openalex.org/W28656058","https://openalex.org/W35338707","https://openalex.org/W41255196","https://openalex.org/W42880690","https://openalex.org/W69348146","https://openalex.org/W73013951","https://openalex.org/W93751600","https://openalex.org/W114225339","https://openalex.org/W117467870","https://openalex.org/W133124514","https://openalex.org/W567697108","https://openalex.org/W577129422","https://openalex.org/W775125723","https://openalex.org/W1480314582","https://openalex.org/W1480405493","https://openalex.org/W1490098830","https://openalex.org/W1501130453","https://openalex.org/W1512750313","https://openalex.org/W1522945997","https://openalex.org/W1534018603","https://openalex.org/W1545407035","https://openalex.org/W1549008998","https://openalex.org/W1550579876","https://openalex.org/W1551140636","https://openalex.org/W1552580535","https://openalex.org/W1552596904","https://openalex.org/W1556439193","https://openalex.org/W1568501149","https://openalex.org/W1585533089","https://openalex.org/W1592391653","https://openalex.org/W1606143631","https://openalex.org/W1608610169","https://openalex.org/W1661653767","https://openalex.org/W1966911791","https://openalex.org/W1968233326","https://openalex.org/W1970175046","https://openalex.org/W1978651524","https://openalex.org/W1984084123","https://openalex.org/W1987191047","https://openalex.org/W1987374077","https://openalex.org/W1987567030","https://openalex.org/W1991650963","https://openalex.org/W1991981864","https://openalex.org/W2001282515","https://openalex.org/W2003017965","https://openalex.org/W2003097233","https://openalex.org/W2005239198","https://openalex.org/W2005814072","https://openalex.org/W2008363667","https://openalex.org/W2012883278","https://openalex.org/W2013110598","https://openalex.org/W2017025480","https://openalex.org/W2017127608","https://openalex.org/W2019451333","https://openalex.org/W2023822915","https://openalex.org/W2029277296","https://openalex.org/W2029435309","https://openalex.org/W2032955726","https://openalex.org/W2033774694","https://openalex.org/W2037328204","https://openalex.org/W2038711624","https://openalex.org/W2040406842","https://openalex.org/W2041930157","https://openalex.org/W2047868398","https://openalex.org/W2049336733","https://openalex.org/W2053038530","https://openalex.org/W2053772225","https://openalex.org/W2054046573","https://openalex.org/W2054289094","https://openalex.org/W2055531460","https://openalex.org/W2063981788","https://openalex.org/W2065869391","https://openalex.org/W2068458083","https://openalex.org/W2071369407","https://openalex.org/W2074507365","https://openalex.org/W2074530527","https://openalex.org/W2076784334","https://openalex.org/W2079626851","https://openalex.org/W2083623540","https://openalex.org/W2083897845","https://openalex.org/W2085964374","https://openalex.org/W2086470346","https://openalex.org/W2088302563","https://openalex.org/W2092576830","https://openalex.org/W2093805757","https://openalex.org/W2098324200","https://openalex.org/W2111324752","https://openalex.org/W2116784584","https://openalex.org/W2120713972","https://openalex.org/W2120756102","https://openalex.org/W2126382654","https://openalex.org/W2130098903","https://openalex.org/W2138126349","https://openalex.org/W2144347980","https://openalex.org/W2148391937","https://openalex.org/W2159753366","https://openalex.org/W2163751633","https://openalex.org/W2171341074","https://openalex.org/W2173219234","https://openalex.org/W2266218826","https://openalex.org/W2319388297","https://openalex.org/W2336123333","https://openalex.org/W2489522148","https://openalex.org/W2495011300","https://openalex.org/W2495407121","https://openalex.org/W2734920594","https://openalex.org/W2807153835","https://openalex.org/W2913966000","https://openalex.org/W2999752128","https://openalex.org/W3144889436","https://openalex.org/W3211677608","https://openalex.org/W3216784059","https://openalex.org/W4206038654","https://openalex.org/W4206381645","https://openalex.org/W4210317869","https://openalex.org/W4233570983","https://openalex.org/W4246772431","https://openalex.org/W4247797067","https://openalex.org/W4256562411","https://openalex.org/W6601181045","https://openalex.org/W6601478224","https://openalex.org/W6602844375","https://openalex.org/W6602911221","https://openalex.org/W6620798145","https://openalex.org/W6629153072","https://openalex.org/W6629959792","https://openalex.org/W6633056259","https://openalex.org/W6633163552","https://openalex.org/W6633770934","https://openalex.org/W6647160770","https://openalex.org/W6654663888","https://openalex.org/W6660707140","https://openalex.org/W6676525128","https://openalex.org/W6677857594","https://openalex.org/W6685473474","https://openalex.org/W6693509663","https://openalex.org/W6723640255","https://openalex.org/W6752046349","https://openalex.org/W6793045953","https://openalex.org/W6817620044","https://openalex.org/W6830173364"],"related_works":["https://openalex.org/W1978386240","https://openalex.org/W2077061463","https://openalex.org/W2171395754","https://openalex.org/W2766759918","https://openalex.org/W2951073329","https://openalex.org/W2299748756","https://openalex.org/W3102684629","https://openalex.org/W4391114601","https://openalex.org/W2039904055","https://openalex.org/W1545104624"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":7}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}