{"id":"https://openalex.org/W3197483653","doi":"https://doi.org/10.1017/s1755020321000411","title":"FRACTIONAL-VALUED MODAL LOGIC","display_name":"FRACTIONAL-VALUED MODAL LOGIC","publication_year":2021,"publication_date":"2021-08-31","ids":{"openalex":"https://openalex.org/W3197483653","doi":"https://doi.org/10.1017/s1755020321000411","mag":"3197483653"},"language":"en","primary_location":{"id":"doi:10.1017/s1755020321000411","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s1755020321000411","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/1F55543D07BBE54A8B26C2804D4D420B/S1755020321000411a.pdf/div-class-title-fractional-valued-modal-logic-div.pdf","source":{"id":"https://openalex.org/S24077076","display_name":"The Review of Symbolic Logic","issn_l":"1755-0203","issn":["1755-0203","1755-0211"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Review of Symbolic Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/1F55543D07BBE54A8B26C2804D4D420B/S1755020321000411a.pdf/div-class-title-fractional-valued-modal-logic-div.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080400178","display_name":"Mario Piazza","orcid":"https://orcid.org/0000-0002-9545-3912"},"institutions":[{"id":"https://openalex.org/I157210198","display_name":"Scuola Normale Superiore","ror":"https://ror.org/03aydme10","country_code":"IT","type":"education","lineage":["https://openalex.org/I157210198"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"MARIO PIAZZA","raw_affiliation_strings":["CLASSE DI LETTERE E FILOSOFIA SCUOLA NORMALE SUPERIORE DI PISA PISA, ITALY E-mail:"],"affiliations":[{"raw_affiliation_string":"CLASSE DI LETTERE E FILOSOFIA SCUOLA NORMALE SUPERIORE DI PISA PISA, ITALY E-mail:","institution_ids":["https://openalex.org/I157210198"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011277020","display_name":"Gabriele Pulcini","orcid":"https://orcid.org/0000-0003-0101-0916"},"institutions":[{"id":"https://openalex.org/I157210198","display_name":"Scuola Normale Superiore","ror":"https://ror.org/03aydme10","country_code":"IT","type":"education","lineage":["https://openalex.org/I157210198"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"GABRIELE PULCINI","raw_affiliation_strings":["CLASSE DI LETTERE E FILOSOFIA SCUOLA NORMALE SUPERIORE DI PISA PISA, ITALY E-mail:"],"affiliations":[{"raw_affiliation_string":"CLASSE DI LETTERE E FILOSOFIA SCUOLA NORMALE SUPERIORE DI PISA PISA, ITALY E-mail:","institution_ids":["https://openalex.org/I157210198"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059726063","display_name":"Matteo Tesi","orcid":"https://orcid.org/0000-0003-2810-5835"},"institutions":[{"id":"https://openalex.org/I116067653","display_name":"University of Rome Tor Vergata","ror":"https://ror.org/02p77k626","country_code":"IT","type":"education","lineage":["https://openalex.org/I116067653"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"MATTEO TESI","raw_affiliation_strings":["DIPARTIMENTO DI STUDI LETTERARI, FILOSOFICI E DI STORIA DELL\u2019ARTE UNIVERSIT\u00c0 DI ROMA \u201cTOR VERGATA\u201d ROME, ITALY E-mail:"],"affiliations":[{"raw_affiliation_string":"DIPARTIMENTO DI STUDI LETTERARI, FILOSOFICI E DI STORIA DELL\u2019ARTE UNIVERSIT\u00c0 DI ROMA \u201cTOR VERGATA\u201d ROME, ITALY E-mail:","institution_ids":["https://openalex.org/I116067653"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5080400178"],"corresponding_institution_ids":["https://openalex.org/I157210198"],"apc_list":null,"apc_paid":null,"fwci":0.42,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.69572166,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":97},"biblio":{"volume":"16","issue":"4","first_page":"1033","last_page":"1052"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9993000030517578,"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":0.9975000023841858,"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/modal-logic","display_name":"Modal logic","score":0.6268473863601685},{"id":"https://openalex.org/keywords/normal-modal-logic","display_name":"Normal modal logic","score":0.5517230033874512},{"id":"https://openalex.org/keywords/multimodal-logic","display_name":"Multimodal logic","score":0.5239025354385376},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5135040879249573},{"id":"https://openalex.org/keywords/sequent-calculus","display_name":"Sequent calculus","score":0.5087149739265442},{"id":"https://openalex.org/keywords/s5","display_name":"S5","score":0.48230695724487305},{"id":"https://openalex.org/keywords/higher-order-logic","display_name":"Higher-order logic","score":0.4582599103450775},{"id":"https://openalex.org/keywords/modal","display_name":"Modal","score":0.4525345265865326},{"id":"https://openalex.org/keywords/proof-theory","display_name":"Proof theory","score":0.43551722168922424},{"id":"https://openalex.org/keywords/semantics","display_name":"Semantics (computer science)","score":0.4267333149909973},{"id":"https://openalex.org/keywords/dynamic-logic","display_name":"Dynamic logic (digital electronics)","score":0.41889864206314087},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3917338252067566},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3796629309654236},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36205965280532837},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.35718709230422974},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.25947532057762146},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.18150338530540466},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.1356571912765503},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.12065282464027405}],"concepts":[{"id":"https://openalex.org/C27508121","wikidata":"https://www.wikidata.org/wiki/Q210841","display_name":"Modal logic","level":3,"score":0.6268473863601685},{"id":"https://openalex.org/C114092440","wikidata":"https://www.wikidata.org/wiki/Q840226","display_name":"Normal modal logic","level":4,"score":0.5517230033874512},{"id":"https://openalex.org/C203659156","wikidata":"https://www.wikidata.org/wiki/Q6934805","display_name":"Multimodal logic","level":3,"score":0.5239025354385376},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5135040879249573},{"id":"https://openalex.org/C65880906","wikidata":"https://www.wikidata.org/wiki/Q1771121","display_name":"Sequent calculus","level":3,"score":0.5087149739265442},{"id":"https://openalex.org/C192609573","wikidata":"https://www.wikidata.org/wiki/Q7388341","display_name":"S5","level":5,"score":0.48230695724487305},{"id":"https://openalex.org/C169896238","wikidata":"https://www.wikidata.org/wiki/Q1644136","display_name":"Higher-order logic","level":3,"score":0.4582599103450775},{"id":"https://openalex.org/C71139939","wikidata":"https://www.wikidata.org/wiki/Q910194","display_name":"Modal","level":2,"score":0.4525345265865326},{"id":"https://openalex.org/C2318724","wikidata":"https://www.wikidata.org/wiki/Q852732","display_name":"Proof theory","level":3,"score":0.43551722168922424},{"id":"https://openalex.org/C184337299","wikidata":"https://www.wikidata.org/wiki/Q1437428","display_name":"Semantics (computer science)","level":2,"score":0.4267333149909973},{"id":"https://openalex.org/C2777796570","wikidata":"https://www.wikidata.org/wiki/Q2351326","display_name":"Dynamic logic (digital electronics)","level":4,"score":0.41889864206314087},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3917338252067566},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3796629309654236},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36205965280532837},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35718709230422974},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.25947532057762146},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.18150338530540466},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.1356571912765503},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.12065282464027405},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","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},{"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/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1017/s1755020321000411","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s1755020321000411","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/1F55543D07BBE54A8B26C2804D4D420B/S1755020321000411a.pdf/div-class-title-fractional-valued-modal-logic-div.pdf","source":{"id":"https://openalex.org/S24077076","display_name":"The Review of Symbolic Logic","issn_l":"1755-0203","issn":["1755-0203","1755-0211"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Review of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:art.torvergata.it:2108/284906","is_oa":true,"landing_page_url":"http://hdl.handle.net/2108/284906","pdf_url":"https://art.torvergata.it/bitstream/2108/284906/1/fractional-valued-modal-logic.pdf","source":{"id":"https://openalex.org/S4306400993","display_name":"Cineca Institutional Research Information System (Tor Vergata University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I116067653","host_organization_name":"University of Rome Tor Vergata","host_organization_lineage":["https://openalex.org/I116067653"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:ricerca.sns.it:11384/109966","is_oa":true,"landing_page_url":"http://hdl.handle.net/11384/109966","pdf_url":"https://ricerca.sns.it/bitstream/11384/109966/1/fractional-valued-modal-logic.pdf","source":{"id":"https://openalex.org/S7407050981","display_name":"Scuola Normale Superiore di Pisa","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:zenodo.org:177002","is_oa":true,"landing_page_url":"https://www.openaccessrepository.it/record/177002","pdf_url":null,"source":{"id":"https://openalex.org/S4306402478","display_name":"INFM-OAR (INFN Catania)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210116497","host_organization_name":"Istituto Nazionale di Fisica Nucleare, Sezione di Catania","host_organization_lineage":["https://openalex.org/I4210116497"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1017/s1755020321000411","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s1755020321000411","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/1F55543D07BBE54A8B26C2804D4D420B/S1755020321000411a.pdf/div-class-title-fractional-valued-modal-logic-div.pdf","source":{"id":"https://openalex.org/S24077076","display_name":"The Review of Symbolic Logic","issn_l":"1755-0203","issn":["1755-0203","1755-0211"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Review of Symbolic Logic","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3197483653.pdf","grobid_xml":"https://content.openalex.org/works/W3197483653.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W25183180","https://openalex.org/W56574371","https://openalex.org/W586261321","https://openalex.org/W1503413362","https://openalex.org/W1540863024","https://openalex.org/W1573218237","https://openalex.org/W1966647830","https://openalex.org/W1969249988","https://openalex.org/W1971043428","https://openalex.org/W1985141036","https://openalex.org/W1990470938","https://openalex.org/W1995718667","https://openalex.org/W2059132792","https://openalex.org/W2093157821","https://openalex.org/W2101642538","https://openalex.org/W2145470702","https://openalex.org/W2152348170","https://openalex.org/W2770391921","https://openalex.org/W2972322463","https://openalex.org/W2980490123","https://openalex.org/W3013452505","https://openalex.org/W3033102388","https://openalex.org/W3082208784","https://openalex.org/W3152800724","https://openalex.org/W4211144022","https://openalex.org/W4213332023","https://openalex.org/W4249736722","https://openalex.org/W4388311772","https://openalex.org/W4388372578"],"related_works":["https://openalex.org/W3108798275","https://openalex.org/W142011187","https://openalex.org/W2963628981","https://openalex.org/W2163751633","https://openalex.org/W2621184258","https://openalex.org/W2534562289","https://openalex.org/W1483655485","https://openalex.org/W2135389919","https://openalex.org/W2129927112","https://openalex.org/W147278437"],"abstract_inverted_index":{"Abstract":[0],"This":[1,20],"paper":[2],"is":[3,21,93],"dedicated":[4],"to":[5,9,17,82],"extending":[6],"and":[7,65,98],"adapting":[8],"modal":[10,45,108],"logic":[11,46],"the":[12,33,37,44,49,62,83,101],"approach":[13],"of":[14,61,74,90,103],"fractional":[15],"semantics":[16,24,86,106],"classical":[18],"logic.":[19,109],"a":[22,94,104],"multi-valued":[23],"governed":[25],"by":[26],"pure":[27],"proof-theoretic":[28,105],"considerations,":[29],"whose":[30],"truth-values":[31],"are":[32],"rational":[34],"numbers":[35],"in":[36,96],"closed":[38],"interval":[39],"$[0,1]$":[40],".":[41],"Focusing":[42],"on":[43,53],"K":[47,75],",":[48],"proposed":[50],"methodology":[51],"relies":[52],"three":[54],"key":[55],"components:":[56],"bilateral":[57],"sequent":[58],"calculus,":[59],"invertibility":[60],"logical":[63],"rules,":[64],"stability":[66],"(proof-invariance).":[67],"We":[68],"show":[69],"that":[70],"our":[71],"semantic":[72],"analysis":[73],"affords":[76],"an":[77],"informational":[78],"refinement":[79],"with":[80],"respect":[81],"standard":[84],"Kripkean":[85],"(a":[87],"new":[88],"proof":[89],"Dugundji\u2019s":[91],"theorem":[92],"case":[95],"point)":[97],"it":[99],"raises":[100],"prospect":[102],"for":[107]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":3}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}