{"id":"https://openalex.org/W7119118929","doi":"https://doi.org/10.1007/s10992-025-09826-2","title":"A Norm-based Truthmaker Semantics for Modal Logic","display_name":"A Norm-based Truthmaker Semantics for Modal Logic","publication_year":2026,"publication_date":"2026-01-06","ids":{"openalex":"https://openalex.org/W7119118929","doi":"https://doi.org/10.1007/s10992-025-09826-2"},"language":"en","primary_location":{"id":"doi:10.1007/s10992-025-09826-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10992-025-09826-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10992-025-09826-2.pdf","source":{"id":"https://openalex.org/S161120620","display_name":"Journal of Philosophical Logic","issn_l":"0022-3611","issn":["0022-3611","1573-0433"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Philosophical Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10992-025-09826-2.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013007890","display_name":"Alessandro Giordani","orcid":"https://orcid.org/0000-0003-4654-2174"},"institutions":[{"id":"https://openalex.org/I189158943","display_name":"University of Milan","ror":"https://ror.org/00wjc7c48","country_code":"IT","type":"education","lineage":["https://openalex.org/I189158943"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Alessandro Giordani","raw_affiliation_strings":["Catholic University of Milan, Milan, Italy"],"affiliations":[{"raw_affiliation_string":"Catholic University of Milan, Milan, Italy","institution_ids":["https://openalex.org/I189158943"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002038158","display_name":"Vita Saitta","orcid":"https://orcid.org/0009-0003-4546-823X"},"institutions":[{"id":"https://openalex.org/I189158943","display_name":"University of Milan","ror":"https://ror.org/00wjc7c48","country_code":"IT","type":"education","lineage":["https://openalex.org/I189158943"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Vita Saitta","raw_affiliation_strings":["Catholic University of Milan, Milan, Italy"],"affiliations":[{"raw_affiliation_string":"Catholic University of Milan, Milan, Italy","institution_ids":["https://openalex.org/I189158943"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5002038158"],"corresponding_institution_ids":["https://openalex.org/I189158943"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2780},"apc_paid":{"value":2190,"currency":"EUR","value_usd":2780},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.05480942,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"55","issue":"1","first_page":"135","last_page":"165"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9830999970436096,"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":0.9830999970436096,"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":0.006899999920278788,"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":0.002400000113993883,"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":0.6898999810218811},{"id":"https://openalex.org/keywords/modal","display_name":"Modal","score":0.6665999889373779},{"id":"https://openalex.org/keywords/semantics","display_name":"Semantics (computer science)","score":0.6500999927520752},{"id":"https://openalex.org/keywords/normal-modal-logic","display_name":"Normal modal logic","score":0.5037999749183655},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.46869999170303345},{"id":"https://openalex.org/keywords/accessibility-relation","display_name":"Accessibility relation","score":0.3917999863624573},{"id":"https://openalex.org/keywords/multimodal-logic","display_name":"Multimodal logic","score":0.384799987077713},{"id":"https://openalex.org/keywords/kripke-semantics","display_name":"Kripke semantics","score":0.3587999939918518},{"id":"https://openalex.org/keywords/modal-operator","display_name":"Modal operator","score":0.3546999990940094}],"concepts":[{"id":"https://openalex.org/C27508121","wikidata":"https://www.wikidata.org/wiki/Q210841","display_name":"Modal logic","level":3,"score":0.6898999810218811},{"id":"https://openalex.org/C71139939","wikidata":"https://www.wikidata.org/wiki/Q910194","display_name":"Modal","level":2,"score":0.6665999889373779},{"id":"https://openalex.org/C184337299","wikidata":"https://www.wikidata.org/wiki/Q1437428","display_name":"Semantics (computer science)","level":2,"score":0.6500999927520752},{"id":"https://openalex.org/C114092440","wikidata":"https://www.wikidata.org/wiki/Q840226","display_name":"Normal modal logic","level":4,"score":0.5037999749183655},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.46869999170303345},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44200000166893005},{"id":"https://openalex.org/C11191006","wikidata":"https://www.wikidata.org/wiki/Q2663311","display_name":"Accessibility relation","level":4,"score":0.3917999863624573},{"id":"https://openalex.org/C203659156","wikidata":"https://www.wikidata.org/wiki/Q6934805","display_name":"Multimodal logic","level":3,"score":0.384799987077713},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3628000020980835},{"id":"https://openalex.org/C160131679","wikidata":"https://www.wikidata.org/wiki/Q2462350","display_name":"Kripke semantics","level":4,"score":0.3587999939918518},{"id":"https://openalex.org/C78344899","wikidata":"https://www.wikidata.org/wiki/Q638442","display_name":"Modal operator","level":4,"score":0.3546999990940094},{"id":"https://openalex.org/C136172866","wikidata":"https://www.wikidata.org/wiki/Q1088088","display_name":"Possible world","level":2,"score":0.35179999470710754},{"id":"https://openalex.org/C62360110","wikidata":"https://www.wikidata.org/wiki/Q96777007","display_name":"Circumscription","level":2,"score":0.35019999742507935},{"id":"https://openalex.org/C25810664","wikidata":"https://www.wikidata.org/wiki/Q44325","display_name":"Ontology","level":2,"score":0.3479999899864197},{"id":"https://openalex.org/C107247716","wikidata":"https://www.wikidata.org/wiki/Q1347436","display_name":"Epistemic modal logic","level":4,"score":0.33500000834465027},{"id":"https://openalex.org/C2780598303","wikidata":"https://www.wikidata.org/wiki/Q65921492","display_name":"Flexibility (engineering)","level":2,"score":0.32839998602867126},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.30649998784065247},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.30489999055862427},{"id":"https://openalex.org/C159032336","wikidata":"https://www.wikidata.org/wiki/Q2488768","display_name":"Non-monotonic logic","level":2,"score":0.2935999929904938},{"id":"https://openalex.org/C2777796570","wikidata":"https://www.wikidata.org/wiki/Q2351326","display_name":"Dynamic logic (digital electronics)","level":4,"score":0.29030001163482666},{"id":"https://openalex.org/C89497691","wikidata":"https://www.wikidata.org/wiki/Q7981058","display_name":"Well-founded semantics","level":5,"score":0.2881999909877777},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.2784999907016754},{"id":"https://openalex.org/C146499914","wikidata":"https://www.wikidata.org/wiki/Q5469969","display_name":"Formal semantics (linguistics)","level":2,"score":0.27709999680519104},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.2759999930858612},{"id":"https://openalex.org/C192609573","wikidata":"https://www.wikidata.org/wiki/Q7388341","display_name":"S5","level":5,"score":0.2685000002384186},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2529999911785126},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.25279998779296875},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2526000142097473}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10992-025-09826-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10992-025-09826-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10992-025-09826-2.pdf","source":{"id":"https://openalex.org/S161120620","display_name":"Journal of Philosophical Logic","issn_l":"0022-3611","issn":["0022-3611","1573-0433"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Philosophical Logic","raw_type":"journal-article"},{"id":"pmh:oai:publicatt.unicatt.it:10807/328419","is_oa":true,"landing_page_url":"https://hdl.handle.net/10807/328419","pdf_url":null,"source":{"id":"https://openalex.org/S4306400564","display_name":"PubliCatt (Universit\u00e0 Cattolica del Sacro Cuore)","issn_l":null,"issn":null,"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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s10992-025-09826-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10992-025-09826-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10992-025-09826-2.pdf","source":{"id":"https://openalex.org/S161120620","display_name":"Journal of Philosophical Logic","issn_l":"0022-3611","issn":["0022-3611","1573-0433"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Philosophical Logic","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7119118929.pdf","grobid_xml":"https://content.openalex.org/works/W7119118929.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W1522516632","https://openalex.org/W2085342194","https://openalex.org/W2105010491","https://openalex.org/W2318919315","https://openalex.org/W2607856979","https://openalex.org/W2724428718","https://openalex.org/W2768154882","https://openalex.org/W2891594412","https://openalex.org/W2891651317","https://openalex.org/W2896358236","https://openalex.org/W2970413504","https://openalex.org/W3112889829","https://openalex.org/W4234951245","https://openalex.org/W4242309855","https://openalex.org/W4251842765","https://openalex.org/W4283581404","https://openalex.org/W4317796398","https://openalex.org/W4388996193","https://openalex.org/W4393935267","https://openalex.org/W4399293238","https://openalex.org/W4401276770","https://openalex.org/W4404858384"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"In":[1],"the":[2,10,115],"last":[3],"few":[4],"decades,":[5],"truthmaker":[6,47,94,120],"semantics":[7,48,85,95,121],"has":[8],"attracted":[9],"attention":[11],"of":[12,30,66,104],"scholars":[13],"from":[14],"various":[15],"areas,":[16],"arguably":[17],"due":[18],"to":[19,35,55,74],"its":[20,24],"philosophical":[21],"underpinning":[22],"and":[23],"flexibility":[25],"in":[26],"addressing":[27],"a":[28,82,93,102],"number":[29],"problems":[31],"that":[32,56,64],"are":[33,69],"difficult":[34],"solve":[36],"using":[37],"alternative":[38],"semantic":[39],"frameworks.":[40],"Attention":[41],"is":[42,63],"now":[43],"focused":[44],"on":[45],"developing":[46],"for":[49,86,96,122],"modal":[50,67,84,98,124],"logic;":[51,89],"this":[52],"paper":[53],"contributes":[54],"direction.":[57],"The":[58],"basic":[59],"idea":[60],"we":[61,80,91,112],"introduce":[62,81],"truthmakers":[65],"sentences":[68],"norms.":[70],"This":[71,107],"allows":[72],"us":[73],"derive":[75],"two":[76],"interesting":[77],"results:":[78],"first,":[79],"new":[83],"minimal":[87],"monotonic":[88],"second,":[90],"provide":[92],"every":[97],"logic":[99],"characterized":[100],"by":[101],"class":[103],"Kripke":[105],"frames.":[106],"is,":[108],"as":[109,111],"far":[110],"can":[113],"tell,":[114],"first":[116],"general":[117],"result":[118],"about":[119],"normal":[123],"logics.":[125]},"counts_by_year":[],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2026-01-08T00:00:00"}