{"id":"https://openalex.org/W1992413343","doi":"https://doi.org/10.1002/malq.19970430112","title":"Minimal Axiomatization in Modal Logic","display_name":"Minimal Axiomatization in Modal Logic","publication_year":1997,"publication_date":"1997-01-01","ids":{"openalex":"https://openalex.org/W1992413343","doi":"https://doi.org/10.1002/malq.19970430112","mag":"1992413343"},"language":"en","primary_location":{"id":"doi:10.1002/malq.19970430112","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.19970430112","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","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/A5079614550","display_name":"Fabio Bellissima","orcid":null},"institutions":[{"id":"https://openalex.org/I102064193","display_name":"University of Siena","ror":"https://ror.org/01tevnk56","country_code":"IT","type":"education","lineage":["https://openalex.org/I102064193"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Fabio Bellissima","raw_affiliation_strings":["Department of Mathematics, University of Siena Via del Capitano 15, I\u201053100 Siena, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Siena Via del Capitano 15, I\u201053100 Siena, Italy","institution_ids":["https://openalex.org/I102064193"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061711232","display_name":"Saverio Cittadini","orcid":null},"institutions":[{"id":"https://openalex.org/I102064193","display_name":"University of Siena","ror":"https://ror.org/01tevnk56","country_code":"IT","type":"education","lineage":["https://openalex.org/I102064193"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Saverio Cittadini","raw_affiliation_strings":["Department of Mathematics, University of Siena Via del Capitano 15, I\u201053100 Siena, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Siena Via del Capitano 15, I\u201053100 Siena, Italy","institution_ids":["https://openalex.org/I102064193"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5079614550"],"corresponding_institution_ids":["https://openalex.org/I102064193"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":1.7551,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.86135217,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"43","issue":"1","first_page":"92","last_page":"102"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9994999766349792,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9954000115394592,"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/mathematics","display_name":"Mathematics","score":0.8814045190811157},{"id":"https://openalex.org/keywords/modal-logic","display_name":"Modal logic","score":0.814084529876709},{"id":"https://openalex.org/keywords/transitive-relation","display_name":"Transitive relation","score":0.8060420751571655},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.6636468172073364},{"id":"https://openalex.org/keywords/frame","display_name":"Frame (networking)","score":0.6047219634056091},{"id":"https://openalex.org/keywords/normal-modal-logic","display_name":"Normal modal logic","score":0.6024092435836792},{"id":"https://openalex.org/keywords/modal","display_name":"Modal","score":0.500201940536499},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.46621567010879517},{"id":"https://openalex.org/keywords/intermediate-logic","display_name":"Intermediate logic","score":0.45931628346443176},{"id":"https://openalex.org/keywords/s5","display_name":"S5","score":0.4143660068511963},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.37963664531707764},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.35941046476364136},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.19680103659629822},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0723242461681366},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.06525018811225891},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.05060186982154846}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8814045190811157},{"id":"https://openalex.org/C27508121","wikidata":"https://www.wikidata.org/wiki/Q210841","display_name":"Modal logic","level":3,"score":0.814084529876709},{"id":"https://openalex.org/C191399111","wikidata":"https://www.wikidata.org/wiki/Q64861","display_name":"Transitive relation","level":2,"score":0.8060420751571655},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.6636468172073364},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.6047219634056091},{"id":"https://openalex.org/C114092440","wikidata":"https://www.wikidata.org/wiki/Q840226","display_name":"Normal modal logic","level":4,"score":0.6024092435836792},{"id":"https://openalex.org/C71139939","wikidata":"https://www.wikidata.org/wiki/Q910194","display_name":"Modal","level":2,"score":0.500201940536499},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46621567010879517},{"id":"https://openalex.org/C33203268","wikidata":"https://www.wikidata.org/wiki/Q5361594","display_name":"Intermediate logic","level":3,"score":0.45931628346443176},{"id":"https://openalex.org/C192609573","wikidata":"https://www.wikidata.org/wiki/Q7388341","display_name":"S5","level":5,"score":0.4143660068511963},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37963664531707764},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.35941046476364136},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.19680103659629822},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0723242461681366},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.06525018811225891},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.05060186982154846},{"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},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C171250308","wikidata":"https://www.wikidata.org/wiki/Q11468","display_name":"Nanotechnology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1002/malq.19970430112","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.19970430112","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"},{"id":"pmh:oai:usiena-air.unisi.it:11365/20443","is_oa":false,"landing_page_url":"http://hdl.handle.net/11365/20443","pdf_url":null,"source":{"id":"https://openalex.org/S4377196319","display_name":"Use Siena air (University of Siena)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I102064193","host_organization_name":"University of Siena","host_organization_lineage":["https://openalex.org/I102064193"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W91391498","https://openalex.org/W1527588453","https://openalex.org/W1971725661","https://openalex.org/W2071467583","https://openalex.org/W2084803705","https://openalex.org/W2085659130","https://openalex.org/W2090086476","https://openalex.org/W2137410044","https://openalex.org/W4249714686","https://openalex.org/W4299812680"],"related_works":["https://openalex.org/W2795425183","https://openalex.org/W3108798275","https://openalex.org/W2260113151","https://openalex.org/W3126675290","https://openalex.org/W2554822349","https://openalex.org/W3122667086","https://openalex.org/W2019891739","https://openalex.org/W4310201982","https://openalex.org/W176661328","https://openalex.org/W2396928407"],"abstract_inverted_index":{"Abstract":[0],"We":[1,42],"consider":[2],"the":[3,8,31,39],"problem":[4],"of":[5,10,35],"finding,":[6],"in":[7],"ambit":[9],"modal":[11],"logic,":[12],"a":[13,21,25,50],"minimal":[14,51],"characterization":[15,52],"for":[16],"finite":[17,46],"Kripke":[18],"frames,":[19],"i.e.,":[20],"formula":[22],"which,":[23],"given":[24],"frame,":[26],"axiomatizes":[27],"its":[28],"theory":[29],"employing":[30],"lowest":[32],"possible":[33],"number":[34],"variables":[36],"and":[37,55],"implies":[38],"other":[40],"axiomatizations.":[41],"show":[43],"that":[44,56],"every":[45],"transitive":[47],"frame":[48],"admits":[49],"over":[53],"K4,":[54],"this":[57],"result":[58],"can":[59],"not":[60],"be":[61],"extended":[62],"to":[63],"K.":[64]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}