{"id":"https://openalex.org/W2053856951","doi":"https://doi.org/10.1002/malq.200410054","title":"Normal derivability in modal logic","display_name":"Normal derivability in modal logic","publication_year":2005,"publication_date":"2005-09-28","ids":{"openalex":"https://openalex.org/W2053856951","doi":"https://doi.org/10.1002/malq.200410054","mag":"2053856951"},"language":"en","primary_location":{"id":"doi:10.1002/malq.200410054","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.200410054","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":"MLQ","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/A5050687353","display_name":"Jan von Plato","orcid":"https://orcid.org/0000-0002-8370-9255"},"institutions":[{"id":"https://openalex.org/I133731052","display_name":"University of Helsinki","ror":"https://ror.org/040af2s02","country_code":"FI","type":"education","lineage":["https://openalex.org/I133731052"]}],"countries":["FI"],"is_corresponding":true,"raw_author_name":"Jan von Plato","raw_affiliation_strings":["Department of Philosophy, P.O. Box 24, 00014 University of Helsinki, Finland"],"affiliations":[{"raw_affiliation_string":"Department of Philosophy, P.O. Box 24, 00014 University of Helsinki, Finland","institution_ids":["https://openalex.org/I133731052"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5050687353"],"corresponding_institution_ids":["https://openalex.org/I133731052"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.11242455,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"51","issue":"6","first_page":"632","last_page":"638"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9761999845504761,"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":0.9761999845504761,"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":0.9681000113487244,"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/T10181","display_name":"Natural Language Processing Techniques","score":0.920199990272522,"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/normalization","display_name":"Normalization (sociology)","score":0.7510488033294678},{"id":"https://openalex.org/keywords/modal","display_name":"Modal","score":0.7090972661972046},{"id":"https://openalex.org/keywords/modal-logic","display_name":"Modal logic","score":0.6863994002342224},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6294727921485901},{"id":"https://openalex.org/keywords/normal-modal-logic","display_name":"Normal modal logic","score":0.5517867207527161},{"id":"https://openalex.org/keywords/composability","display_name":"Composability","score":0.47169211506843567},{"id":"https://openalex.org/keywords/modal-\u03bc-calculus","display_name":"Modal \u03bc-calculus","score":0.4581924378871918},{"id":"https://openalex.org/keywords/natural-deduction","display_name":"Natural deduction","score":0.44034141302108765},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.36889177560806274},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.33777737617492676},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2580386996269226},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.20762580633163452},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.11283880472183228}],"concepts":[{"id":"https://openalex.org/C136886441","wikidata":"https://www.wikidata.org/wiki/Q926129","display_name":"Normalization (sociology)","level":2,"score":0.7510488033294678},{"id":"https://openalex.org/C71139939","wikidata":"https://www.wikidata.org/wiki/Q910194","display_name":"Modal","level":2,"score":0.7090972661972046},{"id":"https://openalex.org/C27508121","wikidata":"https://www.wikidata.org/wiki/Q210841","display_name":"Modal logic","level":3,"score":0.6863994002342224},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6294727921485901},{"id":"https://openalex.org/C114092440","wikidata":"https://www.wikidata.org/wiki/Q840226","display_name":"Normal modal logic","level":4,"score":0.5517867207527161},{"id":"https://openalex.org/C2778814252","wikidata":"https://www.wikidata.org/wiki/Q5156715","display_name":"Composability","level":2,"score":0.47169211506843567},{"id":"https://openalex.org/C173125200","wikidata":"https://www.wikidata.org/wiki/Q5275729","display_name":"Modal \u03bc-calculus","level":5,"score":0.4581924378871918},{"id":"https://openalex.org/C62073222","wikidata":"https://www.wikidata.org/wiki/Q1572108","display_name":"Natural deduction","level":2,"score":0.44034141302108765},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.36889177560806274},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.33777737617492676},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2580386996269226},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.20762580633163452},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.11283880472183228},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","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/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C19165224","wikidata":"https://www.wikidata.org/wiki/Q23404","display_name":"Anthropology","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":1,"locations":[{"id":"doi:10.1002/malq.200410054","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.200410054","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":"MLQ","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.6100000143051147,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W1528233644","https://openalex.org/W2039977878","https://openalex.org/W2060230835","https://openalex.org/W2143786699"],"related_works":["https://openalex.org/W1498755214","https://openalex.org/W2082558313","https://openalex.org/W2138716118","https://openalex.org/W2534562289","https://openalex.org/W3122667086","https://openalex.org/W2077061463","https://openalex.org/W2144619006","https://openalex.org/W2123071520","https://openalex.org/W2067687795","https://openalex.org/W2162253430"],"abstract_inverted_index":{"The":[0],"standard":[1],"rule":[2,42,58],"of":[3,7,35,40,55,59,69],"necessitation":[4],"in":[5,66],"systems":[6],"natural":[8],"deduction":[9],"for":[10],"the":[11,31,41,57,67],"modal":[12,26],"logic":[13],"S4":[14],"concludes":[15],"\u25a1A":[16],"from":[17],"A":[18,22],"whenever":[19],"all":[20,61],"assumptions":[21],"depends":[23],"on":[24],"are":[25,64],"formulas.":[27],"This":[28],"condition":[29],"prevents":[30],"composability":[32],"and":[33,37],"normalization":[34],"derivations,":[36],"therefore":[38],"modifications":[39],"have":[43],"been":[44],"suggested.":[45],"It":[46],"is":[47],"shown":[48],"that":[49],"both":[50],"properties":[51],"hold":[52],"if,":[53],"instead":[54],"changing":[56],"necessitation,":[60],"elimination":[62],"rules":[63],"formulated":[65],"manner":[68],"disjunction":[70],"elimination,":[71],"i.e.":[72],"with":[73],"an":[74],"arbitrary":[75],"consequence.":[76],"(\u00a9":[77],"2005":[78],"WILEY-VCH":[79],"Verlag":[80],"GmbH":[81],"&":[82],"Co.":[83],"KGaA,":[84],"Weinheim)":[85]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
