{"id":"https://openalex.org/W2162253430","doi":"https://doi.org/10.1007/978-3-642-10672-9_18","title":"Classical Natural Deduction for S4 Modal Logic","display_name":"Classical Natural Deduction for S4 Modal Logic","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2162253430","doi":"https://doi.org/10.1007/978-3-642-10672-9_18","mag":"2162253430"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-10672-9_18","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-10672-9_18","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","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":[{"author_position":"first","author":{"id":"https://openalex.org/A5018160333","display_name":"Daisuke Kimura","orcid":"https://orcid.org/0000-0001-5620-8263"},"institutions":[{"id":"https://openalex.org/I161296585","display_name":"Tokyo University of Science","ror":"https://ror.org/05sj3n476","country_code":"JP","type":"education","lineage":["https://openalex.org/I161296585"]},{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Daisuke Kimura","raw_affiliation_strings":["Department of Computer Science, University of Tokyo, 7-3-1 Hongo, Tokyo, 113-8656, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Tokyo, 7-3-1 Hongo, Tokyo, 113-8656, Japan","institution_ids":["https://openalex.org/I74801974","https://openalex.org/I161296585"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081117567","display_name":"Yoshihiko Kakutani","orcid":null},"institutions":[{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]},{"id":"https://openalex.org/I161296585","display_name":"Tokyo University of Science","ror":"https://ror.org/05sj3n476","country_code":"JP","type":"education","lineage":["https://openalex.org/I161296585"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yoshihiko Kakutani","raw_affiliation_strings":["Department of Computer Science, University of Tokyo, 7-3-1 Hongo, Tokyo, 113-8656, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Tokyo, 7-3-1 Hongo, Tokyo, 113-8656, Japan","institution_ids":["https://openalex.org/I74801974","https://openalex.org/I161296585"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5018160333"],"corresponding_institution_ids":["https://openalex.org/I161296585","https://openalex.org/I74801974"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.18013443,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"243","last_page":"258"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","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/T10126","display_name":"Logic, programming, and type systems","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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9990000128746033,"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/T10142","display_name":"Formal Methods in Verification","score":0.9980999827384949,"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/computer-science","display_name":"Computer science","score":0.753726601600647},{"id":"https://openalex.org/keywords/natural-deduction","display_name":"Natural deduction","score":0.6724648475646973},{"id":"https://openalex.org/keywords/modal-logic","display_name":"Modal logic","score":0.6435810923576355},{"id":"https://openalex.org/keywords/modal","display_name":"Modal","score":0.5976977944374084},{"id":"https://openalex.org/keywords/normal-modal-logic","display_name":"Normal modal logic","score":0.5592918992042542},{"id":"https://openalex.org/keywords/dynamic-logic","display_name":"Dynamic logic (digital electronics)","score":0.42385366559028625},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.41019758582115173},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3559299111366272},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.3145323097705841},{"id":"https://openalex.org/keywords/multimodal-logic","display_name":"Multimodal logic","score":0.21865946054458618},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.1081078052520752},{"id":"https://openalex.org/keywords/electrical-engineering","display_name":"Electrical engineering","score":0.09408366680145264},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.04998660087585449}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.753726601600647},{"id":"https://openalex.org/C62073222","wikidata":"https://www.wikidata.org/wiki/Q1572108","display_name":"Natural deduction","level":2,"score":0.6724648475646973},{"id":"https://openalex.org/C27508121","wikidata":"https://www.wikidata.org/wiki/Q210841","display_name":"Modal logic","level":3,"score":0.6435810923576355},{"id":"https://openalex.org/C71139939","wikidata":"https://www.wikidata.org/wiki/Q910194","display_name":"Modal","level":2,"score":0.5976977944374084},{"id":"https://openalex.org/C114092440","wikidata":"https://www.wikidata.org/wiki/Q840226","display_name":"Normal modal logic","level":4,"score":0.5592918992042542},{"id":"https://openalex.org/C2777796570","wikidata":"https://www.wikidata.org/wiki/Q2351326","display_name":"Dynamic logic (digital electronics)","level":4,"score":0.42385366559028625},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41019758582115173},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3559299111366272},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.3145323097705841},{"id":"https://openalex.org/C203659156","wikidata":"https://www.wikidata.org/wiki/Q6934805","display_name":"Multimodal logic","level":3,"score":0.21865946054458618},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.1081078052520752},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.09408366680145264},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.04998660087585449},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","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},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","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/C172385210","wikidata":"https://www.wikidata.org/wiki/Q5339","display_name":"Transistor","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-642-10672-9_18","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-10672-9_18","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Climate action","id":"https://metadata.un.org/sdg/13","score":0.5}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1488538795","https://openalex.org/W1534493251","https://openalex.org/W1571966139","https://openalex.org/W1604633680","https://openalex.org/W1678412398","https://openalex.org/W1988097129","https://openalex.org/W1988824860","https://openalex.org/W2001481147","https://openalex.org/W2008920425","https://openalex.org/W2009354615","https://openalex.org/W2016326123","https://openalex.org/W2029408547","https://openalex.org/W2053198071","https://openalex.org/W2065172121","https://openalex.org/W2094455839","https://openalex.org/W2094706654","https://openalex.org/W2131807903","https://openalex.org/W2134291411","https://openalex.org/W2135287414","https://openalex.org/W2135323348","https://openalex.org/W2145123272","https://openalex.org/W2148062074","https://openalex.org/W2152013675","https://openalex.org/W2323378191"],"related_works":["https://openalex.org/W2028144918","https://openalex.org/W3108798275","https://openalex.org/W176661328","https://openalex.org/W4318188140","https://openalex.org/W2795425183","https://openalex.org/W3126675290","https://openalex.org/W2260113151","https://openalex.org/W2067687795","https://openalex.org/W2534562289","https://openalex.org/W1530784265"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
