{"id":"https://openalex.org/W2014988898","doi":"https://doi.org/10.1215/00294527-2009-013","title":"George Boole's Deductive System","display_name":"George Boole's Deductive System","publication_year":2009,"publication_date":"2009-07-01","ids":{"openalex":"https://openalex.org/W2014988898","doi":"https://doi.org/10.1215/00294527-2009-013","mag":"2014988898"},"language":"en","primary_location":{"id":"doi:10.1215/00294527-2009-013","is_oa":true,"landing_page_url":"https://doi.org/10.1215/00294527-2009-013","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-50/issue-3/George-Booles-Deductive-System/10.1215/00294527-2009-013.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-50/issue-3/George-Booles-Deductive-System/10.1215/00294527-2009-013.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064432959","display_name":"Frank Markham Brown","orcid":null},"institutions":[{"id":"https://openalex.org/I55061410","display_name":"U.S. Air Force Institute of Technology","ror":"https://ror.org/03f9f1d95","country_code":"US","type":"education","lineage":["https://openalex.org/I1294991024","https://openalex.org/I1330347796","https://openalex.org/I1330347796","https://openalex.org/I2802362820","https://openalex.org/I4210089612","https://openalex.org/I4210102105","https://openalex.org/I4210102105","https://openalex.org/I55061410"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Frank Markham Brown","raw_affiliation_strings":["Professor Emeritus Air Force Institute of Technology Dayton OH 45433 USA 86 Shoreline Drive Hilton Head Island SC 29928 USA"],"affiliations":[{"raw_affiliation_string":"Professor Emeritus Air Force Institute of Technology Dayton OH 45433 USA 86 Shoreline Drive Hilton Head Island SC 29928 USA","institution_ids":["https://openalex.org/I55061410"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5064432959"],"corresponding_institution_ids":["https://openalex.org/I55061410"],"apc_list":null,"apc_paid":null,"fwci":0.3428,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.59295027,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"50","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.989799976348877,"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"}},"topics":[{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.989799976348877,"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/T12170","display_name":"History and Theory of Mathematics","score":0.9745000004768372,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9445000290870667,"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/rotation-formalisms-in-three-dimensions","display_name":"Rotation formalisms in three dimensions","score":0.7198038697242737},{"id":"https://openalex.org/keywords/george","display_name":"George (robot)","score":0.5485747456550598},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.499239444732666},{"id":"https://openalex.org/keywords/principal","display_name":"Principal (computer security)","score":0.46776479482650757},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.41771888732910156},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35141390562057495},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.3243812918663025},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.17708134651184082},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.15951570868492126}],"concepts":[{"id":"https://openalex.org/C171018156","wikidata":"https://www.wikidata.org/wiki/Q7370306","display_name":"Rotation formalisms in three dimensions","level":2,"score":0.7198038697242737},{"id":"https://openalex.org/C67101536","wikidata":"https://www.wikidata.org/wiki/Q5535910","display_name":"George (robot)","level":2,"score":0.5485747456550598},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.499239444732666},{"id":"https://openalex.org/C144559511","wikidata":"https://www.wikidata.org/wiki/Q2986279","display_name":"Principal (computer security)","level":2,"score":0.46776479482650757},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.41771888732910156},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35141390562057495},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.3243812918663025},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.17708134651184082},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.15951570868492126},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1215/00294527-2009-013","is_oa":true,"landing_page_url":"https://doi.org/10.1215/00294527-2009-013","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-50/issue-3/George-Booles-Deductive-System/10.1215/00294527-2009-013.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.ndjfl/1257862040","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.ndjfl/1257862040","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1215/00294527-2009-013","is_oa":true,"landing_page_url":"https://doi.org/10.1215/00294527-2009-013","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-50/issue-3/George-Booles-Deductive-System/10.1215/00294527-2009-013.pdf","source":{"id":"https://openalex.org/S78544662","display_name":"Notre Dame Journal of Formal Logic","issn_l":"0029-4527","issn":["0029-4527","1939-0726"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315698","host_organization_name":"Duke University Press","host_organization_lineage":["https://openalex.org/P4310315698","https://openalex.org/P4310315572"],"host_organization_lineage_names":["Duke University Press","Duke University"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Notre Dame Journal of Formal Logic","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320310846","display_name":"University of South Carolina","ror":"https://ror.org/02b6qw903"},{"id":"https://openalex.org/F4320322676","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68"},{"id":"https://openalex.org/F4320324335","display_name":"Universitatea din Bucure\u0219ti","ror":"https://ror.org/02x2v6p15"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2014988898.pdf","grobid_xml":"https://content.openalex.org/works/W2014988898.grobid-xml"},"referenced_works_count":45,"referenced_works":["https://openalex.org/W36236183","https://openalex.org/W113936488","https://openalex.org/W158931356","https://openalex.org/W202658259","https://openalex.org/W588528421","https://openalex.org/W1499231756","https://openalex.org/W1537664757","https://openalex.org/W1554822239","https://openalex.org/W1563590311","https://openalex.org/W1784765900","https://openalex.org/W1967293369","https://openalex.org/W1979431120","https://openalex.org/W1980985059","https://openalex.org/W1982003586","https://openalex.org/W1985599747","https://openalex.org/W1986680211","https://openalex.org/W1993011378","https://openalex.org/W1997704656","https://openalex.org/W2000716540","https://openalex.org/W2002980485","https://openalex.org/W2017096836","https://openalex.org/W2042772917","https://openalex.org/W2048610309","https://openalex.org/W2049603442","https://openalex.org/W2062667682","https://openalex.org/W2065733336","https://openalex.org/W2067583223","https://openalex.org/W2074078071","https://openalex.org/W2074887539","https://openalex.org/W2078687024","https://openalex.org/W2082097877","https://openalex.org/W2104348591","https://openalex.org/W2171148831","https://openalex.org/W2313473167","https://openalex.org/W2314918084","https://openalex.org/W2320479210","https://openalex.org/W2326799546","https://openalex.org/W2482939156","https://openalex.org/W2486886792","https://openalex.org/W2745756257","https://openalex.org/W4205181137","https://openalex.org/W4211037896","https://openalex.org/W4238719637","https://openalex.org/W4244215134","https://openalex.org/W4254246700"],"related_works":["https://openalex.org/W2166247150","https://openalex.org/W4243252198","https://openalex.org/W2109507516","https://openalex.org/W4311714614","https://openalex.org/W2118300983","https://openalex.org/W2112962394","https://openalex.org/W3137189469","https://openalex.org/W2740990710","https://openalex.org/W4235530921","https://openalex.org/W2783283092"],"abstract_inverted_index":{"The":[0],"deductive":[1],"system":[2,87],"in":[3,21,51,60,95],"Boole's":[4,37,67,85,99],"Laws":[5],"of":[6,25,36,58,66,73,84,112],"Thought":[7],"(LT)":[8],"involves":[9],"both":[10],"an":[11],"algebra,":[12],"which":[13],"we":[14,108],"call":[15],"proto-Boolean,":[16],"and":[17,44,69,76,101,126],"a":[18],"\"general":[19],"method":[20],"Logic\"":[22],"making":[23],"use":[24,111],"that":[26,93],"algebra.":[27],"Our":[28,82],"object":[29],"is":[30],"to":[31,39,45,116,121],"elucidate":[32],"these":[33,62],"two":[34],"components":[35],"system,":[38],"prove":[40],"his":[41],"principal":[42],"results,":[43],"draw":[46],"some":[47,56],"conclusions":[48],"not":[49,89],"explicit":[50],"LT.":[52],"We":[53],"also":[54],"discuss":[55],"examples":[57],"incoherence":[59],"LT;":[61],"mask":[63],"the":[64,74,104,113],"genius":[65],"design":[68],"account":[70],"for":[71],"much":[72],"puzzled":[75],"disparaging":[77],"commentary":[78],"LT":[79,117],"has":[80],"received.":[81],"evaluation":[83],"logical":[86],"does":[88],"differ":[90],"substantially":[91],"from":[92],"advanced":[94],"Hailperin's":[96],"exhaustive":[97],"study,":[98],"Logic":[100],"Probability.":[102],"Unlike":[103],"latter":[105],"work,":[106],"however,":[107],"make":[109],"direct":[110],"polynomials":[114],"native":[115],"rather":[118],"than":[119],"appealing":[120],"formalisms":[122],"such":[123],"as":[124],"multisets":[125],"rings.":[127]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
