{"id":"https://openalex.org/W2121620560","doi":"https://doi.org/10.1305/ndjfl/1038949541","title":"A Natural Deduction System for First Degree Entailment","display_name":"A Natural Deduction System for First Degree Entailment","publication_year":1999,"publication_date":"1999-04-01","ids":{"openalex":"https://openalex.org/W2121620560","doi":"https://doi.org/10.1305/ndjfl/1038949541","mag":"2121620560"},"language":"en","primary_location":{"id":"doi:10.1305/ndjfl/1038949541","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1038949541","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-40/issue-2/A-Natural-Deduction-System-for-First-Degree-Entailment/10.1305/ndjfl/1038949541.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-40/issue-2/A-Natural-Deduction-System-for-First-Degree-Entailment/10.1305/ndjfl/1038949541.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019250618","display_name":"Allard Tamminga","orcid":null},"institutions":[{"id":"https://openalex.org/I165143802","display_name":"The University of Queensland","ror":"https://ror.org/00rqy9422","country_code":"AU","type":"education","lineage":["https://openalex.org/I165143802"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Allard M. Tamminga","raw_affiliation_strings":["Department of Philosophy University of Queensland St . Lucia Brisbane QLD 4072 AUSTRALIA","Theoretical Philosophy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Philosophy University of Queensland St . Lucia Brisbane QLD 4072 AUSTRALIA","institution_ids":["https://openalex.org/I165143802"]},{"raw_affiliation_string":"Theoretical Philosophy","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002528469","display_name":"Koji Tanaka","orcid":"https://orcid.org/0000-0003-4747-3457"},"institutions":[{"id":"https://openalex.org/I165143802","display_name":"The University of Queensland","ror":"https://ror.org/00rqy9422","country_code":"AU","type":"education","lineage":["https://openalex.org/I165143802"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Koji Tanaka","raw_affiliation_strings":["Department of Philosophy University of Queensland St . Lucia Brisbane QLD 4072 AUSTRALIA","Department of Philosophy University of Queensland St. Lucia Brisbane QLD 4072 AUSTRALIA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Philosophy University of Queensland St . Lucia Brisbane QLD 4072 AUSTRALIA","institution_ids":["https://openalex.org/I165143802"]},{"raw_affiliation_string":"Department of Philosophy University of Queensland St. Lucia Brisbane QLD 4072 AUSTRALIA","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I165143802"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":15,"citation_normalized_percentile":{"value":0.16487997,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":98},"biblio":{"volume":"40","issue":"2","first_page":null,"last_page":null},"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/T10126","display_name":"Logic, programming, and type systems","score":0.9973999857902527,"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":0.9970999956130981,"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/soundness","display_name":"Soundness","score":0.9244468212127686},{"id":"https://openalex.org/keywords/natural-deduction","display_name":"Natural deduction","score":0.8814243078231812},{"id":"https://openalex.org/keywords/logical-consequence","display_name":"Logical consequence","score":0.722606897354126},{"id":"https://openalex.org/keywords/completeness","display_name":"Completeness (order theory)","score":0.7081828117370605},{"id":"https://openalex.org/keywords/semantics","display_name":"Semantics (computer science)","score":0.5749577283859253},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.56340092420578},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.5000729560852051},{"id":"https://openalex.org/keywords/textual-entailment","display_name":"Textual entailment","score":0.4615604281425476},{"id":"https://openalex.org/keywords/natural-language-processing","display_name":"Natural language processing","score":0.3957059681415558},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3236754536628723},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.29669189453125}],"concepts":[{"id":"https://openalex.org/C39920170","wikidata":"https://www.wikidata.org/wiki/Q693083","display_name":"Soundness","level":2,"score":0.9244468212127686},{"id":"https://openalex.org/C62073222","wikidata":"https://www.wikidata.org/wiki/Q1572108","display_name":"Natural deduction","level":2,"score":0.8814243078231812},{"id":"https://openalex.org/C134752490","wikidata":"https://www.wikidata.org/wiki/Q374182","display_name":"Logical consequence","level":2,"score":0.722606897354126},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.7081828117370605},{"id":"https://openalex.org/C184337299","wikidata":"https://www.wikidata.org/wiki/Q1437428","display_name":"Semantics (computer science)","level":2,"score":0.5749577283859253},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.56340092420578},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.5000729560852051},{"id":"https://openalex.org/C95318506","wikidata":"https://www.wikidata.org/wiki/Q6588467","display_name":"Textual entailment","level":3,"score":0.4615604281425476},{"id":"https://openalex.org/C204321447","wikidata":"https://www.wikidata.org/wiki/Q30642","display_name":"Natural language processing","level":1,"score":0.3957059681415558},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3236754536628723},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.29669189453125},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1305/ndjfl/1038949541","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1038949541","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-40/issue-2/A-Natural-Deduction-System-for-First-Degree-Entailment/10.1305/ndjfl/1038949541.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:dare.uva.nl:openaire_cris_publications/b4804f6b-d99b-4d95-8d97-6b7961c8ee19","is_oa":false,"landing_page_url":"https://handle.uba.uva.nl/personal/pure/en/publications/a-natural-deduction-system-for-first-degree-entailment(b4804f6b-d99b-4d95-8d97-6b7961c8ee19).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400088","display_name":"UvA-DARE (University of Amsterdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887064364","host_organization_name":"University of Amsterdam","host_organization_lineage":["https://openalex.org/I887064364"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Tamminga, A M & Tanaka, K 1999, 'A natural deduction system for first degree entailment', Notre Dame Journal of Formal Logic, vol. 40, no. 2, pp. 258-272.","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:pure.rug.nl:openaire/4fc8e577-061a-422e-bc38-84548bc86037","is_oa":true,"landing_page_url":"https://research.rug.nl/en/publications/4fc8e577-061a-422e-bc38-84548bc86037","pdf_url":null,"source":{"id":"https://openalex.org/S4306400420","display_name":"University of Groningen research database (University of Groningen / Centre for Information Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I169381384","host_organization_name":"University of Groningen","host_organization_lineage":["https://openalex.org/I169381384"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Tamminga, A & Tanaka, K 1999, 'A natural deduction system for first degree entailment', Notre Dame Journal of Formal Logic, vol. 40, no. 2, pp. 258-272. https://doi.org/10.1305/ndjfl/1038949541","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:CULeuclid:euclid.ndjfl/1038949541","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.ndjfl/1038949541","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"},{"id":"pmh:oai:espace.library.uq.edu.au:UQ:58658","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306402388","display_name":"Queensland's institutional digital repository (The University of Queensland)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I165143802","host_organization_name":"The University of Queensland","host_organization_lineage":["https://openalex.org/I165143802"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"},{"id":"pmh:uvapub:oai:dare.uva.nl:publications/b4804f6b-d99b-4d95-8d97-6b7961c8ee19","is_oa":false,"landing_page_url":"https://dare.uva.nl/personal/pure/en/publications/a-natural-deduction-system-for-first-degree-entailment(b4804f6b-d99b-4d95-8d97-6b7961c8ee19).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Notre Dame Journal of Formal Logic, 40(2), 258 - 272. Duke University Press","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1305/ndjfl/1038949541","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1038949541","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-40/issue-2/A-Natural-Deduction-System-for-First-Degree-Entailment/10.1305/ndjfl/1038949541.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":[{"display_name":"Quality Education","score":0.49000000953674316,"id":"https://metadata.un.org/sdg/4"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2121620560.pdf","grobid_xml":"https://content.openalex.org/works/W2121620560.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W297342247","https://openalex.org/W1415044991","https://openalex.org/W1536217426","https://openalex.org/W1593617641","https://openalex.org/W1795577507","https://openalex.org/W1968386460","https://openalex.org/W2011392623","https://openalex.org/W2023605209","https://openalex.org/W2048470700","https://openalex.org/W2057185140","https://openalex.org/W2058110538","https://openalex.org/W2126833102","https://openalex.org/W4211033084","https://openalex.org/W4233253115"],"related_works":["https://openalex.org/W13634261","https://openalex.org/W4250462479","https://openalex.org/W2169644218","https://openalex.org/W56937029","https://openalex.org/W2138973931","https://openalex.org/W12963412","https://openalex.org/W2250460949","https://openalex.org/W3163509751","https://openalex.org/W958050847","https://openalex.org/W3158371345"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2,29],"concerned":[3],"with":[4,64],"a":[5,17,43,49],"natural":[6,34,50],"deduction":[7,35,51],"system":[8,52,63,70],"for":[9,53,76],"First":[10],"Degree":[11],"Entailment":[12],"(FDE).":[13],"First,":[14],"we":[15,47],"exhibit":[16],"brief":[18],"history":[19],"of":[20,23,45,61],"FDE":[21],"and":[22,42,59],"combined":[24],"systems":[25],"whose":[26],"underlying":[27],"idea":[28],"used":[30],"in":[31],"developing":[32],"the":[33,40,62,67,73],"system.":[36],"Then,":[37],"after":[38],"presenting":[39],"language":[41],"semantics":[44,75],"FDE,":[46],"develop":[48],"FDE.":[54,77],"We":[55],"then":[56],"prove":[57],"soundness":[58],"completeness":[60],"respect":[65],"to":[66],"semantics.":[68],"The":[69],"neatly":[71],"represents":[72],"four-valued":[74]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}
