{"id":"https://openalex.org/W2086177561","doi":"https://doi.org/10.1305/ndjfl/1039293019","title":"Basic Predicate Calculus","display_name":"Basic Predicate Calculus","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W2086177561","doi":"https://doi.org/10.1305/ndjfl/1039293019","mag":"2086177561"},"language":"en","primary_location":{"id":"doi:10.1305/ndjfl/1039293019","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1039293019","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-39/issue-1/Basic-Predicate-Calculus/10.1305/ndjfl/1039293019.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-39/issue-1/Basic-Predicate-Calculus/10.1305/ndjfl/1039293019.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048255667","display_name":"Wim Ruitenburg","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Wim Ruitenburg","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5048255667"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.931,"has_fulltext":true,"cited_by_count":48,"citation_normalized_percentile":{"value":0.9139551,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"39","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9976000189781189,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9976000189781189,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9972000122070312,"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":0.9865000247955322,"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/peano-axioms","display_name":"Peano axioms","score":0.7165457010269165},{"id":"https://openalex.org/keywords/predicate-logic","display_name":"Predicate logic","score":0.622008740901947},{"id":"https://openalex.org/keywords/transitive-relation","display_name":"Transitive relation","score":0.5357654690742493},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5341951251029968},{"id":"https://openalex.org/keywords/intuitionistic-logic","display_name":"Intuitionistic logic","score":0.5240926146507263},{"id":"https://openalex.org/keywords/first-order-logic","display_name":"First-order logic","score":0.5063310861587524},{"id":"https://openalex.org/keywords/predicate","display_name":"Predicate (mathematical logic)","score":0.49889659881591797},{"id":"https://openalex.org/keywords/g\u00f6dels-completeness-theorem","display_name":"G\u00f6del's completeness theorem","score":0.49755099415779114},{"id":"https://openalex.org/keywords/completeness","display_name":"Completeness (order theory)","score":0.4796869456768036},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.47393232583999634},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.42060238122940063},{"id":"https://openalex.org/keywords/logical-equivalence","display_name":"Logical equivalence","score":0.418140172958374},{"id":"https://openalex.org/keywords/natural-deduction","display_name":"Natural deduction","score":0.41352224349975586},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3901773989200592},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.386441171169281},{"id":"https://openalex.org/keywords/linear-logic","display_name":"Linear logic","score":0.2673960328102112},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.19086596369743347},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.17403721809387207},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.1346791684627533},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.09486198425292969}],"concepts":[{"id":"https://openalex.org/C97489613","wikidata":"https://www.wikidata.org/wiki/Q842755","display_name":"Peano axioms","level":2,"score":0.7165457010269165},{"id":"https://openalex.org/C19689857","wikidata":"https://www.wikidata.org/wiki/Q4055684","display_name":"Predicate logic","level":3,"score":0.622008740901947},{"id":"https://openalex.org/C191399111","wikidata":"https://www.wikidata.org/wiki/Q64861","display_name":"Transitive relation","level":2,"score":0.5357654690742493},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5341951251029968},{"id":"https://openalex.org/C178421362","wikidata":"https://www.wikidata.org/wiki/Q176786","display_name":"Intuitionistic logic","level":3,"score":0.5240926146507263},{"id":"https://openalex.org/C100481476","wikidata":"https://www.wikidata.org/wiki/Q4055684","display_name":"First-order logic","level":2,"score":0.5063310861587524},{"id":"https://openalex.org/C140146324","wikidata":"https://www.wikidata.org/wiki/Q1144319","display_name":"Predicate (mathematical logic)","level":2,"score":0.49889659881591797},{"id":"https://openalex.org/C200116569","wikidata":"https://www.wikidata.org/wiki/Q902052","display_name":"G\u00f6del's completeness theorem","level":2,"score":0.49755099415779114},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.4796869456768036},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.47393232583999634},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.42060238122940063},{"id":"https://openalex.org/C70846408","wikidata":"https://www.wikidata.org/wiki/Q220433","display_name":"Logical equivalence","level":3,"score":0.418140172958374},{"id":"https://openalex.org/C62073222","wikidata":"https://www.wikidata.org/wiki/Q1572108","display_name":"Natural deduction","level":2,"score":0.41352224349975586},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3901773989200592},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.386441171169281},{"id":"https://openalex.org/C28077239","wikidata":"https://www.wikidata.org/wiki/Q841728","display_name":"Linear logic","level":2,"score":0.2673960328102112},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.19086596369743347},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.17403721809387207},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.1346791684627533},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.09486198425292969},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"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/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1305/ndjfl/1039293019","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1039293019","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-39/issue-1/Basic-Predicate-Calculus/10.1305/ndjfl/1039293019.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/1039293019","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.ndjfl/1039293019","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:10.1305/ndjfl/1039293019","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1039293019","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-39/issue-1/Basic-Predicate-Calculus/10.1305/ndjfl/1039293019.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/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2086177561.pdf","grobid_xml":"https://content.openalex.org/works/W2086177561.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W155669283","https://openalex.org/W578063101","https://openalex.org/W2067332512","https://openalex.org/W2070878538","https://openalex.org/W4239835443","https://openalex.org/W6625571007","https://openalex.org/W6631061298"],"related_works":["https://openalex.org/W3161909158","https://openalex.org/W2007555602","https://openalex.org/W2401016457","https://openalex.org/W1202574048","https://openalex.org/W4286979908","https://openalex.org/W2070926400","https://openalex.org/W2140830696","https://openalex.org/W4238295494","https://openalex.org/W2409304415","https://openalex.org/W2114956963"],"abstract_inverted_index":{"We":[0,26,49],"establish":[1],"a":[2,11],"completeness":[3,45],"theorem":[4],"for":[5,42],"first-order":[6],"basic":[7,55,58],"predicate":[8,16],"logic":[9,17,59],"BQC,":[10],"proper":[12],"subsystem":[13],"of":[14,30,38,54,61],"intuitionistic":[15,62],"IQC,":[18],"using":[19],"Kripke":[20],"models":[21],"with":[22],"transitive":[23],"underlying":[24],"frames.":[25],"develop":[27],"the":[28,35,52,57],"notion":[29,37],"functional":[31],"well-formed":[32],"theory":[33,39],"as":[34],"right":[36],"over":[40],"BQC":[41],"which":[43],"strong":[44],"theorems":[46],"are":[47],"possible.":[48],"also":[50],"derive":[51],"undecidability":[53],"arithmetic,":[56],"equivalent":[60],"Heyting":[63],"Arithmetic":[64],"and":[65],"classical":[66],"Peano":[67],"Arithmetic.":[68]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-08-08T01:25:22.217667","created_date":"2025-10-10T00:00:00"}