{"id":"https://openalex.org/W2020144980","doi":"https://doi.org/10.1305/ndjfl/1040149359","title":"A Finitely Axiomatized Formalization of Predicate Calculus with Equality","display_name":"A Finitely Axiomatized Formalization of Predicate Calculus with Equality","publication_year":1995,"publication_date":"1995-07-01","ids":{"openalex":"https://openalex.org/W2020144980","doi":"https://doi.org/10.1305/ndjfl/1040149359","mag":"2020144980"},"language":"en","primary_location":{"id":"doi:10.1305/ndjfl/1040149359","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1040149359","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-36/issue-3/A-Finitely-Axiomatized-Formalization-of-Predicate-Calculus-with-Equality/10.1305/ndjfl/1040149359.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-36/issue-3/A-Finitely-Axiomatized-Formalization-of-Predicate-Calculus-with-Equality/10.1305/ndjfl/1040149359.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002426804","display_name":"Norman D. Megill","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Norman D. Megill","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5002426804"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.12466565,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"36","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9988999962806702,"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/T10215","display_name":"Semantic Web and Ontologies","score":0.9778000116348267,"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/axiom","display_name":"Axiom","score":0.7021300792694092},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.6424013376235962},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.581874430179596},{"id":"https://openalex.org/keywords/first-order-logic","display_name":"First-order logic","score":0.5396362543106079},{"id":"https://openalex.org/keywords/substitution","display_name":"Substitution (logic)","score":0.5079615712165833},{"id":"https://openalex.org/keywords/predicate","display_name":"Predicate (mathematical logic)","score":0.49355781078338623},{"id":"https://openalex.org/keywords/natural-deduction","display_name":"Natural deduction","score":0.48898041248321533},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.4758148789405823},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3636530637741089},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3303220272064209},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32265979051589966},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.215449720621109},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.1708141267299652}],"concepts":[{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.7021300792694092},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.6424013376235962},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.581874430179596},{"id":"https://openalex.org/C100481476","wikidata":"https://www.wikidata.org/wiki/Q4055684","display_name":"First-order logic","level":2,"score":0.5396362543106079},{"id":"https://openalex.org/C2778220771","wikidata":"https://www.wikidata.org/wiki/Q1522579","display_name":"Substitution (logic)","level":2,"score":0.5079615712165833},{"id":"https://openalex.org/C140146324","wikidata":"https://www.wikidata.org/wiki/Q1144319","display_name":"Predicate (mathematical logic)","level":2,"score":0.49355781078338623},{"id":"https://openalex.org/C62073222","wikidata":"https://www.wikidata.org/wiki/Q1572108","display_name":"Natural deduction","level":2,"score":0.48898041248321533},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.4758148789405823},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3636530637741089},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3303220272064209},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32265979051589966},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.215449720621109},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.1708141267299652},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1305/ndjfl/1040149359","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1040149359","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-36/issue-3/A-Finitely-Axiomatized-Formalization-of-Predicate-Calculus-with-Equality/10.1305/ndjfl/1040149359.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/1040149359","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.ndjfl/1040149359","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:CiteSeerX.psu:10.1.1.134.5862","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.134.5862","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://de2.metamath.org/downloads/finiteaxiom.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1305/ndjfl/1040149359","is_oa":true,"landing_page_url":"https://doi.org/10.1305/ndjfl/1040149359","pdf_url":"https://projecteuclid.org/journals/notre-dame-journal-of-formal-logic/volume-36/issue-3/A-Finitely-Axiomatized-Formalization-of-Predicate-Calculus-with-Equality/10.1305/ndjfl/1040149359.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":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.4099999964237213}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2020144980.pdf","grobid_xml":"https://content.openalex.org/works/W2020144980.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W1481249376","https://openalex.org/W1483568252","https://openalex.org/W1506329803","https://openalex.org/W1532122496","https://openalex.org/W1966945932","https://openalex.org/W1972145536","https://openalex.org/W1972891197","https://openalex.org/W1984979605","https://openalex.org/W2011184850","https://openalex.org/W2011948182","https://openalex.org/W2013434344","https://openalex.org/W2018944629","https://openalex.org/W2040259072","https://openalex.org/W2041833446","https://openalex.org/W2053760476","https://openalex.org/W2056778743","https://openalex.org/W2064417671","https://openalex.org/W2085412574","https://openalex.org/W2100065142","https://openalex.org/W2100738443","https://openalex.org/W4246573604","https://openalex.org/W6629663199","https://openalex.org/W6664538270"],"related_works":["https://openalex.org/W4252559877","https://openalex.org/W2277965188","https://openalex.org/W2099918555","https://openalex.org/W2918085923","https://openalex.org/W1499822848","https://openalex.org/W1502495923","https://openalex.org/W1569934489","https://openalex.org/W4231685078","https://openalex.org/W2355223762","https://openalex.org/W1569638283"],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2,30,71,116],"formalization":[3,39],"of":[4,47,50,56,80,106],"first-order":[5],"predicate":[6,108],"calculus":[7,109],"with":[8,14,95],"equality":[9],"which,":[10],"unlike":[11],"traditional":[12,107],"systems":[13],"axiom":[15],"schemata":[16],"or":[17],"substitution":[18,61],"rules,":[19],"is":[20,40,84,99,110],"finitely":[21,35,88],"axiomatized":[22,89],"in":[23,29,70,115],"the":[24,44,91],"sense":[25],"that":[26],"each":[27],"step":[28],"formal":[31],"proof":[32],"admits":[33],"only":[34],"many":[36],"choices.":[37],"This":[38],"primarily":[41],"based":[42],"on":[43],"inference":[45],"rule":[46],"condensed":[48],"detachment":[49],"Meredith.":[51],"The":[52,78,93],"usual":[53],"primitive":[54],"notions":[55],"free":[57],"variable":[58],"and":[59],"proper":[60],"are":[62,76],"absent,":[63],"making":[64],"it":[65],"easy":[66],"to":[67,86,112],"verify":[68],"proofs":[69],"machine-oriented":[72],"application.":[73],"Completeness":[74],"results":[75],"presented.":[77],"example":[79],"Zermelo-Fraenkel":[81],"set":[82],"theory":[83],"shown":[85,111],"be":[87,113],"under":[90],"formalization.":[92],"relationship":[94],"resolution-based":[96],"theorem":[97],"provers":[98],"briefly":[100],"discussed.":[101],"A":[102],"closely":[103],"related":[104],"axiomatization":[105],"complete":[114],"strong":[117],"metamathematical":[118],"sense.":[119]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
