{"id":"https://openalex.org/W1488621088","doi":"https://doi.org/10.1007/978-3-540-72734-7_10","title":"Density Elimination and Rational Completeness for First-Order Logics","display_name":"Density Elimination and Rational Completeness for First-Order Logics","publication_year":2007,"publication_date":"2007-06-28","ids":{"openalex":"https://openalex.org/W1488621088","doi":"https://doi.org/10.1007/978-3-540-72734-7_10","mag":"1488621088"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-540-72734-7_10","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-72734-7_10","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/A5086733054","display_name":"Agata Ciabattoni","orcid":"https://orcid.org/0000-0001-6947-8772"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Agata Ciabattoni","raw_affiliation_strings":["Institute of Discrete Mathematics and Geometry, Technical University Vienna, Wiedner Hauptstrasse 8-10, A-1040 Wien, Austria","Institute of Discrete Mathematics and Geometry, Technical University Vienna, Wiedner Hauptstrasse 8-10, A-1040 Wien, Austria#TAB#"],"affiliations":[{"raw_affiliation_string":"Institute of Discrete Mathematics and Geometry, Technical University Vienna, Wiedner Hauptstrasse 8-10, A-1040 Wien, Austria","institution_ids":["https://openalex.org/I145847075"]},{"raw_affiliation_string":"Institute of Discrete Mathematics and Geometry, Technical University Vienna, Wiedner Hauptstrasse 8-10, A-1040 Wien, Austria#TAB#","institution_ids":["https://openalex.org/I145847075"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038446877","display_name":"George Metcalfe","orcid":"https://orcid.org/0000-0001-7610-404X"},"institutions":[{"id":"https://openalex.org/I200719446","display_name":"Vanderbilt University","ror":"https://ror.org/02vm5rt34","country_code":"US","type":"education","lineage":["https://openalex.org/I200719446"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"George Metcalfe","raw_affiliation_strings":["Department of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville TN 37240, USA","Department of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville, TN 37240, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville TN 37240, USA","institution_ids":["https://openalex.org/I200719446"]},{"raw_affiliation_string":"Department of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville, TN 37240, USA","institution_ids":["https://openalex.org/I200719446"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5086733054"],"corresponding_institution_ids":["https://openalex.org/I145847075"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.6806,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.68777733,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"132","last_page":"146"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9984999895095825,"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":0.9939000010490417,"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":0.7098823189735413},{"id":"https://openalex.org/keywords/completeness","display_name":"Completeness (order theory)","score":0.643879234790802},{"id":"https://openalex.org/keywords/reduct","display_name":"Reduct","score":0.62530517578125},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5032917857170105},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.4933911859989166},{"id":"https://openalex.org/keywords/quantifier-elimination","display_name":"Quantifier elimination","score":0.47413918375968933},{"id":"https://openalex.org/keywords/second-order-logic","display_name":"Second-order logic","score":0.4590964913368225},{"id":"https://openalex.org/keywords/first-order-logic","display_name":"First-order logic","score":0.44755980372428894},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.43894749879837036},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43457120656967163},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42415037751197815},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.4199387729167938},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4150623083114624},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3548521399497986},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.2839762568473816},{"id":"https://openalex.org/keywords/higher-order-logic","display_name":"Higher-order logic","score":0.2809474468231201},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.21553856134414673},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.1336458921432495},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10719707608222961},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.09350931644439697},{"id":"https://openalex.org/keywords/rough-set","display_name":"Rough set","score":0.08248364925384521}],"concepts":[{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.7098823189735413},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.643879234790802},{"id":"https://openalex.org/C69177213","wikidata":"https://www.wikidata.org/wiki/Q12880812","display_name":"Reduct","level":3,"score":0.62530517578125},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5032917857170105},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.4933911859989166},{"id":"https://openalex.org/C32278780","wikidata":"https://www.wikidata.org/wiki/Q1849020","display_name":"Quantifier elimination","level":2,"score":0.47413918375968933},{"id":"https://openalex.org/C144791301","wikidata":"https://www.wikidata.org/wiki/Q1548746","display_name":"Second-order logic","level":4,"score":0.4590964913368225},{"id":"https://openalex.org/C100481476","wikidata":"https://www.wikidata.org/wiki/Q4055684","display_name":"First-order logic","level":2,"score":0.44755980372428894},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.43894749879837036},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43457120656967163},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42415037751197815},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.4199387729167938},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4150623083114624},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3548521399497986},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2839762568473816},{"id":"https://openalex.org/C169896238","wikidata":"https://www.wikidata.org/wiki/Q1644136","display_name":"Higher-order logic","level":3,"score":0.2809474468231201},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.21553856134414673},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.1336458921432495},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10719707608222961},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.09350931644439697},{"id":"https://openalex.org/C111012933","wikidata":"https://www.wikidata.org/wiki/Q3137210","display_name":"Rough set","level":2,"score":0.08248364925384521},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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:10.1007/978-3-540-72734-7_10","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-72734-7_10","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.86.3524","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.86.3524","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.logic.at/people/agata/CMdensityrev.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1486040955","https://openalex.org/W1496398693","https://openalex.org/W1511669762","https://openalex.org/W1602192439","https://openalex.org/W1883540685","https://openalex.org/W1983382657","https://openalex.org/W1990470938","https://openalex.org/W2082736027","https://openalex.org/W2091957209","https://openalex.org/W2110182592","https://openalex.org/W2112664318","https://openalex.org/W2132638915","https://openalex.org/W2154114798","https://openalex.org/W2156693798","https://openalex.org/W2952815021"],"related_works":["https://openalex.org/W2028271688","https://openalex.org/W2010405422","https://openalex.org/W1964225248","https://openalex.org/W4232120730","https://openalex.org/W2367367674","https://openalex.org/W4387318785","https://openalex.org/W3206443925","https://openalex.org/W2110257077","https://openalex.org/W1493788057","https://openalex.org/W1945182987"],"abstract_inverted_index":null,"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
