{"id":"https://openalex.org/W1966718868","doi":"https://doi.org/10.1093/logcom/exn059","title":"Herbrand's Theorem, Skolemization and Proof Systems for First-Order Lukasiewicz Logic","display_name":"Herbrand's Theorem, Skolemization and Proof Systems for First-Order Lukasiewicz Logic","publication_year":2008,"publication_date":"2008-11-17","ids":{"openalex":"https://openalex.org/W1966718868","doi":"https://doi.org/10.1093/logcom/exn059","mag":"1966718868"},"language":"en","primary_location":{"id":"doi:10.1093/logcom/exn059","is_oa":false,"landing_page_url":"https://doi.org/10.1093/logcom/exn059","pdf_url":null,"source":{"id":"https://openalex.org/S47057106","display_name":"Journal of Logic and Computation","issn_l":"0955-792X","issn":["0955-792X","1465-363X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Logic and Computation","raw_type":"journal-article"},"type":"article","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/A5035315045","display_name":"Matthias Baaz","orcid":"https://orcid.org/0000-0002-7815-2501"},"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":"M. Baaz","raw_affiliation_strings":["Institute of Discrete Mathematics and Geometry, Technical University Vienna, Wiedner Hauptstrasse 8-10, A-1040 Wien, Austria.E-mail: baaz@logic.at","Institute of Discrete Mathematics and Geometry, Technical University Vienna, Wiedner Hauptstrasse 8-10, A-1040 Wien, Austria.E-mail:"],"affiliations":[{"raw_affiliation_string":"Institute of Discrete Mathematics and Geometry, Technical University Vienna, Wiedner Hauptstrasse 8-10, A-1040 Wien, Austria.E-mail: baaz@logic.at","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.E-mail:","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":"G. Metcalfe","raw_affiliation_strings":["Department of Mathematics, Vanderbilt University 1326 Stevenson Center, Nashville TN 37240, USA.E-mail: george.metcalfe@vanderbilt.edu","Department of Mathematics, Vanderbilt University 1326 Stevenson Center, Nashville TN 37240, USA.E-mail:"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Vanderbilt University 1326 Stevenson Center, Nashville TN 37240, USA.E-mail: george.metcalfe@vanderbilt.edu","institution_ids":["https://openalex.org/I200719446"]},{"raw_affiliation_string":"Department of Mathematics, Vanderbilt University 1326 Stevenson Center, Nashville TN 37240, USA.E-mail:","institution_ids":["https://openalex.org/I200719446"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5035315045"],"corresponding_institution_ids":["https://openalex.org/I145847075"],"apc_list":{"value":4151,"currency":"USD","value_usd":4151},"apc_paid":null,"fwci":1.6464,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.83051762,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"20","issue":"1","first_page":"35","last_page":"54"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9998999834060669,"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":0.9998999834060669,"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/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9983999729156494,"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":0.9980999827384949,"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/second-order-logic","display_name":"Second-order logic","score":0.6140279173851013},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.512276828289032},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5117954611778259},{"id":"https://openalex.org/keywords/first-order-logic","display_name":"First-order logic","score":0.4895258843898773},{"id":"https://openalex.org/keywords/higher-order-logic","display_name":"Higher-order logic","score":0.40462690591812134},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3979765772819519},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3744841516017914},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.2027217447757721},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.09209093451499939}],"concepts":[{"id":"https://openalex.org/C144791301","wikidata":"https://www.wikidata.org/wiki/Q1548746","display_name":"Second-order logic","level":4,"score":0.6140279173851013},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.512276828289032},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5117954611778259},{"id":"https://openalex.org/C100481476","wikidata":"https://www.wikidata.org/wiki/Q4055684","display_name":"First-order logic","level":2,"score":0.4895258843898773},{"id":"https://openalex.org/C169896238","wikidata":"https://www.wikidata.org/wiki/Q1644136","display_name":"Higher-order logic","level":3,"score":0.40462690591812134},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3979765772819519},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3744841516017914},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.2027217447757721},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.09209093451499939},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1093/logcom/exn059","is_oa":false,"landing_page_url":"https://doi.org/10.1093/logcom/exn059","pdf_url":null,"source":{"id":"https://openalex.org/S47057106","display_name":"Journal of Logic and Computation","issn_l":"0955-792X","issn":["0955-792X","1465-363X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Logic and Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.575.6492","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.575.6492","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://sitemason.vanderbilt.edu/files/egOQHm/BM08.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.575.7142","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.575.7142","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://sitemason.vanderbilt.edu/files/h3AYCI/BM08a.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.577.1955","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.577.1955","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://sitemason.vanderbilt.edu/files/iVb9qU/BMher.pdf","raw_type":"text"},{"id":"pmh:oai:boris.unibe.ch:4814","is_oa":false,"landing_page_url":"https://boris.unibe.ch/4814/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401086","display_name":"Bern Open Repository and Information System (University of Bern)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I118564535","host_organization_name":"University of Bern","host_organization_lineage":["https://openalex.org/I118564535"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Baaz, Matthias; Metcalfe, George (2010). Herbrand's Theorem, Skolemization and Proof Systems for First-Order Lukasiewicz Logic. Journal of logic and computation, 20(1), pp. 35-54. Oxford: Oxford University Press 10.1093/logcom/exn059 <http://dx.doi.org/10.1093/logcom/exn059>","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W37690025","https://openalex.org/W1488621088","https://openalex.org/W1542113445","https://openalex.org/W1546296649","https://openalex.org/W1586892257","https://openalex.org/W1915714774","https://openalex.org/W1962847297","https://openalex.org/W1984723670","https://openalex.org/W1985104705","https://openalex.org/W1989632075","https://openalex.org/W1990470938","https://openalex.org/W1992818631","https://openalex.org/W2015436680","https://openalex.org/W2033088754","https://openalex.org/W2087171264","https://openalex.org/W2088476380","https://openalex.org/W2110182592","https://openalex.org/W2112664318","https://openalex.org/W2119094149","https://openalex.org/W2150732096","https://openalex.org/W2156452084","https://openalex.org/W2156693798","https://openalex.org/W2170862108","https://openalex.org/W2171279236","https://openalex.org/W2188802573","https://openalex.org/W2245367736","https://openalex.org/W2474062823","https://openalex.org/W2655567646","https://openalex.org/W4239833221"],"related_works":["https://openalex.org/W4387318785","https://openalex.org/W2142816242","https://openalex.org/W1981373951","https://openalex.org/W1580672106","https://openalex.org/W4388397425","https://openalex.org/W3101683417","https://openalex.org/W4255026600","https://openalex.org/W117698297","https://openalex.org/W2574949295","https://openalex.org/W1528524720"],"abstract_inverted_index":{"An":[0],"approximate":[1],"Herbrand":[2],"theorem":[3],"is":[4,41],"established":[5],"for":[6,43,59,72],"first-order":[7,45,62],"infinite-valued":[8],"\u0141ukasiewicz":[9,63],"Logic":[10],"and":[11,65],"used":[12,24],"to":[13,25],"obtain":[14],"a":[15,36,52,66],"proof-theoretic":[16],"proof":[17,27],"of":[18,32],"Skolemization.":[19],"These":[20],"results":[21],"are":[22],"then":[23],"define":[26],"systems":[28],"in":[29],"the":[30,44,60],"framework":[31],"hypersequents.":[33],"In":[34],"particular,":[35],"calculus":[37,54,68],"lacking":[38],"cut":[39],"elimination":[40],"defined":[42],"logic":[46],"characterized":[47],"by":[48],"linearly":[49],"ordered":[50],"MV-algebras,":[51],"cut-free":[53,67],"with":[55,69],"an":[56],"infinitary":[57],"rule":[58],"full":[61],"Logic,":[64],"finitary":[70],"rules":[71],"its":[73],"one-variable":[74],"fragment.":[75]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2013,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}