{"id":"https://openalex.org/W1989431146","doi":"https://doi.org/10.1016/s0168-0072(01)00048-3","title":"Complexity of t-tautologies","display_name":"Complexity of t-tautologies","publication_year":2001,"publication_date":"2001-12-01","ids":{"openalex":"https://openalex.org/W1989431146","doi":"https://doi.org/10.1016/s0168-0072(01)00048-3","mag":"1989431146"},"language":"en","primary_location":{"id":"doi:10.1016/s0168-0072(01)00048-3","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0168-0072(01)00048-3","pdf_url":null,"source":{"id":"https://openalex.org/S172477885","display_name":"Annals of Pure and Applied Logic","issn_l":"0168-0072","issn":["0168-0072","1873-2461"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Pure and Applied Logic","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":"Matthias Baaz","raw_affiliation_strings":["Institut f\u00fcr Algebra und Diskrete Mathematik, Technische Universit\u00e4t Wien A-1040, Austria"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Algebra und Diskrete Mathematik, Technische Universit\u00e4t Wien A-1040, Austria","institution_ids":["https://openalex.org/I145847075"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036484429","display_name":"Petr H\u00e1jek","orcid":"https://orcid.org/0000-0001-5579-1215"},"institutions":[{"id":"https://openalex.org/I202391551","display_name":"Czech Academy of Sciences","ror":"https://ror.org/053avzc18","country_code":"CZ","type":"government","lineage":["https://openalex.org/I202391551"]},{"id":"https://openalex.org/I4210155092","display_name":"Czech Academy of Sciences, Institute of Computer Science","ror":"https://ror.org/0496n6574","country_code":"CZ","type":"facility","lineage":["https://openalex.org/I202391551","https://openalex.org/I4210155092"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Petr H\u00e1jek","raw_affiliation_strings":["Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague, Czech Republic","Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague, Czech Republic#TAB#"],"affiliations":[{"raw_affiliation_string":"Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague, Czech Republic","institution_ids":["https://openalex.org/I4210155092"]},{"raw_affiliation_string":"Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague, Czech Republic#TAB#","institution_ids":["https://openalex.org/I202391551"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109033991","display_name":"Franco Montagna","orcid":null},"institutions":[{"id":"https://openalex.org/I102064193","display_name":"University of Siena","ror":"https://ror.org/01tevnk56","country_code":"IT","type":"education","lineage":["https://openalex.org/I102064193"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Franco Montagna","raw_affiliation_strings":["Dipartimento di Matematica, Via del capitano 15, 531 00 Siena, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, Via del capitano 15, 531 00 Siena, Italy","institution_ids":["https://openalex.org/I102064193"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110701511","display_name":"Helmut Veith","orcid":null},"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":false,"raw_author_name":"Helmut Veith","raw_affiliation_strings":["Institut f\u00fcr Informationssysteme, Technische Universit\u00e4t Wien, A-1040, Austria"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Informationssysteme, Technische Universit\u00e4t Wien, A-1040, Austria","institution_ids":["https://openalex.org/I145847075"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5035315045"],"corresponding_institution_ids":["https://openalex.org/I145847075"],"apc_list":{"value":3390,"currency":"USD","value_usd":3390},"apc_paid":null,"fwci":3.6561,"has_fulltext":false,"cited_by_count":54,"citation_normalized_percentile":{"value":0.92505322,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"113","issue":"1-3","first_page":"3","last_page":"11"},"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/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/tautology","display_name":"Tautology (logic)","score":0.9803103804588318},{"id":"https://openalex.org/keywords/decidability","display_name":"Decidability","score":0.7272059321403503},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7072615623474121},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5086313486099243},{"id":"https://openalex.org/keywords/propositional-variable","display_name":"Propositional variable","score":0.43602675199508667},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4200233519077301},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1994500458240509},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.15741506218910217},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.09611639380455017},{"id":"https://openalex.org/keywords/intermediate-logic","display_name":"Intermediate logic","score":0.08867946267127991}],"concepts":[{"id":"https://openalex.org/C166374712","wikidata":"https://www.wikidata.org/wiki/Q209555","display_name":"Tautology (logic)","level":5,"score":0.9803103804588318},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.7272059321403503},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7072615623474121},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5086313486099243},{"id":"https://openalex.org/C14523651","wikidata":"https://www.wikidata.org/wiki/Q3492863","display_name":"Propositional variable","level":4,"score":0.43602675199508667},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4200233519077301},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1994500458240509},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.15741506218910217},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.09611639380455017},{"id":"https://openalex.org/C33203268","wikidata":"https://www.wikidata.org/wiki/Q5361594","display_name":"Intermediate logic","level":3,"score":0.08867946267127991}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1016/s0168-0072(01)00048-3","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0168-0072(01)00048-3","pdf_url":null,"source":{"id":"https://openalex.org/S172477885","display_name":"Annals of Pure and Applied Logic","issn_l":"0168-0072","issn":["0168-0072","1873-2461"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Pure and Applied Logic","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.34.4947","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.34.4947","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.cas.cz/vvvvedci/hajek/cs15.ps","raw_type":"text"},{"id":"pmh:oai:usiena-air.unisi.it:11365/17613","is_oa":false,"landing_page_url":"http://hdl.handle.net/11365/17613","pdf_url":null,"source":{"id":"https://openalex.org/S4377196319","display_name":"Use Siena air (University of Siena)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I102064193","host_organization_name":"University of Siena","host_organization_lineage":["https://openalex.org/I102064193"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.6200000047683716}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1516119557","https://openalex.org/W1968172834","https://openalex.org/W1977670033","https://openalex.org/W1979726628","https://openalex.org/W2024065710","https://openalex.org/W2060794945","https://openalex.org/W2082093772","https://openalex.org/W2087171264","https://openalex.org/W2110182592","https://openalex.org/W2326267538","https://openalex.org/W4246378692","https://openalex.org/W4312874483"],"related_works":["https://openalex.org/W2384278060","https://openalex.org/W4224944532","https://openalex.org/W2328349573","https://openalex.org/W2995607835","https://openalex.org/W1528592560","https://openalex.org/W2053762111","https://openalex.org/W4297670065","https://openalex.org/W2440791454","https://openalex.org/W1618267488","https://openalex.org/W4205250428"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":4}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}