{"id":"https://openalex.org/W1990606699","doi":"https://doi.org/10.1017/s147106840100103x","title":"Transformation-based bottom-up computation of the well-founded model","display_name":"Transformation-based bottom-up computation of the well-founded model","publication_year":2001,"publication_date":"2001-09-01","ids":{"openalex":"https://openalex.org/W1990606699","doi":"https://doi.org/10.1017/s147106840100103x","mag":"1990606699"},"language":"en","primary_location":{"id":"doi:10.1017/s147106840100103x","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s147106840100103x","pdf_url":null,"source":{"id":"https://openalex.org/S59670734","display_name":"Theory and Practice of Logic Programming","issn_l":"1471-0684","issn":["1471-0684","1475-3081"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory and Practice of Logic Programming","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/A5004990891","display_name":"Stefan Brass","orcid":null},"institutions":[{"id":"https://openalex.org/I170201317","display_name":"University of Pittsburgh","ror":"https://ror.org/01an3r305","country_code":"US","type":"education","lineage":["https://openalex.org/I170201317"]},{"id":"https://openalex.org/I3130035786","display_name":"University Ucinf","ror":"https://ror.org/02cs9pv18","country_code":"CL","type":"education","lineage":["https://openalex.org/I3130035786"]}],"countries":["CL","US"],"is_corresponding":false,"raw_author_name":"STEFAN BRASS","raw_affiliation_strings":["School of Information Sciences, University of Pittsburgh, 135 North Bellefield Ave., Pittsburgh, PA 15260, USA; e-mail:","School of Information Sciences, University of Pittsburgh, 135 North Bellefield Ave., Pittsburgh, PA 15260, USA","e-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information Sciences, University of Pittsburgh, 135 North Bellefield Ave., Pittsburgh, PA 15260, USA; e-mail:","institution_ids":["https://openalex.org/I170201317","https://openalex.org/I3130035786"]},{"raw_affiliation_string":"School of Information Sciences, University of Pittsburgh, 135 North Bellefield Ave., Pittsburgh, PA 15260, USA","institution_ids":["https://openalex.org/I170201317"]},{"raw_affiliation_string":"e-mail:","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081145311","display_name":"J\u00fcrgen Dix","orcid":null},"institutions":[{"id":"https://openalex.org/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"J\u00dcRGEN DIX","raw_affiliation_strings":["Department of Computer Science, The University of Manchester, Oxford Road, Manchester, M13 9PL UK; e-mail:","Department of Computer Science, The University of Manchester, Oxford Road, Manchester, M13 9PL UK","e-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, The University of Manchester, Oxford Road, Manchester, M13 9PL UK; e-mail:","institution_ids":["https://openalex.org/I28407311"]},{"raw_affiliation_string":"Department of Computer Science, The University of Manchester, Oxford Road, Manchester, M13 9PL UK","institution_ids":["https://openalex.org/I28407311"]},{"raw_affiliation_string":"e-mail:","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052849771","display_name":"Burkhard Freitag","orcid":null},"institutions":[{"id":"https://openalex.org/I186354981","display_name":"University of Passau","ror":"https://ror.org/05ydjnb78","country_code":"DE","type":"education","lineage":["https://openalex.org/I186354981"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"BURKHARD FREITAG","raw_affiliation_strings":["Fakult\u00e4t f\u00fcr Mathematik und Informatik, Universit\u00e4t Passau, D-94030 Passau, Germany;","Fakult\u00e4t f\u00fcr Mathematik und Informatik, Universit\u00e4t Passau, D-94030 Passau, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fakult\u00e4t f\u00fcr Mathematik und Informatik, Universit\u00e4t Passau, D-94030 Passau, Germany;","institution_ids":["https://openalex.org/I186354981"]},{"raw_affiliation_string":"Fakult\u00e4t f\u00fcr Mathematik und Informatik, Universit\u00e4t Passau, D-94030 Passau, Germany","institution_ids":["https://openalex.org/I186354981"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032911591","display_name":"Ulrich Zukowski","orcid":null},"institutions":[{"id":"https://openalex.org/I186354981","display_name":"University of Passau","ror":"https://ror.org/05ydjnb78","country_code":"DE","type":"education","lineage":["https://openalex.org/I186354981"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"ULRICH ZUKOWSKI","raw_affiliation_strings":["Fakult\u00e4t f\u00fcr Mathematik und Informatik, Universit\u00e4t Passau, D-94030 Passau, Germany;","Fakult\u00e4t f\u00fcr Mathematik und Informatik, Universit\u00e4t Passau, D-94030 Passau, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fakult\u00e4t f\u00fcr Mathematik und Informatik, Universit\u00e4t Passau, D-94030 Passau, Germany;","institution_ids":["https://openalex.org/I186354981"]},{"raw_affiliation_string":"Fakult\u00e4t f\u00fcr Mathematik und Informatik, Universit\u00e4t Passau, D-94030 Passau, Germany","institution_ids":["https://openalex.org/I186354981"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":18.7546,"has_fulltext":false,"cited_by_count":88,"citation_normalized_percentile":{"value":0.99234358,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"1","issue":"5","first_page":"497","last_page":"538"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","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/T11010","display_name":"Logic, Reasoning, and Knowledge","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/T10126","display_name":"Logic, programming, and type systems","score":0.9968000054359436,"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/T10142","display_name":"Formal Methods in Verification","score":0.9872000217437744,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7927110195159912},{"id":"https://openalex.org/keywords/magic","display_name":"MAGIC (telescope)","score":0.6615582704544067},{"id":"https://openalex.org/keywords/program-transformation","display_name":"Program transformation","score":0.6442622542381287},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5830204486846924},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.5308464765548706},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.49557268619537354},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.465060293674469},{"id":"https://openalex.org/keywords/remainder","display_name":"Remainder","score":0.4292190968990326},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.4195464551448822},{"id":"https://openalex.org/keywords/program-analysis","display_name":"Program analysis","score":0.41230159997940063},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3950863182544708},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.2583150267601013},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.1647184193134308}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7927110195159912},{"id":"https://openalex.org/C2777704519","wikidata":"https://www.wikidata.org/wiki/Q45732","display_name":"MAGIC (telescope)","level":2,"score":0.6615582704544067},{"id":"https://openalex.org/C2778361913","wikidata":"https://www.wikidata.org/wiki/Q7248437","display_name":"Program transformation","level":2,"score":0.6442622542381287},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5830204486846924},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.5308464765548706},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.49557268619537354},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.465060293674469},{"id":"https://openalex.org/C39613435","wikidata":"https://www.wikidata.org/wiki/Q846677","display_name":"Remainder","level":2,"score":0.4292190968990326},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.4195464551448822},{"id":"https://openalex.org/C98183937","wikidata":"https://www.wikidata.org/wiki/Q2112188","display_name":"Program analysis","level":2,"score":0.41230159997940063},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3950863182544708},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.2583150267601013},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.1647184193134308},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s147106840100103x","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s147106840100103x","pdf_url":null,"source":{"id":"https://openalex.org/S59670734","display_name":"Theory and Practice of Logic Programming","issn_l":"1471-0684","issn":["1471-0684","1475-3081"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory and Practice of Logic Programming","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":51,"referenced_works":["https://openalex.org/W12006093","https://openalex.org/W72396871","https://openalex.org/W83671853","https://openalex.org/W91931761","https://openalex.org/W127451913","https://openalex.org/W158212583","https://openalex.org/W158383006","https://openalex.org/W165704037","https://openalex.org/W193610518","https://openalex.org/W194413726","https://openalex.org/W203410698","https://openalex.org/W1486205590","https://openalex.org/W1491260788","https://openalex.org/W1497544880","https://openalex.org/W1505455772","https://openalex.org/W1518971173","https://openalex.org/W1553202793","https://openalex.org/W1565166142","https://openalex.org/W1586430014","https://openalex.org/W1592688312","https://openalex.org/W1596858679","https://openalex.org/W1672891595","https://openalex.org/W1706499668","https://openalex.org/W1830798555","https://openalex.org/W1844282718","https://openalex.org/W1885514099","https://openalex.org/W1968513265","https://openalex.org/W1968592673","https://openalex.org/W1971140053","https://openalex.org/W1978108034","https://openalex.org/W1981961379","https://openalex.org/W1995270677","https://openalex.org/W1995303925","https://openalex.org/W2003531456","https://openalex.org/W2010904739","https://openalex.org/W2011992362","https://openalex.org/W2013815977","https://openalex.org/W2019968021","https://openalex.org/W2026433347","https://openalex.org/W2031868932","https://openalex.org/W2034019663","https://openalex.org/W2036258467","https://openalex.org/W2041259062","https://openalex.org/W2060470146","https://openalex.org/W2070598037","https://openalex.org/W2085609918","https://openalex.org/W2115128204","https://openalex.org/W2127643521","https://openalex.org/W2132745831","https://openalex.org/W2142386424","https://openalex.org/W2611415697"],"related_works":["https://openalex.org/W2888997865","https://openalex.org/W2112914024","https://openalex.org/W2525463489","https://openalex.org/W2970480852","https://openalex.org/W4205784628","https://openalex.org/W1970625600","https://openalex.org/W1483759049","https://openalex.org/W1993524544","https://openalex.org/W2374474610","https://openalex.org/W2066597891"],"abstract_inverted_index":{"We":[0,85,235],"present":[1],"a":[2,181,199,228,239],"framework":[3,55],"for":[4,46,68],"expressing":[5],"bottom-up":[6],"algorithms":[7],"to":[8,56,64,99,134,165,202,211,219,250,258],"compute":[9],"the":[10,22,78,81,104,114,125,135,153,185,189,245,251],"well-founded":[11,115,154,186],"model":[12,155,187],"of":[13,24,80,90,137,152,184,188,230],"non-disjunctive":[14],"logic":[15],"programs.":[16,48],"Our":[17],"method":[18,118,170],"is":[19,74,198],"based":[20],"on":[21],"notion":[23],"conditional":[25],"facts":[26],"and":[27,35,39,43,124,144,205,254],"elementary":[28],"program":[29],"transformations":[30,92,231],"studied":[31],"by":[32,227],"B":[33],"RASS":[34],"D":[36],"IX":[37],"(Brass":[38],"Dix,":[40,44,145],"1994;":[41],"Brass":[42,143],"1999)":[45],"disjunctive":[47],"However,":[49,132],"even":[50],"if":[51,222],"we":[52,147],"restrict":[53],"their":[54,59],"nondisjunctive":[57],"programs,":[58],"\u2018residual":[60],"program\u2019":[61],"can":[62,224],"grow":[63],"exponential":[65],"size,":[66],"whereas":[67],"function-free":[69],"programs":[70,175],"our":[71,91,138,168,196,233],"\u2018program":[72],"remainder\u2019":[73],"always":[75,179],"polynomial":[76],"in":[77,142,232],"size":[79],"extensional":[82],"database":[83],"(EDB).":[84],"show":[86,194],"that":[87,156,195,215,244],"particular":[88],"orderings":[89],"(we":[93],"call":[94],"them":[95],"strategies":[96,214],")":[97],"correspond":[98],"well-known":[100],"computational":[101],"methods":[102,209],"like":[103],"alternating":[105,127],"fixpoint":[106,128],"approach":[107,197],"(Van":[108],"Gelder,":[109,112],"1989;":[110],"Van":[111],"1993),":[113],"magic":[116,126,172],"sets":[117],"(Kemp":[119],"et":[120],"al":[121],".,":[122],"1995)":[123],"procedure":[129],"(Morishita,":[130],"1996).":[131],"due":[133],"confluence":[136],"calculi":[139],"(first":[140],"noted":[141],"1998),":[146],"come":[148],"up":[149],"with":[150],"computations":[151],"are":[157,216],"provably":[158],"better":[159],"than":[160],"these":[161],"methods.":[162],"In":[163],"contrast":[164],"other":[166],"approaches,":[167],"transformation":[169],"treats":[171],"set":[173],"transformed":[174],"correctly,":[176],"i.e.":[177],"it":[178],"computes":[180],"relevant":[182],"part":[183],"original":[190],"program.":[191],"These":[192],"results":[193,247],"valuable":[200],"tool":[201],"analyze,":[203],"compare,":[204],"optimize":[206,259],"existing":[207],"evaluation":[208],"or":[210],"create":[212],"new":[213],"automatically":[217],"proven":[218],"be":[220,225,256],"correct":[221],"they":[223],"described":[226],"sequence":[229],"framework.":[234],"have":[236],"also":[237],"developed":[238],"prototypical":[240],"implementation.":[241],"Experiments":[242],"illustrate":[243],"theoretical":[246],"carry":[248],"over":[249],"implemented":[252],"prototype":[253],"may":[255],"used":[257],"real":[260],"life":[261],"systems.":[262]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}