{"id":"https://openalex.org/W2080633262","doi":"https://doi.org/10.1145/1183278.1183284","title":"Splitting an operator","display_name":"Splitting an operator","publication_year":2006,"publication_date":"2006-10-01","ids":{"openalex":"https://openalex.org/W2080633262","doi":"https://doi.org/10.1145/1183278.1183284","mag":"2080633262"},"language":"en","primary_location":{"id":"doi:10.1145/1183278.1183284","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1183278.1183284","pdf_url":null,"source":{"id":"https://openalex.org/S117153874","display_name":"ACM Transactions on Computational Logic","issn_l":"1529-3785","issn":["1529-3785","1557-945X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Computational Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://lirias.kuleuven.be/handle/123456789/125390","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071976409","display_name":"Joost Vennekens","orcid":"https://orcid.org/0000-0002-0791-0176"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Joost Vennekens","raw_affiliation_strings":["K.U. Leuven, Leuven, Belgium","K. U. Leuven, Leuven, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"K.U. Leuven, Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]},{"raw_affiliation_string":"K. U. Leuven, Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040039553","display_name":"David Gilis","orcid":null},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"David Gilis","raw_affiliation_strings":["K.U. Leuven, Leuven, Belgium","K. U. Leuven, Leuven, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"K.U. Leuven, Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]},{"raw_affiliation_string":"K. U. Leuven, Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090754913","display_name":"Marc Denecker","orcid":"https://orcid.org/0000-0002-0422-7339"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Marc Denecker","raw_affiliation_strings":["K.U. Leuven, Leuven, Belgium","K. U. Leuven, Leuven, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"K.U. Leuven, Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]},{"raw_affiliation_string":"K. U. Leuven, Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.1964,"has_fulltext":false,"cited_by_count":42,"citation_normalized_percentile":{"value":0.93808396,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"7","issue":"4","first_page":"765","last_page":"797"},"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":0.9994000196456909,"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":0.9970999956130981,"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/abstract-model-theory","display_name":"Abstract model theory","score":0.6253551840782166},{"id":"https://openalex.org/keywords/rotation-formalisms-in-three-dimensions","display_name":"Rotation formalisms in three dimensions","score":0.60965895652771},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5928351283073425},{"id":"https://openalex.org/keywords/modal-\u03bc-calculus","display_name":"Modal \u03bc-calculus","score":0.5844907760620117},{"id":"https://openalex.org/keywords/default-logic","display_name":"Default logic","score":0.5602632164955139},{"id":"https://openalex.org/keywords/logic-programming","display_name":"Logic programming","score":0.5573208928108215},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.5501889586448669},{"id":"https://openalex.org/keywords/multimodal-logic","display_name":"Multimodal logic","score":0.5373522043228149},{"id":"https://openalex.org/keywords/higher-order-logic","display_name":"Higher-order logic","score":0.4950934946537018},{"id":"https://openalex.org/keywords/well-founded-semantics","display_name":"Well-founded semantics","score":0.48227766156196594},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.480826735496521},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4683465361595154},{"id":"https://openalex.org/keywords/non-monotonic-logic","display_name":"Non-monotonic logic","score":0.4616263210773468},{"id":"https://openalex.org/keywords/semantics","display_name":"Semantics (computer science)","score":0.45907777547836304},{"id":"https://openalex.org/keywords/intermediate-logic","display_name":"Intermediate logic","score":0.4142482280731201},{"id":"https://openalex.org/keywords/classical-logic","display_name":"Classical logic","score":0.41199591755867004},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4041394889354706},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39504870772361755},{"id":"https://openalex.org/keywords/operational-semantics","display_name":"Operational semantics","score":0.3875083327293396},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.3512536883354187},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.33690202236175537},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3318289816379547},{"id":"https://openalex.org/keywords/autoepistemic-logic","display_name":"Autoepistemic logic","score":0.30384498834609985},{"id":"https://openalex.org/keywords/denotational-semantics","display_name":"Denotational semantics","score":0.20584726333618164},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.18299445509910583},{"id":"https://openalex.org/keywords/zeroth-order-logic","display_name":"Zeroth-order logic","score":0.12653791904449463}],"concepts":[{"id":"https://openalex.org/C161445131","wikidata":"https://www.wikidata.org/wiki/Q4669950","display_name":"Abstract model theory","level":5,"score":0.6253551840782166},{"id":"https://openalex.org/C171018156","wikidata":"https://www.wikidata.org/wiki/Q7370306","display_name":"Rotation formalisms in three dimensions","level":2,"score":0.60965895652771},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5928351283073425},{"id":"https://openalex.org/C173125200","wikidata":"https://www.wikidata.org/wiki/Q5275729","display_name":"Modal \u03bc-calculus","level":5,"score":0.5844907760620117},{"id":"https://openalex.org/C160236029","wikidata":"https://www.wikidata.org/wiki/Q842421","display_name":"Default logic","level":5,"score":0.5602632164955139},{"id":"https://openalex.org/C128838566","wikidata":"https://www.wikidata.org/wiki/Q275603","display_name":"Logic programming","level":2,"score":0.5573208928108215},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.5501889586448669},{"id":"https://openalex.org/C203659156","wikidata":"https://www.wikidata.org/wiki/Q6934805","display_name":"Multimodal logic","level":3,"score":0.5373522043228149},{"id":"https://openalex.org/C169896238","wikidata":"https://www.wikidata.org/wiki/Q1644136","display_name":"Higher-order logic","level":3,"score":0.4950934946537018},{"id":"https://openalex.org/C89497691","wikidata":"https://www.wikidata.org/wiki/Q7981058","display_name":"Well-founded semantics","level":5,"score":0.48227766156196594},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.480826735496521},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4683465361595154},{"id":"https://openalex.org/C159032336","wikidata":"https://www.wikidata.org/wiki/Q2488768","display_name":"Non-monotonic logic","level":2,"score":0.4616263210773468},{"id":"https://openalex.org/C184337299","wikidata":"https://www.wikidata.org/wiki/Q1437428","display_name":"Semantics (computer science)","level":2,"score":0.45907777547836304},{"id":"https://openalex.org/C33203268","wikidata":"https://www.wikidata.org/wiki/Q5361594","display_name":"Intermediate logic","level":3,"score":0.4142482280731201},{"id":"https://openalex.org/C32241873","wikidata":"https://www.wikidata.org/wiki/Q236975","display_name":"Classical logic","level":2,"score":0.41199591755867004},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4041394889354706},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39504870772361755},{"id":"https://openalex.org/C156325763","wikidata":"https://www.wikidata.org/wiki/Q1930895","display_name":"Operational semantics","level":3,"score":0.3875083327293396},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.3512536883354187},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.33690202236175537},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3318289816379547},{"id":"https://openalex.org/C3845977","wikidata":"https://www.wikidata.org/wiki/Q4826262","display_name":"Autoepistemic logic","level":4,"score":0.30384498834609985},{"id":"https://openalex.org/C207648694","wikidata":"https://www.wikidata.org/wiki/Q1189746","display_name":"Denotational semantics","level":4,"score":0.20584726333618164},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.18299445509910583},{"id":"https://openalex.org/C110039528","wikidata":"https://www.wikidata.org/wiki/Q8069651","display_name":"Zeroth-order logic","level":4,"score":0.12653791904449463},{"id":"https://openalex.org/C23409769","wikidata":"https://www.wikidata.org/wiki/Q7310750","display_name":"Relationship between string theory and quantum field theory","level":4,"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/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"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/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C108568745","wikidata":"https://www.wikidata.org/wiki/Q234181","display_name":"Quantum gravity","level":3,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/1183278.1183284","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1183278.1183284","pdf_url":null,"source":{"id":"https://openalex.org/S117153874","display_name":"ACM Transactions on Computational Logic","issn_l":"1529-3785","issn":["1529-3785","1557-945X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Computational Logic","raw_type":"journal-article"},{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/125390","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/123456789/125390","pdf_url":null,"source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ACM Transactions on Computational Logic, vol. 7 (4), (765-802)","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/125390","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/123456789/125390","pdf_url":null,"source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ACM Transactions on Computational Logic, vol. 7 (4), (765-802)","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W3747978","https://openalex.org/W8715149","https://openalex.org/W10111591","https://openalex.org/W31561947","https://openalex.org/W59877118","https://openalex.org/W140702174","https://openalex.org/W169516610","https://openalex.org/W174921238","https://openalex.org/W1489867543","https://openalex.org/W1494976167","https://openalex.org/W1505432843","https://openalex.org/W1541434994","https://openalex.org/W1565496223","https://openalex.org/W1568301188","https://openalex.org/W1611226978","https://openalex.org/W1860179216","https://openalex.org/W1924904173","https://openalex.org/W1968513265","https://openalex.org/W1993742694","https://openalex.org/W2001805670","https://openalex.org/W2003531456","https://openalex.org/W2012767403","https://openalex.org/W2031868932","https://openalex.org/W2037518358","https://openalex.org/W2046213250","https://openalex.org/W2067326626","https://openalex.org/W2089296451","https://openalex.org/W2093713825","https://openalex.org/W2102048877","https://openalex.org/W2111353076","https://openalex.org/W2141740710","https://openalex.org/W2151403295","https://openalex.org/W2155322595","https://openalex.org/W2295882966","https://openalex.org/W2523427404","https://openalex.org/W2899766884","https://openalex.org/W2988172561","https://openalex.org/W4206370914","https://openalex.org/W4231492400"],"related_works":["https://openalex.org/W2006784674","https://openalex.org/W1510566887","https://openalex.org/W2553959513","https://openalex.org/W2024430355","https://openalex.org/W150743059","https://openalex.org/W1764920750","https://openalex.org/W1998093438","https://openalex.org/W2950990748","https://openalex.org/W4212806761","https://openalex.org/W2080633262"],"abstract_inverted_index":{"It":[0],"is":[1,9],"well":[2],"known":[3],"that,":[4],"under":[5,15],"certain":[6],"conditions,":[7],"it":[8],"possible":[10],"to":[11,21],"split":[12],"logic":[13,60,109,126,129],"programs":[14],"stable":[16],"model":[17],"semantics,":[18],"that":[19,33],"is,":[20],"divide":[22],"such":[23,32,57],"a":[24,27,69,77,88,98,111],"program":[25,39],"into":[26],"number":[28],"of":[29,36,84,103,118],"different":[30],"\u201clevels\u201d,":[31],"the":[34,37,82,116],"models":[35,46],"entire":[38],"can":[40],"be":[41],"constructed":[42],"by":[43,121],"incrementally":[44],"constructing":[45],"for":[47,53,74,92,107,125],"each":[48,108],"level.":[49],"Similar":[50],"results":[51,106,124],"exist":[52],"other":[54],"nonmonotonic":[55],"formalisms,":[56],"as":[58],"auto-epistemic":[59,128],"and":[61,100,130],"default":[62,131],"logic.":[63,132],"In":[64],"this":[65,95],"work,":[66],"we":[67],"present":[68],"general,":[70],"algebraic":[71],"splitting":[72,105],"theory":[73,86,91],"logics":[75],"with":[76,81,110],"fixpoint":[78,90,112],"semantics.":[79,113],"Together":[80],"framework":[83],"approximation":[85],",":[87],"general":[89],"arbitrary":[93],"operators,":[94],"gives":[96],"us":[97],"uniform":[99],"powerful":[101],"way":[102],"deriving":[104],"We":[114],"demonstrate":[115],"usefulness":[117],"these":[119],"results,":[120],"generalizing":[122],"existing":[123],"programming,":[127]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2016-06-24T00:00:00"}