{"id":"https://openalex.org/W3205533508","doi":"https://doi.org/10.24963/kr.2021/57","title":"Lifted Inference with Tree Axioms","display_name":"Lifted Inference with Tree Axioms","publication_year":2021,"publication_date":"2021-09-01","ids":{"openalex":"https://openalex.org/W3205533508","doi":"https://doi.org/10.24963/kr.2021/57","mag":"3205533508"},"language":"en","primary_location":{"id":"doi:10.24963/kr.2021/57","is_oa":true,"landing_page_url":"https://doi.org/10.24963/kr.2021/57","pdf_url":"https://proceedings.kr.org/2021/57/kr2021-0057-van-bremen-et-al.pdf","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Eighteenth International Conference on Principles of Knowledge Representation and Reasoning","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://proceedings.kr.org/2021/57/kr2021-0057-van-bremen-et-al.pdf","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043401121","display_name":"Timothy van Bremen","orcid":"https://orcid.org/0009-0004-0538-3044"},"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":"Timothy van Bremen","raw_affiliation_strings":["KU Leuven"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"KU Leuven","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021262042","display_name":"Ond\u0159ej Ku\u017eelka","orcid":"https://orcid.org/0000-0002-6523-9114"},"institutions":[{"id":"https://openalex.org/I44504214","display_name":"Czech Technical University in Prague","ror":"https://ror.org/03kqpb082","country_code":"CZ","type":"education","lineage":["https://openalex.org/I44504214"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Ond\u0159ej Ku\u017eelka","raw_affiliation_strings":["Czech Technical University in Prague"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Czech Technical University in Prague","institution_ids":["https://openalex.org/I44504214"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8396,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.7917796,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"599","last_page":"608"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.9998000264167786,"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/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.9998000264167786,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9886999726295471,"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/T11273","display_name":"Advanced Graph Neural Networks","score":0.9865000247955322,"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":0.649393618106842},{"id":"https://openalex.org/keywords/binary-tree","display_name":"Binary tree","score":0.6411957740783691},{"id":"https://openalex.org/keywords/sentence","display_name":"Sentence","score":0.6270809769630432},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.5565231442451477},{"id":"https://openalex.org/keywords/binary-relation","display_name":"Binary relation","score":0.5560577511787415},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5531512498855591},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.5370634198188782},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.455495685338974},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45474645495414734},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4537397623062134},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44523224234580994},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.4219313859939575},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3545522093772888},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.35267844796180725},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3502158522605896},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.28777819871902466},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.11390805244445801}],"concepts":[{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.649393618106842},{"id":"https://openalex.org/C197855036","wikidata":"https://www.wikidata.org/wiki/Q380172","display_name":"Binary tree","level":2,"score":0.6411957740783691},{"id":"https://openalex.org/C2777530160","wikidata":"https://www.wikidata.org/wiki/Q41796","display_name":"Sentence","level":2,"score":0.6270809769630432},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.5565231442451477},{"id":"https://openalex.org/C65180967","wikidata":"https://www.wikidata.org/wiki/Q130901","display_name":"Binary relation","level":2,"score":0.5560577511787415},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5531512498855591},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.5370634198188782},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.455495685338974},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45474645495414734},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4537397623062134},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44523224234580994},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.4219313859939575},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3545522093772888},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.35267844796180725},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3502158522605896},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.28777819871902466},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.11390805244445801},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.24963/kr.2021/57","is_oa":true,"landing_page_url":"https://doi.org/10.24963/kr.2021/57","pdf_url":"https://proceedings.kr.org/2021/57/kr2021-0057-van-bremen-et-al.pdf","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Eighteenth International Conference on Principles of Knowledge Representation and Reasoning","raw_type":"proceedings-article"}],"best_oa_location":{"id":"doi:10.24963/kr.2021/57","is_oa":true,"landing_page_url":"https://doi.org/10.24963/kr.2021/57","pdf_url":"https://proceedings.kr.org/2021/57/kr2021-0057-van-bremen-et-al.pdf","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Eighteenth International Conference on Principles of Knowledge Representation and Reasoning","raw_type":"proceedings-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G12500569","display_name":null,"funder_award_id":"CZ.02.1.01/0.0","funder_id":"https://openalex.org/F4320321006","funder_display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky"},{"id":"https://openalex.org/G4131035492","display_name":null,"funder_award_id":"CZ.02.1.01","funder_id":"https://openalex.org/F4320321006","funder_display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky"},{"id":"https://openalex.org/G4818322051","display_name":null,"funder_award_id":"019/0000765","funder_id":"https://openalex.org/F4320334253","funder_display_name":"Research Center for Informatics, Czech Technical University in Prague"},{"id":"https://openalex.org/G6076044179","display_name":null,"funder_award_id":"20-19104Y","funder_id":"https://openalex.org/F4320321006","funder_display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky"}],"funders":[{"id":"https://openalex.org/F4320321006","display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky","ror":"https://ror.org/01pv73b02"},{"id":"https://openalex.org/F4320327336","display_name":"Vlaamse regering","ror":null},{"id":"https://openalex.org/F4320334253","display_name":"Research Center for Informatics, Czech Technical University in Prague","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3205533508.pdf","grobid_xml":"https://content.openalex.org/works/W3205533508.grobid-xml"},"referenced_works_count":38,"referenced_works":["https://openalex.org/W51516856","https://openalex.org/W73939759","https://openalex.org/W1489366126","https://openalex.org/W1606383219","https://openalex.org/W1823181550","https://openalex.org/W1977970897","https://openalex.org/W1978493550","https://openalex.org/W1989783863","https://openalex.org/W2017018565","https://openalex.org/W2028114585","https://openalex.org/W2058120853","https://openalex.org/W2079785597","https://openalex.org/W2096659722","https://openalex.org/W2124580444","https://openalex.org/W2133873188","https://openalex.org/W2141007910","https://openalex.org/W2159284075","https://openalex.org/W2516421545","https://openalex.org/W2542487480","https://openalex.org/W2552825470","https://openalex.org/W2616697817","https://openalex.org/W2798674957","https://openalex.org/W2952812825","https://openalex.org/W2963742388","https://openalex.org/W3013481747","https://openalex.org/W3041494771","https://openalex.org/W3104376605","https://openalex.org/W3151822599","https://openalex.org/W4298136200","https://openalex.org/W6600264618","https://openalex.org/W6602986204","https://openalex.org/W6629417139","https://openalex.org/W6644605137","https://openalex.org/W6644887767","https://openalex.org/W6654736592","https://openalex.org/W6657298784","https://openalex.org/W6725938230","https://openalex.org/W6738002306"],"related_works":["https://openalex.org/W178365807","https://openalex.org/W1555836633","https://openalex.org/W4240676090","https://openalex.org/W2081441417","https://openalex.org/W2375873920","https://openalex.org/W2514761403","https://openalex.org/W1765478077","https://openalex.org/W2384156205","https://openalex.org/W1983002393","https://openalex.org/W1945695511"],"abstract_inverted_index":{"We":[0],"consider":[1],"the":[2,22,30,59,87,105],"problem":[3],"of":[4,25,27,89],"weighted":[5,23],"first-order":[6,12],"model":[7],"counting":[8],"(WFOMC):":[9],"given":[10,60],"a":[11,90,102],"sentence":[13,41,84],"\u03d5":[14,28,85,100],"and":[15,71],"domain":[16,31,61],"size":[17,62],"n":[18],"\u2208":[19],"\u2115,":[20],"determine":[21],"sum":[24],"models":[26],"over":[29],"{1,":[32],"...,":[33],"n}.":[34],"Past":[35],"work":[36],"has":[37],"shown":[38],"that":[39,53,94],"any":[40,82],"using":[42],"at":[43],"most":[44],"two":[45],"logical":[46],"variables":[47],"admits":[48],"an":[49],"algorithm":[50],"for":[51],"WFOMC":[52],"runs":[54],"in":[55,58,99,104],"time":[56],"polynomial":[57],"(Van":[63],"den":[64,68],"Broeck":[65],"2011;":[66],"Van":[67],"Broeck,":[69],"Meert,":[70],"Darwiche":[72],"2014).":[73],"In":[74],"this":[75,79],"paper,":[76],"we":[77],"extend":[78],"result":[80],"to":[81],"two-variable":[83],"with":[86],"addition":[88],"tree":[91,103],"axiom,":[92],"stating":[93],"some":[95],"distinguished":[96],"binary":[97],"relation":[98],"forms":[101],"graph-theoretic":[106],"sense.":[107]},"counts_by_year":[{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}