{"id":"https://openalex.org/W2950040887","doi":"https://doi.org/10.48550/arxiv.0809.0922","title":"Superposition for Fixed Domains","display_name":"Superposition for Fixed Domains","publication_year":2008,"publication_date":"2008-09-04","ids":{"openalex":"https://openalex.org/W2950040887","doi":"https://doi.org/10.48550/arxiv.0809.0922","mag":"2950040887"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:0809.0922","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/0809.0922","pdf_url":"https://arxiv.org/pdf/0809.0922","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/0809.0922","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089611784","display_name":"Matthias Horbach","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210109712","display_name":"Max Planck Institute for Informatics","ror":"https://ror.org/01w19ak89","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210109712"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Horbach, Matthias","raw_affiliation_strings":["Max-Planck-Institute for Informatics, , Saarbr\u00fccken, Germany#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Max-Planck-Institute for Informatics, , Saarbr\u00fccken, Germany#TAB#","institution_ids":["https://openalex.org/I4210109712"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046034681","display_name":"Christoph Weidenbach","orcid":"https://orcid.org/0000-0001-6002-0458","observed_orcids":["https://orcid.org/0000-0001-6002-0458"]},"institutions":[{"id":"https://openalex.org/I4210109712","display_name":"Max Planck Institute for Informatics","ror":"https://ror.org/01w19ak89","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210109712"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Weidenbach, Christoph","raw_affiliation_strings":["Max-Planck-Institute for Informatics, , Saarbr\u00fccken, Germany#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Max-Planck-Institute for Informatics, , Saarbr\u00fccken, Germany#TAB#","institution_ids":["https://openalex.org/I4210109712"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210109712"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.8389000296592712,"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/T10126","display_name":"Logic, programming, and type systems","score":0.8389000296592712,"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":0.11129999905824661,"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":0.02199999988079071,"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/superposition-calculus","display_name":"superposition calculus","score":0.9900000095367432},{"id":"https://openalex.org/keywords/first-order-logic","display_name":"first-order logic","score":0.7490000128746033},{"id":"https://openalex.org/keywords/minimal-models","display_name":"minimal models","score":0.5720000267028809},{"id":"https://openalex.org/keywords/skolem-functions","display_name":"Skolem functions","score":0.8009999990463257},{"id":"https://openalex.org/keywords/horn-theories","display_name":"Horn theories","score":0.550000011920929},{"id":"https://openalex.org/keywords/refutational-completeness","display_name":"refutational completeness","score":0.7649999856948853},{"id":"https://openalex.org/keywords/existential-quantification","display_name":"existential quantification","score":0.628000020980835},{"id":"https://openalex.org/keywords/decision-making-methods","display_name":"decision procedures","score":0.5019999742507935}],"concepts":[{"id":"https://openalex.org/C27753989","wikidata":"https://www.wikidata.org/wiki/Q284885","display_name":"Superposition principle","level":2,"score":0.7836403846740723},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.366122841835022},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24268659949302673}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:0809.0922","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/0809.0922","pdf_url":"https://arxiv.org/pdf/0809.0922","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"doi:10.48550/arxiv.0809.0922","doi":"https://doi.org/10.48550/arxiv.0809.0922","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.0809.0922","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:0809.0922","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/0809.0922","pdf_url":"https://arxiv.org/pdf/0809.0922","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, justice, and strong institutions","score":0.8100000023841858}],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W1562775594","https://openalex.org/W1996064523","https://openalex.org/W2026328078","https://openalex.org/W2167556778","https://openalex.org/W2585777010"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W4308749380","https://openalex.org/W2037841693","https://openalex.org/W1979597421","https://openalex.org/W2372481764","https://openalex.org/W2610947892","https://openalex.org/W1977264433","https://openalex.org/W2746368218","https://openalex.org/W4308448008","https://openalex.org/W2347371661"],"abstract_inverted_index":{"Superposition":[0],"is":[1,63,92],"an":[2],"established":[3],"decision":[4],"procedure":[5],"for":[6,30,100],"a":[7,26,39,45,87,101],"variety":[8],"of":[9,16,47,112,124,133],"first-order":[10,102],"logic":[11],"theories":[12,109],"represented":[13],"by":[14,22],"sets":[15],"clauses.":[17],"A":[18],"satisfiable":[19],"theory,":[20],"saturated":[21,40,107],"superposition,":[23],"implicitly":[24],"defines":[25],"minimal":[27,49,126],"term-generated":[28,51],"model":[29,127],"the":[31,48,69,98,119,125,131],"theory.":[32],"Proving":[33],"universal":[34],"properties":[35,123],"with":[36,84],"respect":[37,85],"to":[38,44,86,121],"theory":[41],"directly":[42],"leads":[43],"modification":[46],"model's":[50],"domain,":[52],"as":[53],"new":[54],"Skolem":[55],"functions":[56],"are":[57],"introduced.":[58],"For":[59,106],"many":[60],"applications,":[61],"this":[62],"not":[64],"desired.":[65],"Therefore,":[66],"we":[67,115],"propose":[68],"first":[70],"superposition":[71],"calculus":[72,91,120],"that":[73],"can":[74,81,116],"explicitly":[75],"represent":[76],"existentially":[77],"quantified":[78],"variables":[79],"and":[80,94,110],"thus":[82],"compute":[83],"given":[88],"domain.":[89],"This":[90],"sound":[93],"refutationally":[95],"complete":[96],"in":[97],"limit":[99],"fixed":[103],"domain":[104],"semantics.":[105],"Horn":[108],"classes":[111],"positive":[113],"formulas,":[114],"even":[117],"employ":[118],"prove":[122],"itself,":[128],"going":[129],"beyond":[130],"scope":[132],"known":[134],"superposition-based":[135],"approaches.":[136]},"counts_by_year":[],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}