{"id":"https://openalex.org/W2915001220","doi":"https://doi.org/10.1017/s1471068406002997","title":"Decomposable theories","display_name":"Decomposable theories","publication_year":2007,"publication_date":"2007-08-24","ids":{"openalex":"https://openalex.org/W2915001220","doi":"https://doi.org/10.1017/s1471068406002997","mag":"2915001220"},"language":"en","primary_location":{"id":"doi:10.1017/s1471068406002997","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s1471068406002997","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/A5026554612","display_name":"Khalil Djelloul","orcid":null},"institutions":[{"id":"https://openalex.org/I4210115196","display_name":"Laboratoire d\u2019Informatique Fondamentale de Marseille","ror":"https://ror.org/022my8t07","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I21491767","https://openalex.org/I4210115196","https://openalex.org/I4210142724","https://openalex.org/I4210159245"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"KHALIL DJELLOUL","raw_affiliation_strings":["Parc scientifique et technologique de Luminy, Laboratoire d'Informatique Fondamentale de Marseille, 163 avenue de Luminy - Case 901, 13288 Marseille, cedex 9, France (e-mail:","LIF - Laboratoire d'informatique Fondamentale de Marseille - UMR 6166 (CMI 39, Rue Joliot Curie 13453 MARSEILLE CEDEX 13 - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Parc scientifique et technologique de Luminy, Laboratoire d'Informatique Fondamentale de Marseille, 163 avenue de Luminy - Case 901, 13288 Marseille, cedex 9, France (e-mail:","institution_ids":["https://openalex.org/I4210115196"]},{"raw_affiliation_string":"LIF - Laboratoire d'informatique Fondamentale de Marseille - UMR 6166 (CMI 39, Rue Joliot Curie 13453 MARSEILLE CEDEX 13 - France)","institution_ids":["https://openalex.org/I4210115196"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5026554612"],"corresponding_institution_ids":["https://openalex.org/I4210115196"],"apc_list":{"value":3550,"currency":"USD","value_usd":3550},"apc_paid":null,"fwci":4.8327,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.95115168,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":null,"biblio":{"volume":"7","issue":"5","first_page":"583","last_page":"632"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9983000159263611,"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":0.9983000159263611,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9937000274658203,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9677000045776367,"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/correctness","display_name":"Correctness","score":0.7689213752746582},{"id":"https://openalex.org/keywords/rewriting","display_name":"Rewriting","score":0.6418938040733337},{"id":"https://openalex.org/keywords/completeness","display_name":"Completeness (order theory)","score":0.5670623183250427},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5313950777053833},{"id":"https://openalex.org/keywords/boolean-data-type","display_name":"Boolean data type","score":0.4194210469722748},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4123508334159851},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38257816433906555},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37920865416526794},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3436585068702698},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1548469364643097},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.09005886316299438}],"concepts":[{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.7689213752746582},{"id":"https://openalex.org/C154690210","wikidata":"https://www.wikidata.org/wiki/Q1668499","display_name":"Rewriting","level":2,"score":0.6418938040733337},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.5670623183250427},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5313950777053833},{"id":"https://openalex.org/C7342684","wikidata":"https://www.wikidata.org/wiki/Q520777","display_name":"Boolean data type","level":2,"score":0.4194210469722748},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4123508334159851},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38257816433906555},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37920865416526794},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3436585068702698},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1548469364643097},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.09005886316299438},{"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:10.1017/s1471068406002997","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s1471068406002997","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W53188152","https://openalex.org/W60619409","https://openalex.org/W181592997","https://openalex.org/W196411404","https://openalex.org/W1480487311","https://openalex.org/W1558366171","https://openalex.org/W1602542416","https://openalex.org/W1602567617","https://openalex.org/W1607870219","https://openalex.org/W1612885523","https://openalex.org/W1766332311","https://openalex.org/W1973576343","https://openalex.org/W1999346653","https://openalex.org/W2001818070","https://openalex.org/W2002089154","https://openalex.org/W2010104109","https://openalex.org/W2030445287","https://openalex.org/W2033074970","https://openalex.org/W2035855976","https://openalex.org/W2066030913","https://openalex.org/W2096975981","https://openalex.org/W2100738443","https://openalex.org/W2113722134","https://openalex.org/W2181289644","https://openalex.org/W2546487582","https://openalex.org/W2574677321","https://openalex.org/W2604976281","https://openalex.org/W4212983671","https://openalex.org/W4213232664","https://openalex.org/W4302339081","https://openalex.org/W6633199964","https://openalex.org/W6659647051"],"related_works":["https://openalex.org/W2120204135","https://openalex.org/W2404647514","https://openalex.org/W1796293478","https://openalex.org/W1667647204","https://openalex.org/W4247536566","https://openalex.org/W4299818930","https://openalex.org/W2467059325","https://openalex.org/W263998227","https://openalex.org/W2963664616","https://openalex.org/W2622168976"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"present":[2,41],"in":[3,13,49,58,159],"this":[4],"paper":[5],"a":[6,27,42,67,78,87,140],"general":[7,43],"algorithm":[8,44,55,118],"for":[9,45],"solving":[10,46,154],"first-order":[11,47,68],"formulas":[12,48,83,155],"particular":[14],"theories":[15,32],"called":[16],"decomposable":[17,31,51,124,141],"theories.":[18,125],"First":[19],"of":[20,30,36,61,81,90,94,116,122,134,151],"all,":[21],"using":[22],"special":[23],"quantifiers,":[24],"we":[25,40,127],"give":[26,144],"formal":[28],"characterization":[29],"and":[33,143],"show":[34,128],"some":[35,145],"their":[37],"properties.":[38],"Then,":[39],"any":[50],"theory":[52,131,142],"T.":[53],"The":[54,114],"is":[56,107,139],"given":[57],"the":[59,109,120,123,130],"form":[60],"five":[62],"rewriting":[63],"rules.":[64],"It":[65],"transforms":[66],"formula":[69,110],"\u03d5,":[70],"which":[71],"can":[72],"possibly":[73],"contain":[74],"free":[75,103],"variables,":[76],"into":[77,86],"conjunction":[79],"\u03c6":[80,106],"solved":[82],"easily":[84],"transformable":[85],"Boolean":[88],"combination":[89],"existentially":[91],"quantified":[92],"conjunctions":[93],"atomic":[95],"formulas.":[96],"In":[97],"particular,":[98],"if":[99],"\u03d5":[100],"has":[101],"no":[102],"variables":[104],"then":[105],"either":[108],"true":[111],"or":[112,136],"\u00actrue.":[113],"correctness":[115],"our":[117,152],"proves":[119],"completeness":[121],"Finally,":[126],"that":[129],"${\\cal":[132,160],"T}$":[133,161],"finite":[135],"infinite":[137],"trees":[138],"benchmarks":[146],"realized":[147],"by":[148],"an":[149],"implementation":[150],"algorithm,":[153],"on":[156],"two-partner":[157],"games":[158],"with":[162],"more":[163],"than":[164],"160":[165],"nested":[166],"alternated":[167],"quantifiers.":[168]},"counts_by_year":[],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}
