{"id":"https://openalex.org/W1991463353","doi":"https://doi.org/10.1093/jigpal/jzt025","title":"Expressing properties in second- and third-order logic: hypercube graphs and SATQBF","display_name":"Expressing properties in second- and third-order logic: hypercube graphs and SATQBF","publication_year":2013,"publication_date":"2013-07-22","ids":{"openalex":"https://openalex.org/W1991463353","doi":"https://doi.org/10.1093/jigpal/jzt025","mag":"1991463353"},"language":"en","primary_location":{"id":"doi:10.1093/jigpal/jzt025","is_oa":false,"landing_page_url":"https://doi.org/10.1093/jigpal/jzt025","pdf_url":null,"source":{"id":"https://openalex.org/S2734381524","display_name":"Logic Journal of IGPL","issn_l":"1367-0751","issn":["1367-0751","1368-9894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logic Journal of IGPL","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/A5035972346","display_name":"Flavio Ferrarotti","orcid":"https://orcid.org/0000-0003-2278-8233"},"institutions":[{"id":"https://openalex.org/I41156924","display_name":"Victoria University of Wellington","ror":"https://ror.org/0040r6f76","country_code":"NZ","type":"education","lineage":["https://openalex.org/I41156924"]}],"countries":["NZ"],"is_corresponding":true,"raw_author_name":"F. Ferrarotti","raw_affiliation_strings":["School of Information Management, Victoria University of Wellington, PO Box 600, Wellington 6140, New Zealand","School of Information Management Victoria University of Wellington PO Box 600, Wellington, 6140 New Zealand"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information Management, Victoria University of Wellington, PO Box 600, Wellington 6140, New Zealand","institution_ids":["https://openalex.org/I41156924"]},{"raw_affiliation_string":"School of Information Management Victoria University of Wellington PO Box 600, Wellington, 6140 New Zealand","institution_ids":["https://openalex.org/I41156924"]}]},{"author_position":"middle","author":{"id":null,"display_name":"W. Ren","orcid":null},"institutions":[{"id":"https://openalex.org/I51158804","display_name":"Massey University","ror":"https://ror.org/052czxv31","country_code":"NZ","type":"education","lineage":["https://openalex.org/I51158804"]}],"countries":["NZ"],"is_corresponding":false,"raw_author_name":"W. Ren","raw_affiliation_strings":["School of Engineering and Advanced Technology, Massey University, Private Box 756, Wellington 6140, New Zealand"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Engineering and Advanced Technology, Massey University, Private Box 756, Wellington 6140, New Zealand","institution_ids":["https://openalex.org/I51158804"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102093735","display_name":"J. M. T. Torres","orcid":null},"institutions":[{"id":"https://openalex.org/I4210091250","display_name":"University of Cuenca del Plata","ror":"https://ror.org/00d7rqp94","country_code":"AR","type":"education","lineage":["https://openalex.org/I4210091250"]},{"id":"https://openalex.org/I73822459","display_name":"National University of San Luis","ror":"https://ror.org/00mczdx43","country_code":"AR","type":"education","lineage":["https://openalex.org/I73822459"]}],"countries":["AR"],"is_corresponding":false,"raw_author_name":"J. M. T. Torres","raw_affiliation_strings":["ICTIC, Universidad de la Cuenca del Plata, Corrientes, Argentina and Department of Informatics, Universidad Nacional de San Luis, Ejercito de Los Andes 950, D5700HHW San Luis, Argentina"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ICTIC, Universidad de la Cuenca del Plata, Corrientes, Argentina and Department of Informatics, Universidad Nacional de San Luis, Ejercito de Los Andes 950, D5700HHW San Luis, Argentina","institution_ids":["https://openalex.org/I4210091250","https://openalex.org/I73822459"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5035972346"],"corresponding_institution_ids":["https://openalex.org/I41156924"],"apc_list":{"value":4151,"currency":"USD","value_usd":4151},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.06787138,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"22","issue":"2","first_page":"355","last_page":"386"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9933000206947327,"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"}},"topics":[{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9933000206947327,"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/T10142","display_name":"Formal Methods in Verification","score":0.9919999837875366,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9882000088691711,"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/order","display_name":"Order (exchange)","score":0.5852822065353394},{"id":"https://openalex.org/keywords/hypercube","display_name":"Hypercube","score":0.4567164182662964},{"id":"https://openalex.org/keywords/library-science","display_name":"Library science","score":0.42229196429252625},{"id":"https://openalex.org/keywords/humanities","display_name":"Humanities","score":0.4175824820995331},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.40933215618133545},{"id":"https://openalex.org/keywords/art","display_name":"Art","score":0.2831957936286926},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2299313247203827},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.20292943716049194},{"id":"https://openalex.org/keywords/business","display_name":"Business","score":0.11868998408317566}],"concepts":[{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5852822065353394},{"id":"https://openalex.org/C50820777","wikidata":"https://www.wikidata.org/wiki/Q213723","display_name":"Hypercube","level":2,"score":0.4567164182662964},{"id":"https://openalex.org/C161191863","wikidata":"https://www.wikidata.org/wiki/Q199655","display_name":"Library science","level":1,"score":0.42229196429252625},{"id":"https://openalex.org/C15708023","wikidata":"https://www.wikidata.org/wiki/Q80083","display_name":"Humanities","level":1,"score":0.4175824820995331},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40933215618133545},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.2831957936286926},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2299313247203827},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.20292943716049194},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.11868998408317566},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1093/jigpal/jzt025","is_oa":false,"landing_page_url":"https://doi.org/10.1093/jigpal/jzt025","pdf_url":null,"source":{"id":"https://openalex.org/S2734381524","display_name":"Logic Journal of IGPL","issn_l":"1367-0751","issn":["1367-0751","1368-9894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Logic Journal of IGPL","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":6,"referenced_works":["https://openalex.org/W1968490853","https://openalex.org/W1996184580","https://openalex.org/W2002690977","https://openalex.org/W2022519515","https://openalex.org/W2065251436","https://openalex.org/W3127113455"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2916710807","https://openalex.org/W4286907761","https://openalex.org/W2413588304","https://openalex.org/W3205447645","https://openalex.org/W2009411567","https://openalex.org/W2371629703","https://openalex.org/W2097769911","https://openalex.org/W2774705104","https://openalex.org/W72835634"],"abstract_inverted_index":{"It":[0],"follows":[1],"from":[2],"the":[3,38,87,93,112,117,131,140,169,182,191],"famous":[4],"Fagin's":[5],"theorem":[6],"that":[7,41,55,129],"all":[8],"problems":[9,30,44,54],"in":[10,14,74,84,139],"NP":[11,53],"are":[12,24,45,51,71,150],"expressible":[13],"existential":[15],"second-order":[16,85,120],"logic":[17,86,127,148],"(\u2203SO),":[18],"and":[19,35,47,63,92,146,187],"vice":[20],"versa.":[21],"Indeed,":[22],"there":[23,50],"well-known":[25],"\u2203SO":[26,39,65],"characterizations":[27],"of":[28,78,89,96,104,111,142,156,159,164,171,177,184,193],"NP-complete":[29],"such":[31],"as":[32,162],"3-colourability,":[33],"Hamiltonicity":[34],"clique.":[36],"Furthermore,":[37],"sentences":[40],"characterize":[42,83],"those":[43],"simple":[46,62],"elegant.":[48],"However,":[49],"also":[52,107],"do":[56],"not":[57],"seem":[58],"to":[59,115,153],"possess":[60],"equally":[61],"elegant":[64],"characterizations.":[66],"In":[67,80],"this":[68,75],"work,":[69],"we":[70,82,123],"mainly":[72],"interested":[73],"latter":[76],"class":[77,88,132],"problems.":[79],"particular,":[81],"hypercube":[90],"graphs":[91],"classes":[94],"SATQBFk":[95],"satisfiable":[97],"quantified":[98],"Boolean":[99],"lformulae":[100],"with":[101],"k":[102],"alternations":[103],"quantifiers.":[105],"We":[106],"provide":[108],"detailed":[109],"descriptions":[110],"strategies":[113],"followed":[114],"obtain":[116],"corresponding":[118],"non-trivial":[119],"sentences.":[121],"Finally,":[122],"sketch":[124],"a":[125,157,175],"third-order":[126,147,188],"sentence":[128],"defines":[130],"SATQBF":[133],"=":[134],"\u222ak\u22651SATQBFk.":[135],"The":[136],"sub-formulae":[137],"used":[138,166],"construction":[141],"these":[143],"complex":[144,172,185],"second-":[145,186],"sentences,":[149],"good":[151],"candidates":[152],"form":[154],"part":[155],"library":[158,176],"formulae.":[160],"Same":[161],"libraries":[163],"frequently":[165],"functions":[167],"simplify":[168,181],"writing":[170,183],"computer":[173],"programs,":[174],"formulae":[178],"could":[179],"potentially":[180],"queries,":[189],"minimizing":[190],"probability":[192],"error.":[194]},"counts_by_year":[{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}