{"id":"https://openalex.org/W2121227486","doi":"https://doi.org/10.1145/1352582.1352589","title":"Proof search in H\u00e1jek's basic logic","display_name":"Proof search in H\u00e1jek's basic logic","publication_year":2008,"publication_date":"2008-06-01","ids":{"openalex":"https://openalex.org/W2121227486","doi":"https://doi.org/10.1145/1352582.1352589","mag":"2121227486"},"language":"en","primary_location":{"id":"doi:10.1145/1352582.1352589","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1352582.1352589","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023349661","display_name":"Simone Bova","orcid":"https://orcid.org/0000-0002-1069-7257"},"institutions":[{"id":"https://openalex.org/I102064193","display_name":"University of Siena","ror":"https://ror.org/01tevnk56","country_code":"IT","type":"education","lineage":["https://openalex.org/I102064193"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Simone Bova","raw_affiliation_strings":["Universit\u00e0 degli Studi di Siena, Siena, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e0 degli Studi di Siena, Siena, Italy","institution_ids":["https://openalex.org/I102064193"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109033991","display_name":"Franco Montagna","orcid":null},"institutions":[{"id":"https://openalex.org/I102064193","display_name":"University of Siena","ror":"https://ror.org/01tevnk56","country_code":"IT","type":"education","lineage":["https://openalex.org/I102064193"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Franco Montagna","raw_affiliation_strings":["Universit\u00e0 degli Studi di Siena, Siena, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e0 degli Studi di Siena, Siena, Italy","institution_ids":["https://openalex.org/I102064193"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.414,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.69481701,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"9","issue":"3","first_page":"1","last_page":"26"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9993000030517578,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9993000030517578,"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":0.9991000294685364,"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":0.9934999942779541,"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/invertible-matrix","display_name":"Invertible matrix","score":0.6521810293197632},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5629779100418091},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.5234360694885254},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.48791787028312683},{"id":"https://openalex.org/keywords/conjunctive-normal-form","display_name":"Conjunctive normal form","score":0.47263380885124207},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.45507892966270447},{"id":"https://openalex.org/keywords/valuation","display_name":"Valuation (finance)","score":0.42628172039985657},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.425863116979599},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.4151160418987274},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.41170182824134827},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3264886736869812},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2297903299331665},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.10759660601615906}],"concepts":[{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.6521810293197632},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5629779100418091},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.5234360694885254},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.48791787028312683},{"id":"https://openalex.org/C16221470","wikidata":"https://www.wikidata.org/wiki/Q846564","display_name":"Conjunctive normal form","level":2,"score":0.47263380885124207},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.45507892966270447},{"id":"https://openalex.org/C186027771","wikidata":"https://www.wikidata.org/wiki/Q4008379","display_name":"Valuation (finance)","level":2,"score":0.42628172039985657},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.425863116979599},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.4151160418987274},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41170182824134827},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3264886736869812},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2297903299331665},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.10759660601615906},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"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:10.1145/1352582.1352589","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1352582.1352589","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"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.7599999904632568}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W73629738","https://openalex.org/W1963547452","https://openalex.org/W1989431146","https://openalex.org/W2064377529","https://openalex.org/W2082093772","https://openalex.org/W2087171264","https://openalex.org/W2110182592","https://openalex.org/W2114225134","https://openalex.org/W2156270920","https://openalex.org/W2752885492","https://openalex.org/W3004540582","https://openalex.org/W3145128584","https://openalex.org/W4285719527","https://openalex.org/W4301808069","https://openalex.org/W6647571053","https://openalex.org/W6996888795"],"related_works":["https://openalex.org/W4251428025","https://openalex.org/W4289867043","https://openalex.org/W2784467519","https://openalex.org/W2366459771","https://openalex.org/W1973736094","https://openalex.org/W2350707375","https://openalex.org/W1594413440","https://openalex.org/W2804796737","https://openalex.org/W2013155780","https://openalex.org/W1968050632"],"abstract_inverted_index":{"We":[0,15],"introduce":[1],"a":[2,11,39,58,89,98,107,133],"proof":[3],"system":[4],"for":[5,61,102,105,138],"H\u00e1jek's":[6],"logic":[7],"BL":[8,37,62,139],"based":[9],"on":[10],"relational":[12],"hypersequents":[13],"framework.":[14],"prove":[16],"that":[17,50],"the":[18,45,79,84,95,117,120],"rules":[19],"of":[20,36,47,81,83,97,119],"our":[21],"logical":[22],"calculus,":[23],"called":[24,42],"RHBL":[25,54],",":[26,55,75],"are":[27],"sound":[28],"and":[29],"invertible":[30],"with":[31],"respect":[32],"to":[33,109],"any":[34],"valuation":[35],"into":[38],"suitable":[40],"algebra,":[41],"(\u03c9)[0,1].":[43],"Refining":[44],"notion":[46],"reduction":[48,121],"tree":[49,122],"arises":[51],"naturally":[52],"from":[53],"we":[56,93,130],"obtain":[57],"decision":[59],"algorithm":[60,101,137],"provability":[63],"whose":[64],"running":[65],"time":[66,100,135],"upper":[67],"bound":[68],"is":[69,78,91,124],"2":[70],"O":[71,125],"(":[72,126],"n":[73,77,127],")":[74],"where":[76],"number":[80],"connectives":[82],"input":[85],"formula.":[86],"Moreover,":[87],"if":[88],"formula":[90],"unprovable,":[92],"exploit":[94],"constructiveness":[96],"polynomial":[99,134],"leaves":[103],"validity":[104],"providing":[106],"procedure":[108],"build":[110],"countermodels":[111],"in":[112],"(\u03c9)[0,":[113],"1].":[114],"Finally,":[115],"since":[116],"size":[118],"branches":[123],"3":[128],"),":[129],"can":[131],"describe":[132],"verification":[136],"unprovability.":[140]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}