{"id":"https://openalex.org/W4239243811","doi":"https://doi.org/10.2178/jsl/1082418532","title":"Implicit proofs","display_name":"Implicit proofs","publication_year":2004,"publication_date":"2004-06-01","ids":{"openalex":"https://openalex.org/W4239243811","doi":"https://doi.org/10.2178/jsl/1082418532"},"language":"en","primary_location":{"id":"doi:10.2178/jsl/1082418532","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1082418532","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"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":"Journal of Symbolic 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/A5069803587","display_name":"Jan Kraj\u0131\u0301\u010dek","orcid":"https://orcid.org/0000-0003-0670-3957"},"institutions":[{"id":"https://openalex.org/I4210120266","display_name":"Czech Academy of Sciences, Institute of Mathematics","ror":"https://ror.org/02tv1yf50","country_code":"CZ","type":"facility","lineage":["https://openalex.org/I202391551","https://openalex.org/I4210120266"]}],"countries":["CZ"],"is_corresponding":true,"raw_author_name":"Jan Kraj\u00ed\u010dek","raw_affiliation_strings":["Mathematical Institute, Academy of Sciences, \u017ditn\u00e1 25, Prague 1, CZ-115 67, The Czech Republic, E-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute, Academy of Sciences, \u017ditn\u00e1 25, Prague 1, CZ-115 67, The Czech Republic, E-mail:","institution_ids":["https://openalex.org/I4210120266"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5069803587"],"corresponding_institution_ids":["https://openalex.org/I4210120266"],"apc_list":null,"apc_paid":null,"fwci":0.5426,"has_fulltext":false,"cited_by_count":40,"citation_normalized_percentile":{"value":0.83434212,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"69","issue":"2","first_page":"387","last_page":"397"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9994000196456909,"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":0.9994000196456909,"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":0.9980999827384949,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9979000091552734,"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/mathematical-proof","display_name":"Mathematical proof","score":0.8669613003730774},{"id":"https://openalex.org/keywords/soundness","display_name":"Soundness","score":0.850542426109314},{"id":"https://openalex.org/keywords/proof-complexity","display_name":"Proof complexity","score":0.6425645351409912},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5805777907371521},{"id":"https://openalex.org/keywords/structural-proof-theory","display_name":"Structural proof theory","score":0.5746145844459534},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.5659974217414856},{"id":"https://openalex.org/keywords/exponentiation","display_name":"Exponentiation","score":0.5647763013839722},{"id":"https://openalex.org/keywords/proof-theory","display_name":"Proof theory","score":0.5459139347076416},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5068829655647278},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4916101098060608},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4183931052684784},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.40339401364326477},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3658420443534851},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.33248797059059143},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.26047283411026},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.0691629946231842}],"concepts":[{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.8669613003730774},{"id":"https://openalex.org/C39920170","wikidata":"https://www.wikidata.org/wiki/Q693083","display_name":"Soundness","level":2,"score":0.850542426109314},{"id":"https://openalex.org/C105605280","wikidata":"https://www.wikidata.org/wiki/Q7249999","display_name":"Proof complexity","level":3,"score":0.6425645351409912},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5805777907371521},{"id":"https://openalex.org/C195653647","wikidata":"https://www.wikidata.org/wiki/Q7625047","display_name":"Structural proof theory","level":4,"score":0.5746145844459534},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.5659974217414856},{"id":"https://openalex.org/C81539297","wikidata":"https://www.wikidata.org/wiki/Q33456","display_name":"Exponentiation","level":2,"score":0.5647763013839722},{"id":"https://openalex.org/C2318724","wikidata":"https://www.wikidata.org/wiki/Q852732","display_name":"Proof theory","level":3,"score":0.5459139347076416},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5068829655647278},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4916101098060608},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4183931052684784},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.40339401364326477},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3658420443534851},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.33248797059059143},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.26047283411026},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0691629946231842},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"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},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2178/jsl/1082418532","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1082418532","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"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":"Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1082418532","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1082418532","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"","raw_type":"Text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W256005661","https://openalex.org/W1988083342","https://openalex.org/W1997908783","https://openalex.org/W2075488709","https://openalex.org/W2091961944","https://openalex.org/W2161149481","https://openalex.org/W2171353564","https://openalex.org/W4248733413"],"related_works":["https://openalex.org/W2626436722","https://openalex.org/W1852594029","https://openalex.org/W171706349","https://openalex.org/W153148314","https://openalex.org/W2463991046","https://openalex.org/W2922318846","https://openalex.org/W1558859407","https://openalex.org/W2120139360","https://openalex.org/W2461509449","https://openalex.org/W1528233644"],"abstract_inverted_index":{"Abstract.":[0],"We":[1],"describe":[2],"a":[3,10,15,93],"general":[4],"method":[5],"how":[6],"to":[7,51,97,105],"construct":[8],"from":[9],"prepositional":[11,63],"proof":[12,19,44,94],"system":[13,20,24,45,95],"P":[14,30],"possibly":[16],"much":[17,106],"stronger":[18,107],"iP":[21,25],".":[22,86],"The":[23],"operates":[26],"with":[27,71],"exponentially":[28],"long":[29],"-proofs":[31],"described":[32],"\u201cimplicitly\u201d":[33],"by":[34],"polynomial":[35],"size":[36],"circuits.":[37],"As":[38],"an":[39],"example":[40],"we":[41],"prove":[42],"that":[43],"i":[46,80],"EF,":[47,49],"implicit":[48],"corresponds":[50],"bounded":[52],"arithmetic":[53],"theory":[54],"and":[55,66],"hence,":[56],"in":[57,85,103],"particular,":[58],"polynomially":[59],"simulates":[60],"the":[61,67,77,90],"quantified":[62],"calculus":[64],"G":[65],"-consequences":[68],"of":[69,74,79,89],"proved":[70],"one":[72],"use":[73],"exponentiation.":[75],"Furthermore,":[76],"soundness":[78],"EF":[81],"is":[82],"not":[83],"provable":[84],"An":[87],"iteration":[88],"construction":[91],"yields":[92],"corresponding":[96],"T":[98],"2":[99],"+":[100],"Exp":[101],"and,":[102],"principle,":[104],"theories.":[108]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":27},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-07-21T08:15:58.654021","created_date":"2022-05-12T00:00:00"}