{"id":"https://openalex.org/W3040328617","doi":"https://doi.org/10.1007/s11225-020-09912-3","title":"The Entropy-Limit (Conjecture) for $$\\Sigma _2$$-Premisses","display_name":"The Entropy-Limit (Conjecture) for $$\\Sigma _2$$-Premisses","publication_year":2020,"publication_date":"2020-06-30","ids":{"openalex":"https://openalex.org/W3040328617","doi":"https://doi.org/10.1007/s11225-020-09912-3","mag":"3040328617"},"language":"en","primary_location":{"id":"doi:10.1007/s11225-020-09912-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11225-020-09912-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11225-020-09912-3.pdf","source":{"id":"https://openalex.org/S30880287","display_name":"Studia Logica","issn_l":"0039-3215","issn":["0039-3215","1572-8730"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Studia Logica","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11225-020-09912-3.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005264460","display_name":"J\u00fcrgen Landes","orcid":"https://orcid.org/0000-0003-3105-6624"},"institutions":[{"id":"https://openalex.org/I8204097","display_name":"Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen","ror":"https://ror.org/05591te55","country_code":"DE","type":"education","lineage":["https://openalex.org/I8204097"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"J\u00fcrgen Landes","raw_affiliation_strings":["Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen, Munich, Germany"],"affiliations":[{"raw_affiliation_string":"Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen, Munich, Germany","institution_ids":["https://openalex.org/I8204097"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5005264460"],"corresponding_institution_ids":["https://openalex.org/I8204097"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.8051,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.70909634,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"109","issue":"2","first_page":"423","last_page":"442"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9544000029563904,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9544000029563904,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9496999979019165,"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":0.9273999929428101,"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/conjecture","display_name":"Conjecture","score":0.8681343197822571},{"id":"https://openalex.org/keywords/sigma","display_name":"Sigma","score":0.626152753829956},{"id":"https://openalex.org/keywords/predicate","display_name":"Predicate (mathematical logic)","score":0.6092966794967651},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5777789950370789},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5625625848770142},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5508720874786377},{"id":"https://openalex.org/keywords/quantifier","display_name":"Quantifier (linguistics)","score":0.46539127826690674},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42830508947372437},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.35420355200767517},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2636682689189911},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.13097891211509705},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.10470247268676758},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0993584394454956},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07193732261657715},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06731316447257996}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.8681343197822571},{"id":"https://openalex.org/C2778049214","wikidata":"https://www.wikidata.org/wiki/Q7512234","display_name":"Sigma","level":2,"score":0.626152753829956},{"id":"https://openalex.org/C140146324","wikidata":"https://www.wikidata.org/wiki/Q1144319","display_name":"Predicate (mathematical logic)","level":2,"score":0.6092966794967651},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5777789950370789},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5625625848770142},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5508720874786377},{"id":"https://openalex.org/C2778523021","wikidata":"https://www.wikidata.org/wiki/Q5532504","display_name":"Quantifier (linguistics)","level":2,"score":0.46539127826690674},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42830508947372437},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35420355200767517},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2636682689189911},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.13097891211509705},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.10470247268676758},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0993584394454956},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07193732261657715},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06731316447257996},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s11225-020-09912-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11225-020-09912-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11225-020-09912-3.pdf","source":{"id":"https://openalex.org/S30880287","display_name":"Studia Logica","issn_l":"0039-3215","issn":["0039-3215","1572-8730"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Studia Logica","raw_type":"journal-article"},{"id":"pmh:oai:air.unimi.it:2434/938991","is_oa":true,"landing_page_url":"https://hdl.handle.net/2434/938991","pdf_url":null,"source":{"id":"https://openalex.org/S4306400516","display_name":"Archivio Istituzionale della Ricerca (Universita Degli Studi Di Milano)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I189158943","host_organization_name":"University of Milan","host_organization_lineage":["https://openalex.org/I189158943"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:epub.ub.uni-muenchen.de:73131","is_oa":true,"landing_page_url":"https://epub.ub.uni-muenchen.de/73131/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401845","display_name":"Open access LMU (Ludwid Maxmilian's Universitat Munchen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I8204097","host_organization_name":"Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen","host_organization_lineage":["https://openalex.org/I8204097"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Studia Logica","raw_type":"doc-type:article"}],"best_oa_location":{"id":"doi:10.1007/s11225-020-09912-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11225-020-09912-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11225-020-09912-3.pdf","source":{"id":"https://openalex.org/S30880287","display_name":"Studia Logica","issn_l":"0039-3215","issn":["0039-3215","1572-8730"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Studia Logica","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5871973332","display_name":null,"funder_award_id":"405961989","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6921471979","display_name":null,"funder_award_id":"432308570","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3040328617.pdf","grobid_xml":"https://content.openalex.org/works/W3040328617.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W596488402","https://openalex.org/W983961703","https://openalex.org/W1509562192","https://openalex.org/W1640236959","https://openalex.org/W1746952621","https://openalex.org/W1976934354","https://openalex.org/W1992373581","https://openalex.org/W1992871063","https://openalex.org/W1999096610","https://openalex.org/W2036892044","https://openalex.org/W2038827320","https://openalex.org/W2051165274","https://openalex.org/W2064277984","https://openalex.org/W2083716186","https://openalex.org/W2102203084","https://openalex.org/W2134644511","https://openalex.org/W2137806332","https://openalex.org/W2143528652","https://openalex.org/W2318251225","https://openalex.org/W2336339972","https://openalex.org/W2483318275","https://openalex.org/W2529761800","https://openalex.org/W2601722430","https://openalex.org/W3045338440","https://openalex.org/W3132567942","https://openalex.org/W4232668672","https://openalex.org/W4241196600","https://openalex.org/W4299551239"],"related_works":["https://openalex.org/W2759379989","https://openalex.org/W2359046535","https://openalex.org/W2032208719","https://openalex.org/W1578347593","https://openalex.org/W3027422232","https://openalex.org/W3194471551","https://openalex.org/W2157959936","https://openalex.org/W4375956809","https://openalex.org/W4200006962","https://openalex.org/W1545562450"],"abstract_inverted_index":{"Abstract":[0],"The":[1,66],"application":[2,17],"of":[3,56,108,140],"the":[4,34,61,77,81,120,144,150],"maximum":[5,35],"entropy":[6,36],"principle":[7,37],"to":[8,18,45,85,124],"determine":[9],"probabilities":[10],"on":[11,38,60],"finite":[12,46,54],"domains":[13,20],"is":[14,83],"well-understood.":[15],"Its":[16],"infinite":[19],"still":[21],"lacks":[22],"a":[23,50,64,126],"well-studied":[24],"comprehensive":[25],"approach.":[26],"There":[27],"are":[28],"two":[29,73],"different":[30],"strategies":[31,74],"for":[32,87,93,105,129,143,149],"applying":[33,43],"first-order":[39],"predicate":[40],"languages:":[41],"(i)":[42],"it":[44],"sublanguages":[47],"and":[48,147],"taking":[49],"limit;":[51],"(ii)":[52],"comparing":[53],"entropies":[55],"probability":[57],"functions":[58],"defined":[59],"language":[62],"as":[63,90,92],"whole.":[65],"entropy-limit":[67,151],"conjecture":[68,82],"roughly":[69],"says":[70],"that":[71,119],"these":[72],"result":[75],"in":[76,113],"same":[78],"probabilities.":[79],"While":[80],"known":[84],"hold":[86],"monadic":[88],"languages":[89],"well":[91],"premiss":[94,106],"sentences":[95,107],"containing":[96],"only":[97,100],"existential":[98],"or":[99],"universal":[101],"quantifiers,":[102],"its":[103],"status":[104],"greater":[109],"quantifier":[110],"complexity":[111],"is,":[112],"general,":[114],"unknown.":[115],"I":[116,137],"here":[117],"show":[118],"first":[121,145],"approach":[122],"fails":[123],"provide":[125],"sensible":[127],"answer":[128],"some":[130],"$$\\Sigma":[131],"_2$$":[132],"<mml:math":[133],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msub><mml:mi>\u03a3</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math>":[134],"-premiss":[135],"sentences.":[136],"discuss":[138],"implications":[139],"this":[141],"failure":[142],"strategy":[146],"consequences":[148],"conjecture.":[152]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2020-07-10T00:00:00"}