{"id":"https://openalex.org/W7168375410","doi":"https://doi.org/10.48550/arxiv.2607.12826","title":"Solution of the Hempel's statistical ambiguity problem and Causal AI","display_name":"Solution of the Hempel's statistical ambiguity problem and Causal AI","publication_year":2026,"publication_date":"2026-07-14","ids":{"openalex":"https://openalex.org/W7168375410","doi":"https://doi.org/10.48550/arxiv.2607.12826"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2607.12826","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.12826","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2607.12826","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5140942247","display_name":"Evgenii Vityaev","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Vityaev, Evgenii","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5140942247"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.7232999801635742,"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/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.7232999801635742,"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/T10656","display_name":"Child and Animal Learning Development","score":0.06159999966621399,"subfield":{"id":"https://openalex.org/subfields/3204","display_name":"Developmental and Educational Psychology"},"field":{"id":"https://openalex.org/fields/32","display_name":"Psychology"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10778","display_name":"Philosophy and History of Science","score":0.039799999445676804,"subfield":{"id":"https://openalex.org/subfields/1207","display_name":"History and Philosophy of Science"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/ambiguity","display_name":"Ambiguity","score":0.7687000036239624},{"id":"https://openalex.org/keywords/spurious-relationship","display_name":"Spurious relationship","score":0.7106999754905701},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.6435999870300293},{"id":"https://openalex.org/keywords/statistical-inference","display_name":"Statistical inference","score":0.6122000217437744},{"id":"https://openalex.org/keywords/causal-inference","display_name":"Causal inference","score":0.5338000059127808},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.507099986076355},{"id":"https://openalex.org/keywords/statistical-model","display_name":"Statistical model","score":0.507099986076355},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.48260000348091125}],"concepts":[{"id":"https://openalex.org/C2780522230","wikidata":"https://www.wikidata.org/wiki/Q1140419","display_name":"Ambiguity","level":2,"score":0.7687000036239624},{"id":"https://openalex.org/C97256817","wikidata":"https://www.wikidata.org/wiki/Q1462316","display_name":"Spurious relationship","level":2,"score":0.7106999754905701},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.6435999870300293},{"id":"https://openalex.org/C134261354","wikidata":"https://www.wikidata.org/wiki/Q938438","display_name":"Statistical inference","level":2,"score":0.6122000217437744},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5390999913215637},{"id":"https://openalex.org/C158600405","wikidata":"https://www.wikidata.org/wiki/Q5054566","display_name":"Causal inference","level":2,"score":0.5338000059127808},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.507099986076355},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.507099986076355},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.48260000348091125},{"id":"https://openalex.org/C95167961","wikidata":"https://www.wikidata.org/wiki/Q4483495","display_name":"Fiducial inference","level":5,"score":0.44339999556541443},{"id":"https://openalex.org/C11671645","wikidata":"https://www.wikidata.org/wiki/Q5054567","display_name":"Causal model","level":2,"score":0.4320000112056732},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40950000286102295},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38580000400543213},{"id":"https://openalex.org/C48057537","wikidata":"https://www.wikidata.org/wiki/Q3551145","display_name":"Statistical theory","level":2,"score":0.37880000472068787},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3709000051021576},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.36320000886917114},{"id":"https://openalex.org/C64357122","wikidata":"https://www.wikidata.org/wiki/Q1149766","display_name":"Causality (physics)","level":2,"score":0.3528999984264374},{"id":"https://openalex.org/C163504300","wikidata":"https://www.wikidata.org/wiki/Q2364925","display_name":"Causal structure","level":2,"score":0.33219999074935913},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.3192000091075897},{"id":"https://openalex.org/C87007009","wikidata":"https://www.wikidata.org/wiki/Q210832","display_name":"Statistical hypothesis testing","level":2,"score":0.31299999356269836}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2607.12826","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.12826","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2607.12826","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.12826","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[{"score":0.656701385974884,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0,154,175],"paper":[1],"addresses":[2],"Carl":[3,26],"Hempel's":[4],"longstanding":[5],"problem":[6,107],"of":[7,31,45,63,71,92,100,117,130],"statistical":[8,20,37,66,105,178],"ambiguity":[9,106,179],"in":[10,13,40,196],"inductive-statistical":[11],"inference,":[12],"which":[14,163,192],"contradictory":[15],"predictions":[16,169],"are":[17,173,234],"derived":[18,170],"from":[19,171],"laws.":[21],"To":[22],"avoid":[23],"such":[24,197],"predictions,":[25],"Hempel":[27],"proposed":[28],"the":[29,36,41,46,60,90,104,128,177],"Requirement":[30],"Maximal":[32],"Specificity":[33],"(RMS)":[34],"for":[35,162,215],"laws":[38],"used":[39,195],"inference.":[42],"An":[43],"analysis":[44],"RMS":[47,225,233],"refinements":[48],"made":[49,86],"by":[50,148],"Wesley":[51],"Salmon,":[52],"Alberto":[53],"Coffa,":[54],"and":[55,78,125,203,242],"James":[56],"Fetzer":[57],"led":[58],"to":[59,89,103,224,232],"following":[61],"definition":[62,116],"maximally":[64],"specific":[65],"laws:":[67],"\"the":[68],"lawlike":[69],"premises":[70],"an":[72],"adequate":[73],"explanation":[74],"must":[75],"specify":[76],"all":[77,150],"only":[79],"those":[80],"properties":[81],"whose":[82],"presence":[83],"or":[84],"absence":[85],"a":[87,101,136,187,213],"difference":[88],"occurrence":[91],"its":[93],"explanandum-phenomenon.\"":[94],"However,":[95],"there":[96],"was":[97],"no":[98],"proof":[99],"solution":[102],"based":[108],"on":[109],"this":[110],"definition.":[111],"We":[112],"use":[113],"Nancy":[114],"Cartwright's":[115],"causes":[118],"that":[119,142,168],"raise":[120],"probabilities":[121],"across":[122],"background":[123],"contexts,":[124],"then":[126],"introduce":[127],"concept":[129],"Causal":[131,159,201,204],"Rules.":[132],"Then":[133],"we":[134,164],"define":[135],"special":[137],"semantic":[138,182],"probabilistic":[139,183,188],"inference":[140,184,211],"procedure":[141,155,185],"incrementally":[143],"refines":[144],"these":[145],"causal":[146,189,210,240],"rules":[147],"incorporating":[149],"statistically":[151],"relevant":[152],"information.":[153],"yields":[156],"Maximally":[157],"Specific":[158],"Relationships":[160],"(MSCRs),":[161],"prove":[165],"(Theorem":[166],"1)":[167],"them":[172],"consistent.":[174],"resolves":[176],"problem.":[180],"The":[181],"provides":[186],"learning":[190],"system,":[191],"may":[193],"be":[194],"new":[198],"areas":[199],"as":[200,212],"AI":[202],"Machine":[205],"Learning.":[206],"They":[207],"fundamentally":[208],"explore":[209],"tool":[214],"understanding":[216],"cause-and-effect":[217],"relationships":[218],"within":[219],"complex":[220],"systems.":[221],"Properties":[222],"similar":[223],"remain":[226],"under":[227],"discussion.":[228],"Several":[229],"notions":[230],"related":[231],"considered:":[235],"invariant":[236,239],"feature":[237],"learning,":[238],"prediction,":[241],"spurious":[243],"association.":[244]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-07-16T00:00:00"}