{"id":"https://openalex.org/W7154186618","doi":"https://doi.org/10.48550/arxiv.2604.09272","title":"A Domain-Theoretic Foundation for Imprecise Probability and Credal Sets","display_name":"A Domain-Theoretic Foundation for Imprecise Probability and Credal Sets","publication_year":2026,"publication_date":"2026-04-10","ids":{"openalex":"https://openalex.org/W7154186618","doi":"https://doi.org/10.48550/arxiv.2604.09272"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.09272","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.09272","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.2604.09272","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058087229","display_name":"Abbas Edalat","orcid":"https://orcid.org/0000-0002-6211-1991"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Edalat, Abbas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133518935","display_name":"Pietro Di Gianantonio","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Di Gianantonio, Pietro","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5091894566","display_name":"Amin Farjudian","orcid":"https://orcid.org/0000-0002-1879-0763"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Farjudian, Amin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"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":0.9351999759674072,"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":0.9351999759674072,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.03579999879002571,"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.00930000003427267,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/imprecise-probability","display_name":"Imprecise probability","score":0.6624000072479248},{"id":"https://openalex.org/keywords/soundness","display_name":"Soundness","score":0.6216999888420105},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.5889000296592712},{"id":"https://openalex.org/keywords/conditional-probability","display_name":"Conditional probability","score":0.5577999949455261},{"id":"https://openalex.org/keywords/probability-measure","display_name":"Probability measure","score":0.47999998927116394},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.4348999857902527},{"id":"https://openalex.org/keywords/bayesian-network","display_name":"Bayesian network","score":0.4074000120162964},{"id":"https://openalex.org/keywords/event","display_name":"Event (particle physics)","score":0.40450000762939453},{"id":"https://openalex.org/keywords/possibility-theory","display_name":"Possibility theory","score":0.3930000066757202},{"id":"https://openalex.org/keywords/probability-theory","display_name":"Probability theory","score":0.3894999921321869}],"concepts":[{"id":"https://openalex.org/C130648207","wikidata":"https://www.wikidata.org/wiki/Q6007562","display_name":"Imprecise probability","level":3,"score":0.6624000072479248},{"id":"https://openalex.org/C39920170","wikidata":"https://www.wikidata.org/wiki/Q693083","display_name":"Soundness","level":2,"score":0.6216999888420105},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.5889000296592712},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5769000053405762},{"id":"https://openalex.org/C44492722","wikidata":"https://www.wikidata.org/wiki/Q327069","display_name":"Conditional probability","level":2,"score":0.5577999949455261},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.47999998927116394},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.4348999857902527},{"id":"https://openalex.org/C33724603","wikidata":"https://www.wikidata.org/wiki/Q812540","display_name":"Bayesian network","level":2,"score":0.4074000120162964},{"id":"https://openalex.org/C2779662365","wikidata":"https://www.wikidata.org/wiki/Q5416694","display_name":"Event (particle physics)","level":2,"score":0.40450000762939453},{"id":"https://openalex.org/C137912672","wikidata":"https://www.wikidata.org/wiki/Q1967096","display_name":"Possibility theory","level":4,"score":0.3930000066757202},{"id":"https://openalex.org/C122203268","wikidata":"https://www.wikidata.org/wiki/Q5862903","display_name":"Probability theory","level":2,"score":0.3894999921321869},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3855000138282776},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.3741999864578247},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.36250001192092896},{"id":"https://openalex.org/C160234255","wikidata":"https://www.wikidata.org/wiki/Q812535","display_name":"Bayesian inference","level":3,"score":0.3560999929904938},{"id":"https://openalex.org/C79772020","wikidata":"https://www.wikidata.org/wiki/Q5159264","display_name":"Conditional independence","level":2,"score":0.35190001130104065},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3513999879360199},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35100001096725464},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.3450999855995178},{"id":"https://openalex.org/C43555835","wikidata":"https://www.wikidata.org/wiki/Q2300258","display_name":"Conditional probability distribution","level":2,"score":0.3402000069618225},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.3310000002384186},{"id":"https://openalex.org/C18998212","wikidata":"https://www.wikidata.org/wiki/Q7246856","display_name":"Probabilistic logic network","level":5,"score":0.31790000200271606},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.31540000438690186},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.3012000024318695},{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.3009999990463257},{"id":"https://openalex.org/C162376815","wikidata":"https://www.wikidata.org/wiki/Q2158281","display_name":"Frequentist inference","level":4,"score":0.3000999987125397},{"id":"https://openalex.org/C128394911","wikidata":"https://www.wikidata.org/wiki/Q1987578","display_name":"Unit interval","level":2,"score":0.298799991607666},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.28870001435279846},{"id":"https://openalex.org/C95167961","wikidata":"https://www.wikidata.org/wiki/Q4483495","display_name":"Fiducial inference","level":5,"score":0.2818000018596649},{"id":"https://openalex.org/C3746660","wikidata":"https://www.wikidata.org/wiki/Q1068763","display_name":"Rule of inference","level":2,"score":0.28139999508857727},{"id":"https://openalex.org/C143017306","wikidata":"https://www.wikidata.org/wiki/Q3318133","display_name":"Probabilistic relevance model","level":4,"score":0.2782000005245209},{"id":"https://openalex.org/C29585364","wikidata":"https://www.wikidata.org/wiki/Q1079166","display_name":"Domain theory","level":2,"score":0.27239999175071716},{"id":"https://openalex.org/C55508974","wikidata":"https://www.wikidata.org/wiki/Q190763","display_name":"Venn diagram","level":2,"score":0.2667999863624573},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2644999921321869}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.09272","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.09272","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.2604.09272","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.09272","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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,24,95],"develop":[1],"a":[2,16,57,86,124,137,154],"domain-theoretic":[3,138],"framework":[4,181],"for":[5,67,91,100],"imprecise":[6,92,166,175],"probability":[7,39,61,167],"reasoning":[8],"and":[9,36,62,105,108,114,146,152,185,196],"inference":[10,65,193],"on":[11,188],"general":[12],"topological":[13],"spaces":[14],"with":[15,165],"countably":[17],"based":[18],"continuous":[19],"lattice":[20],"of":[21,29,38,59,74,79,88,123,134,140,157,172],"open":[22],"sets.":[23],"address":[25],"two":[26,76],"distinct":[27],"forms":[28],"uncertainty:":[30],"partial":[31,195],"or":[32],"incomplete":[33],"event":[34],"descriptions,":[35],"sets":[37,45,159],"distributions":[40],"as":[41,47,49],"represented":[42],"by":[43,161],"credal":[44,129,158],"--":[46],"well":[48],"their":[50],"combination.":[51],"Within":[52],"this":[53],"framework,":[54],"we":[55,109,150],"construct":[56],"theory":[58,87,145],"conditional":[60,89,101,106],"derive":[63],"novel":[64],"rules":[66],"performing":[68],"Bayesian":[69,103],"updating":[70],"in":[71],"the":[72,111,121,132,170],"presence":[73],"these":[75],"complementary":[77],"types":[78],"imprecision.":[80],"These":[81],"results":[82,142],"are":[83],"extended":[84],"to":[85,131],"independence":[90],"probabilistic":[93,176,192],"events.":[94],"also":[96],"formulate":[97],"logical":[98],"predicates":[99],"probability,":[102],"updating,":[104],"independence,":[107],"obtain":[110],"relevant":[112],"soundness":[113],"completeness":[115],"results.":[116],"A":[117],"key":[118],"contribution":[119],"is":[120],"construction":[122],"Scott-continuous":[125],"mapping":[126],"from":[127,143],"any":[128],"set":[130],"domain":[133],"intervals,":[135],"providing":[136],"realisation":[139],"classical":[141],"capacity":[144],"Choquet":[147],"integration.":[148],"Finally,":[149],"introduce":[151],"study":[153],"new":[155],"family":[156],"generated":[160],"iterated":[162],"function":[163],"systems":[164],"weights,":[168],"broadening":[169],"scope":[171],"computationally":[173],"tractable":[174],"models.":[177],"The":[178],"resulting":[179],"computable":[180],"unifies":[182],"logical,":[183],"topological,":[184],"measure-theoretic":[186],"perspectives":[187],"uncertainty,":[189],"supporting":[190],"robust":[191],"under":[194],"set-valued":[197],"information.":[198]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-04-14T00:00:00"}
