DC FieldValueLanguage
dc.contributor.authorDoder, Draganen_US
dc.contributor.authorOgnjanović, Zoranen_US
dc.date.accessioned2023-11-30T12:12:28Z-
dc.date.available2023-11-30T12:12:28Z-
dc.date.issued2023-
dc.identifier.issn0168-0072-
dc.identifier.urihttp://researchrepository.mi.sanu.ac.rs/handle/123456789/5233-
dc.description.abstractThis work presents a proof-theoretical and model-theoretical approach to probabilistic temporal logic. We present two novel logics; each of them extends both the language of linear time logic (LTL) and the language of probabilistic logic with polynomial weight formulas. The first logic is designed for reasoning about probabilities of temporal events, allowing statements like “the probability that A will hold in next moment is at least the probability that B will always hold” and conditional probability statements like “probability that A will always hold, given that B holds, is at least one half”, where A and B are arbitrary statements. We axiomatize this logic, provide corresponding sigma additive semantics and prove that the axiomatization is sound and strongly complete. We show that the satisfiability problem for our logic is decidable, by presenting a procedure which runs in polynomial space. We also present a logic with much richer language, in which probabilities are not attached only to temporal events, but the language allows arbitrary nesting of probability and temporal operators, allowing statements like “probability that tomorrow the chance of rain will be less than 80% is at least a half”. For this logic we prove a decidability result.en_US
dc.publisherElsevieren_US
dc.relation.ispartofAnnals of Pure and Applied Logicen_US
dc.subjectLinear-time temporal logic | Probabilistic logic | Completeness theorem | Decidabilityen_US
dc.titleProbabilistic temporal logic with countably additive semanticsen_US
dc.typeArticleen_US
dc.identifier.doi10.1016/j.apal.2023.103389-
dc.identifier.scopus2-s2.0-85178324203-
dc.contributor.affiliationMathematicsen_US
dc.contributor.affiliationMathematical Institute of the Serbian Academy of Sciences and Artsen_US
dc.relation.firstpage103389-
dc.relation.issue9-
dc.relation.volume175-
dc.description.rank~M21-
item.cerifentitytypePublications-
item.openairetypeArticle-
item.fulltextWith Fulltext-
item.grantfulltextopen-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
crisitem.author.orcid0000-0003-2508-6480-
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