Correlated Boolean operators for uncertainty logic

Enrique Miralles-Dolz, Ander Gray, Edoardo Patelli, Scott Ferson

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

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Abstract

We present a correlated and gate which may be used to propagate uncertainty and dependence through Boolean functions, since any Boolean function may be expressed as a combination of and and not operations. We argue that the and gate is a bivariate copula family, which has the interpretation of constructing bivariate Bernoulli random variables following a given Pearson correlation coefficient and marginal probabilities. We show how this copula family may be used to propagate uncertainty in the form of probabilities of events, probability intervals, and probability boxes, with only partial or no knowledge of the dependency between events, expressed as an interval for the correlation coefficient. These results generalise previous results by Fréchet on the conjunction of two events with unknown dependencies. We show an application propagating uncertainty through a fault tree for a pressure tank. This paper comes with an open-source Julia library for performing uncertainty logic.

Original languageEnglish
Title of host publicationInformation Processing and Management of Uncertainty in Knowledge-Based Systems
Subtitle of host publication19th International Conference, IPMU 2022, Proceedings
EditorsDavide Ciucci, Inés Couso, Jesús Medina, Dominik Ślęzak, Davide Petturiti, Bernadette Bouchon-Meunier, Ronald R. Yager
Place of PublicationCham, Switzerland
PublisherSpringer
Pages798-811
Number of pages14
ISBN (Electronic)9783031089718
ISBN (Print)9783031089701
DOIs
Publication statusPublished - 4 Jul 2022
Event19th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2022 - Milan, Italy
Duration: 11 Jul 202215 Jul 2022

Publication series

NameCommunications in Computer and Information Science
Volume1601 CCIS
ISSN (Print)1865-0929
ISSN (Electronic)1865-0937

Conference

Conference19th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2022
Country/TerritoryItaly
CityMilan
Period11/07/2215/07/22

Keywords

  • Boolean functions
  • copula
  • imprecise probability
  • uncertainty logic
  • uncertainty propagation

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