The relationship between strong belief and assumption

Adam Brandenburger, Amanda Friedenberg, H. Jerome Keisler

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We define two maps, one map from the set of conditional probability systems (CPS’s) onto the set of lexicographic probability systems (LPS’s), and another map from the set of LPS’s with full support onto the set of CPS’s. We use these maps to establish a relationship between strong belief (defined on CPS’s) and assumption (defined on LPS’s). This establishes a relationship at the abstract level between these two widely used notions of belief in an extended probability-theoretic setting.

Original languageEnglish (US)
Article number175
Issue number5
StatePublished - May 2023


  • Assumption
  • Conditional probability systems
  • Lexicographic probability systems
  • Strong belief

ASJC Scopus subject areas

  • Philosophy
  • General Social Sciences


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