The relationship between strong belief and assumption

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.

Automated summary

The article introduces two mappings, one from Conditional Probability Systems (CPS's) to Lexicographic Probability Systems (LPS's), and another from LPS's with full support to CPS's. These mappings establish a relationship between strong belief (defined on CPS's) and assumption (defined on LPS's) at an abstract level in an extended probability-theoretic context.