A view on conditional measures through local representability of binary relations

We consider binary relations ⪯ admitting a conditional measure of uncertainty φ (precisely plausibility, possibility and their dual functions), which locally represents ⪯: for every pair A⪯B, the measure φ(·|C) almost represents for any hypothesis C⊇A∨B, and represents ⪯ under the most specific hypothesis C=A∨B.