Why are logical and set operators different?
Logical and set-theoretic operations are not always compatible in the realm of uncertain numbers the way they are for real numbers. For example, set-theoretical union and logical disjunction are two formally distinct operations. It is only in special cases that they can be identified with each other. These special cases become rarer when we go from real numbers to uncertain numbers. In Risk Calc, the operators not ! or | || ||| and & && |&| denote logical operators. These logical operators act on truth values, not sets or arbitrary numerical values. For instance, the expression x | y asks Risk Calc to evaluate the truth value of a disjunction. The arguments of this disjunction are presumed to be truth values themselves. Under ordinary logic, the arguments could only have values of zero (false) or one (true). In traditional fuzzy logic and probability theory, they could have values anywhere on the unit interval (between zero and one) representing graded degrees of falsity and truth, or
