[dragonwriter]

For example, in Bayesian logic:

x AND y is xy, x OR y is x + y - xy

Whereas in (Zadeh) fuzzy logic:

x AND y is min(x, y), x OR y is max(x, y)

IIRC, “fuzzy logic” is actually a class that includes all generalizations of crisp binary logic to continuous values over [0,1] with operators meeting a set of definitions which basically boil down to “reduces to crisp logic when the input values are constrained to 0 and 1”, so that Bayesian logic is a fuzzy logic.

The Zadeh operators in particular I remember being constructed, or at keast rationalized, as ways to combine the degree of truth of propositions as distinct from the probability of truth of uncertain proposition. But I think interest in the kind of epistemic differences in alternative extensions to propositional logic faded with the lack of a practical need in terms of computational efficiency to avoid Bayesian probability (and I think there was also a separate philosophical battle and the side in favor of “Bayesianism is the only meaningful extension of propositional logic” was winning that battle when the computational problems were resolved, which helped sweep aside the alternatives.)

[tr352]

> For example, in Bayesian logic: x AND y is xy, x OR y is x + y - xy

No it isn't. P(x AND y) = P(x)P(y) only in the special case where x and y are independent. Unlike fuzzy logic, probabilistic logic is not truth functional.

[dragonwriter]

> No it isn’t. P(x AND y) = P(x)P(y) only if x and y are independent.

You are obviously correct, and I shouldn’t post when I should be sleeping.

> Unlike fuzzy logic, probabilistic logic is not truth functional.

Its been a long time since I had much engagement with fuzzy logic, but I distinctly remember it being constructed as a class such that Bayesian probability was a fuzzy logic, though the others of interest were much simpler. But that may be as wrong as the other part of that post...