By that argument, conjunction is also called "addition". Perhaps there's a different reason?
The choice of terminology, contrasting "logical addition" with "logical multiplication", obviously indicates that logical addition is supposed to be analogous to addition. What is the analogy?
Actually, you can add 1 and -1 to get 0, which breaks the model... Hmm...
P(A u B) = P(A) + P(B) - P(A^B)
P(A ^ B) = P(A u B) - P(A) - P(B)
And to the guy who said xor is addition — no it’s not:
P(A xor B) = P(A) + P(B) - 2 * P(A^B)
In Probability, when you have a space of outcomes, doing a Union on two disjoint events (sets of outcomes) the probabilities add. Whereas doing an Intersection on two non-disjoint events those probabilities multiply. If two events have no outcomes in common, for instance, the probability of them both occurring is zero.
When you “condition” probability on an event X happening, you restrict the space of all outcomes to that set X, and intersect every event with it.
When you condiition B[n] = A[n] given that (A[n-1] AND … A[1]) having already happened, you have a sales funnel and each step is independent of the previous, so the probabilities multiply.
It is also called a Markov Chain if you have a discrete set of possibilities at each step so you can form a matrix.
Though the original topic was truth values, not probabilities. To make it short, conjunctions in probability are multiplicative when they are independent, and disjunctions in probability are additive when they are mutually exclusive.
A chain of conjunctions doesn't necessarily guarantee the truth value of the first proposition being preserved, so we have the much less interesting:
A ⊬ ((A ∧ B) ∧ C) ... ∧ n