For example, a military general who knows that he will be attacked from either the east or the north must divide his forces between both fronts, even if the attack will only come from one direction; thus what he has is “attack from east ⅋ attack from north”. (If he had spies out that would be able to inform him in advance where the attack was coming from so that he could concentrate his forces there, then he would instead have an additive disjunction “attack from east ⊕ attack from north”.)

Additive conjunction (“with”) 1 & 2 has the neutral element T. It
expresses that only one of the actions described by 1 and 2 will be
performed. But we can deduce or anticipate from an environment which
of them will be performed. This formula can be considered as an analogy
with the statements if-then-else and case in programming languages.
Somethimes it is called external nondeterminism (dependent choice);