Is it not simply just belief with an A in place of the B? It sounds to me like a self-consciously coined neologism, perhaps related to A's position before B in the alphabet, suggesting that aliefs come before beliefs in some sense.
EDIT: a brief look at the original paper[0] doesn't give any immediate answers, but it seems to confirm my guess:
"Alief is a more primitive state than either belief or imagination: it directly activates behavioral response patterns"
