"If the cost of this basket of consumption increases, the interest rate will fall (reducing basic income thereby reducing demand and lowering prices)."
This is assuming the whole of this society uses only that currency as money correct? Otherwise prices could go up for other reasons, regardless of this currency's rate of deflation -- making it harder to afford a decent living.

In other words, it is entirely possible at the lowered interest rates of his currency would in no way affect global demand and so wouldn't lower prices either.

So this system would need to be accepted by all of earth from day 1 in order to function no?