Assuming adaptive expectations it could be shown that "the" Phillips curve (with the unemployment rate on the horizontal axis and inflation on the vertical) would shift upward over time. The true picture would then consist of a short-term Phillips curve where the trade-off holds for a while, but a long-term Phillips curve which is vertical.
Some rational expectations models went further, and implied that stimulatory monetary and fiscal policies would be fully expected and reflected in prices without having quantity effects. This would mean that there would be no short-term Phillips curves, just a long-term vertical relationship. Looking at South African empirical information in this regard, there are unfortunately severe data problems.