It is really great to see old macroeconomic concepts keep coming up. This is what makes the old concepts a classic.
If we look at the entire debate on inflation today- i.e. Why are Central Banks lowering the rates when inflation expectations (and in some regions actual inflation) are expected to be elevated?
It comes down to the old idea of cost push vs demand pull inflation (see the difference here).
Basically, inflation is expected to be high because of higher costs (cost-push) as prices of both, food/commodities and fuel are expected to rise in future (see this note from IMF chief economist, Simon Johnson for details). As both are used as intermediate goods for many items there is expected to be a rise in inflation across the board.
However, the Central Bankers (in US, UK and Canada) expect the demand to slow down in their regions and this would lead to lower prices across the board. They expect the negative of the demand-pull inflation to be stronger than the cost push inflation. And that is the reason they have lowered their rates.
So, which one will win? As of now, the probability of occurring of higher food and fuel prices seems to be higher than weakening demand. We are still not sure whether the talk about slowing economy is true or is too much of a hype. Again, forecasting is difficult and only time will tell what happens.