Normally inflation falls when there's a recession, but this time that is not happening. Central banks (including the FED) have pumped too much liquidity into the system over recent years and even with the threat of recession, we're seeing some scary inflation data.
From the U.S. Bureau of Labor Statistics: "For the year ended January 2020, within final demand foods, prices for fresh and dry vegetables increased 21.4 percent, while prices for pork increased 14.9 percent. Over that period, prices for eggs for fresh use decreased 22.1 percent and prices for fresh fruits and melons decreased 9.3 percent.
Within energy, prices for gasoline increased 23.1 percent and prices for home heating oil and distillates increased 12.0 percent for the year ended January 2020. Prices for liquefied petroleum gas decreased 32.5 percent."
Declining inflation expectations are wrong and will turn up when more data keeps coming.