Monetary Transmission in New Keynesian - Euler Equation
Real interest rate = Nominal interest rate - Expected inflation


Reducing the nominal interest rate by more than the decline in the expected inflation, with respect to the inflation target, leads the real interest rate to go down.
When the real interest rate goes down, the real exchange rate depreciates, both lead real monetary conditions to loosen. [Real monetary conditions = a1*RR_gap + (1*a1)*RER_gap].
Looser real monetary conditions lead to higher aggregate demand 'output gap' (higher domestic demand due to lower real interest rate and higher external demand due to the real exchange rate depreciation). [IS curve - Euler equation]
Higher aggregate demand puts more pressure on the real marginal costs, which in addition to higher inflation expectations that are directly affected by reducing the nominal interest rate, increase the inflation rate.