Refer to figures.
EASA learning objective 022.04.03.01.04 states: 'Describe the effects of the aircraft’s acceleration and turns on instrument indications'.

An air driven attitude indicator uses a 'vertically tied' gyro to give a datum against which the roll and pitch attitude of an aircraft can be displayed. The gyro rotor is rotated anticlockwise, erected and maintained parallel with Earth horizontal using air from a vacuum pump attached to the aircraft engine. Due to the two methods used to keep the gyroscope vertically tied, indication errors will occur when accelerating and decelerating. These errors are:

Acceleration - Nose up + roll right
Deceleration - Nose down + roll left

Erection Error (Pitch):

Having spun up the rotor, air leaves the gyro case via 4 ports placed at 90° intervals at the bottom of the case. Each of these ports has a pendulous vane , pivoted at the top, which hangs down to cover half the port when the gyro is vertical. The purpose of the pendulous vanes is to keep the gyro erect. When the gyro is vertical the airflow out of each port is identical so the reaction forces cancel each other out. If the gyro wanders off the vertical some of the vanes will swing closed while others will swing open causing unequal air jets and a subsequent reaction. This reaction causes the gyro to precess back to the vertical.

Unfortunately this erection arrangement will give rise to errors when the aircraft accelerates or decelerates. Longitudinal acceleration will cause the lateral pendulous vanes to swing back causing an unbalanced sideways airflow which causes the gyro to precess in a direction 90° anticlockwise to the force. This causes the gyro assembly to tilt towards the pilot which lowers the horizon line and gives a pitch up indication. The opposite occurs during deceleration causing a pitch down indication.

Pendulous Error (Roll):

To assist in keeping it erect the gyro assembly is designed to behave like a pendulum, in level unaccelerated flight it tends to remain vertical but any linear acceleration will cause the base of the gyro assembly to swing forwards or backwards. For instance, when the aircraft accelerates the base of the unit will swing towards the pilot, precession causes this force to be a applied at 90° in an anticlockwise direction so the gyro will tilt to the left. As the gyro is attached to the horizon bar the AI will therefore indicate a roll to the right. The opposite occurs during deceleration, the base of the unit swings away from the pilot causing the gyro and horizon to tilt to the right which indicates a roll to the left.

Note: The attached figures illustrate an acceleration scenario—the opposite applies to deceleration.