I'm not 100% sure but I think that attack speed for pets is additive, whereas for players it has a soft cap, like All Resistances stat and armour stat.
Never mind, I just tested it myself and it is definitely multiplicitive.
By the way, I'm talking about for sentries. It may be different for other pets. I also found a source here that says it is multiplicative for sentries.
For example, say my weapon has 1.00 attacks per second and I have 50% IAS on gear, as well as a 50% Tasker and Theo:
If the bonuses are multiplicitive: Pet attack speed = 1.00 * 1.5 * 1.5 = 2.25
If the bonuses are additive: Pet attack speed = 1.00 * (1+0.5+0.5) = 2.00
This is important to know for hitting attack speed breakpoints exactly.
Again, not 100% sure!
By the way, I'm talking about for sentries. It may be different for other pets. I also found a source here that says it is multiplicative for sentries.