Why is the rate of reaction calculated as d[A]/dt? For example, for a simple chemical reaction like 

$$\ce{A -&gt; C}$$

the rate of the reaction could be calculated as the rate of appearance of $\ce{C}$ or the disappearance of $\ce{A}$, which makes a logical sense. But if the reaction is

$$\ce{A + B -&gt; C}$$

as I read somewhere the rate could be calculated the same way as the first case either as the disappearance of $\ce{A}$ or $\ce{B}$, or the appearance of $\ce{C}$. Is it logical to calculate the rate as the disappearance of $\ce{A}$ or $\ce{B}$ as the rate?

Think about it, isn't the appearance of $\ce{C}$, the combined effect of the disappearance of both $\ce{A}$ and $\ce{B}$, which mean if the rate of the equation can be calculated as the change in concentration of $\ce{C}$ using the product, shouldn't the rate be calculated as the change in concentration of $\ce{A}$ plus the change in concentration of $\ce{B}$ through some time change $t$?
Although the appearance of C is due to the combined disappearance of A and B, the relation is still 1:1 between A and C. Therefore, the rate that A disappears = the rate that B disappears = the rate that C appears.

Let's look at an analogy in stoichiometry. Say I have 1 mole of A and 1 mole of B. Will I make 1 or 2 moles of C? By your logic, I should make 2 moles of C. But I don't.