For example, the Chief of the Foundry grants +1/+1 to other artifact creatures I control. If I have two copies of Chief of the Foundry in play, does that mean all other artifact creatures I control get +2/+2 and do they then grant each other +1/+1 since they are "other" artifact creatures?
You are correct in your interpretation. Each static ability is separately applied from each other, so they stack.
It's not directly talking about abilities stacking, but:
112.2c An object may have multiple abilities. If the object is represented by a card, then aside from certain defined abilities that may be strung together on a single line (see rule 702, “Keyword Abilities”), each paragraph break in a card’s text marks a separate ability. If the object is not represented by a card, the effect that created it may have given it multiple abilities. An object may also be granted additional abilities by a spell or ability. If an object has multiple instances of the same ability, each instance functions independently. This may or may not produce more effects than a single instance; refer to the specific ability for more information. #