What is the logical problem of evil?

The logical problem of evil is usually cast as an argument for the logical inconsistency of a number of claims that traditional theism holds. These include the claims: 1) God exists 2) God is omnipotent 3) God is omniscient 4) God is perfectly good and 5) Evil exists. The argument says that statements 1-4 are inconsistent with 5, since an omniscient God would know about all evils, an omnipotent God would be able to prevent them, and a perfectly good God would have an overriding reason to do so. The logical problem of evil can then be cast as a deductive argument from the premise that evil does in fact exist to the conclusion that the God of traditional theism (omnipotent, omniscient, perfectly good) does not exist. The logical problem can be contrasted with the evidential problem of evil, which does not claim that just any evil would be inconsistent with God, but that the existence of the kind of terrible suffering which we know to exist gives good evidence for the conclusion that such a God does not exist.