In the final analysis there are no logical arguments because the premise of "I am" which establishes God is just that a premise which cannot be accepted without the holy spirit. Any attempts at it would be no different than explaining color to a person blind from birth.
MAJOR PREMISE: Only God, if God exists, has the ability to accurately predict the future.
MINOR PREMISE: The future was accurately predicted in the Bible concerning the rise of the Roman Empire, the fate of other political entities, and the events in the life of Jesus Christ centuries before they occurred.
CONCLUSION: God exists.
And another:
MAJOR PREMISE: Only God, if God exists, has the ability to raise human beings from the dead.
MINOR PREMISE: Human beings have been raised from the dead.
CONCLUSION: God exists.