No.  Logic or science can not prove the existence of a god.\n\nThey can, however, prove that a god does not exist.  For example:  Zeus and the other Greek gods were said to live on Mount Olympus.  As soon as Mt. Olympus was thoroughly explored, then those gods were disproven.\n\nThe Judean-Christian god (if the bible is taken literally) can be disproven by logic.  However, a deist's god that created everything and walked away would be impossible to disprove.