Religion is the banana skinn, and spirituality is the banana. Religion has three aspects - values, rituals and symbols.
The rituals and symbols forms the logic portion you talk about - because it is a good way of taking one to the actual values.
If I ask you to meditate, to look deep with in you to experience that you are peice, you may not go and do that with out giving a reason - because the intellect does not go for something that is not profitable from its perspective.
If you read the latest innovation in the field of science like string theory and hyperspace, it is completely out of logic - so does spirituality.
In science, knowledge brings faith. But in spirituality, faith brings knowledge - because faith is the best tool you can have to experience your inner being, your true nature, by settling your mind, by going beyond the zone of logic - because the nature of energy/conciousness that fills everything and anything is beyond logic.
Science ends in wonder - go deep in to anything, it brings you wonder.
Spirituality starts with wonder. When you are like a child, when you wonder at everything, you get amuzed by the play and display of conciousness - and you experience the joy that is bubbling up with in you with out any reason