In philosophy, we normally divide the logic into two main branches classical logic and non-classical logic. Definitely there are major differences in the way both functions. Classical is the Aristotlean binary logic; Non-classical includes all the other forms, and many are becoming popular now.
When we see the human history, there is always war of logic between different ideologies or philosophies. When Christians, Muslims, Hindus, buddhists, atheists have different logic and philosophy of life, different nationalities, cultures, traditions do possess such variations. As there are variations(they have similarities too… not that there is an infinite gulf between them), their interactions could be difficult. Conflicts can arise. It becomes all the more today as there is greater awareness of equality and justice. The question is whose logic should be followed? Should we follow the logic that is common to both or should we follow the exclusive items? Whether there is a mediation (like the constitution) always available? If it is there too, it may not followed completely.
I think it is all the more severe in the post-modern culture, where the peripheries are valued (earlier only center was important and conflicts were suppressed or not allowed) and when there is no one yardstick to measure. Definitely the fundamentalist and extremist groups of different religions, cultures and nationalities do take advantage of this by churning the emotions.
Traditionally it was ‘US vs THEM or I vs YOU’. But one was superior and so there was always a way to decide. Today, it is again the same; but we don’t accept (atleast officially or in terms of constitution) that one is superior. Thus we need a movement from this inappropriate paradigm to something more adequate and appropriate -‘US & THEM or I & YOU’. (Instead of Us & Them, some would have preferred only Us. But I feel using in this way would do more justice to the similarities and differences). US & THEM could form one reconciled(harmonious) society, which could be symbolically represented by a rainbow. More than any structural method to create this harmony, it requires a conscious effort from all.