Polylogism is the belief that different people or groups have different forms of logic. Since logic is the art of non-contradiction, polylogism can only have two possible meanings. Either reality is different for each group, or logic is a loose term for method of acquiring knowledge. The latter, though, is not how it is used. Those speaking of polylogism state that the conclusions from the different logics are different. This means that although they both claim to be methods of acquiring knowledge, the truth of the knowledge is different for different groups. This can only mean reality is different for the different groups.
Polylogism is an absurd idea. It hides behind a more realistic idea, though. People can acquire knowledge in different ways. There are various methods one can use in approaching truth. Some of these methods are legitimate while others are not. Polylogism pretends to encompass the legitimate methods by claiming different cultures are more prone to using particular methods.
This is just camouflage. Polylogism is nothing but social subjectivism. It claims that knowledge is whatever you want it to be, but applies it to groups. Cultures, tribes, or races are the deciders of truth, and reality conforms to their views. What's true for a Greek philosopher is not true for an Eastern philosopher. This does not mean that the two believe different things. It means that the two are both right, even though they contradict one another. It is a denial of the Law of Identity.