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Different meanings of "contradiction"

The term "contradiction " is often used with different meanings in logic and axiomatic.
When we say "there is a contradiction," we say, for example, is self-expression, "the four-sided triangle" or "hand moves and is still at the same time."
We can also say that there is a logical relationship of contradictoriness , Understood in a formal way, as with the propositions p-p, or with formulas A and-A.
also a "contradiction" may signal an inconsistency or contrariety. This in turn may reflect the logical structure of two propositional forms, for example p and q, p-q.
But there may be incompatible with the meaning of propositions , such as occurs with "John is in Europe" and "John is in Canada," which can not be true at the same time.
Finally, you can also talk about contradiction in a formal axiomatic system , in the sense of formal contradictoriness, or in the sense that for any interpretation of the axioms can not all be true simultaneously.