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I have created stubs for inconsistency and contradiction
Thanks; I added some remarks about paraconsistent logic.
Although the language is not always used this way, I find it helpful (when considering paraconsistent logics) to strictly distinguish a contradiction from an inconsistency as follows:
(Since the definition of contradiction depends on the operator $\neg$, one might also say a $\neg$-contradiction in case of multiple candidates for negation, as in linear logic.)
One can generalise this to speak of more general contexts or even entire logics as being contradictory, inconsistent, or paraconsistent; then we recover the usual meaning of when a logic is paraconsistent.
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