Ex contradictione nihil sequitur

In the logical semantics of knowledge bases (K8) the handling of contradictions poses a problem not solvable by standard logic. An adequate logic for KBs must be capable of tolerating inconsistency in a KB without losing its deductive content. This is also the bottom line of so-called paraconsistent logics. But paraconsistent logic does not address the question whether contradictory information should be accepted or not in the derivation of further information depending on it. We propose two computational logics based on the notions of support and acceptance handling contradictions in a conservative, resp. skeptical, manner: they neither lead to the break-down of the system nor are they accepted as valid pieces of information.