Four-valued Logics for Reasoning with Uncertainty in Prioritized Data

We present an approach for drawing plausible conclusions from inconsistent and incomplete knowledge-bases, which may also be prioritized. Our method is based on a four-valued semantics that is particularly suitable for reasoning with uncertainty. Our inference mechanism is closely related to some other well-known formalisms for handling inconsistent data, such as reasoning with maximal consistent subsets and possibilistic logic. It is shown that the formalism presented here is nonmonotonic, paraconsistent, and is capable of managing ranked data without having the \drowning problem".