Logical bilattices and inconsistent data

The notion of a bilattice was first proposed by Ginsberg (1988) as a general framework for many applications. This notion was further investigated and applied for various goals by Fitting (1989, 1990, 1991, 1993). In this paper, we develop proof systems which correspond to bilattices in an essential way. We then show how to use those bilattices for efficient inferences from possibly inconsistent data. For this, we incorporate certain ideas of Kifer and Lozinskii (1992) concerning inconsistencies, which happen to well suit the framework of bilattices. The outcome is a paraconsistent logic with many desirable properties