Quasi-classical logic: Non-trivializable classical reasoning from inconsistent information

Abstract

Here we present a new paraconsistent logic, called quasi-classical logic (or QC logic) that allows the derivation of non-trivializable classical inferences. For this it is necessary that queries are in conjunctive normal form and the reasoning process is essentially that of clause finding. We present a proof-theoretic definition, and semantics, and show that the consequence relation observes reflexivity, monotonicity and transitivity, but fails cut and supraclassicality. Finally we discuss some of the advantages of this logic, over other paraconsistent logics, for applications in information systems.